Search results for: numerical simulations
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4843

Search results for: numerical simulations

3163 Applying Element Free Galerkin Method on Beam and Plate

Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: numerical computation, element-free Galerkin (EFG), moving least squares (MLS), meshless methods

Procedia PDF Downloads 287
3162 Coupled Flexural-Lateral-Torsional of Shear Deformable Thin-Walled Beams with Asymmetric Cross-Section–Closed Form Exact Solution

Authors: Mohammed Ali Hjaji, Magdi Mohareb

Abstract:

This paper develops the exact solutions for coupled flexural-lateral-torsional static response of thin-walled asymmetric open members subjected to general loading. Using the principle of stationary total potential energy, the governing differential equations of equilibrium are formulated as well as the associated boundary conditions. The formulation is based on a generalized Timoshenko-Vlasov beam theory and accounts for the effects of shear deformation due to bending and warping, and captures the effects of flexural–torsional coupling due to cross-section asymmetry. Closed-form solutions are developed for cantilever and simply supported beams under various forces. In order to demonstrate the validity and the accuracy of this solution, numerical examples are presented and compared with well-established ABAQUS finite element solutions and other numerical results available in the literature. In addition, the results are compared against non-shear deformable beam theories in order to demonstrate the shear deformation effects.

Keywords: asymmetric cross-section, flexural-lateral-torsional response, Vlasov-Timoshenko beam theory, closed form solution

Procedia PDF Downloads 474
3161 Numerical Analysis of Wire Laser Additive Manufacturing for Low Carbon Steels+

Authors: Juan Manuel Martinez Alvarez, Michele Chiumenti

Abstract:

This work explores the benefit of the thermo-metallurgical simulation to tackle the Wire Laser Additive Manufacturing (WLAM) of low-carbon steel components. The Finite Element Analysis is calibrated by process monitoring via thermal imaging and thermocouples measurements, to study the complex thermo-metallurgical behavior inherent to the WLAM process of low carbon steel parts.A critical aspect is the analysis of the heterogeneity in the resulting microstructure. This heterogeneity depends on both the thermal history and the residual stresses experienced during the WLAM process. Because of low carbon grades are highly sensitive to quenching, a high-gradient microstructure often arises due to the layer-by-layer metal deposition in WLAM. The different phases have been identified by scanning electron microscope. A clear influence of the heterogeneities on the final mechanical performance has been established by the subsequent mechanical characterization. The thermo-metallurgical analysis has been used to determine the actual thermal history and the corresponding thermal gradients during the printing process. The correlation between the thermos-mechanical evolution, the printing parameters and scanning sequence has been established. Therefore, an enhanced printing strategy, including optimized process window has been used to minimize the microstructure heterogeneity at ArcelorMittal.

Keywords: additive manufacturing, numerical simulation, metallurgy, steel

Procedia PDF Downloads 76
3160 Numerical Simulation of Fracturing Behaviour of Pre-Cracked Crystalline Rock Using a Cohesive Grain-Based Distinct Element Model

Authors: Mahdi Saadat, Abbas Taheri

Abstract:

Understanding the cracking response of crystalline rocks at mineralogical scale is of great importance during the design procedure of mining structures. A grain-based distinct element model (GBM) is employed to numerically study the cracking response of Barre granite at micro- and macro-scales. The GBM framework is augmented with a proposed distinct element-based cohesive model to reproduce the micro-cracking response of the inter- and intra-grain contacts. The cohesive GBM framework is implemented in PFC2D distinct element codes. The microstructural properties of Barre granite are imported in PFC2D to generate synthetic specimens. The microproperties of the model is calibrated against the laboratory uniaxial compressive and Brazilian split tensile tests. The calibrated model is then used to simulate the fracturing behaviour of pre-cracked Barre granite with different flaw configurations. The numerical results of the proposed model demonstrate a good agreement with the experimental counterparts. The GBM framework proposed thus appears promising for further investigation of the influence of grain microstructure and mineralogical properties on the cracking behaviour of crystalline rocks.

Keywords: discrete element modelling, cohesive grain-based model, crystalline rock, fracturing behavior

Procedia PDF Downloads 133
3159 Modeling Continuous Flow in a Curved Channel Using Smoothed Particle Hydrodynamics

Authors: Indri Mahadiraka Rumamby, R. R. Dwinanti Rika Marthanty, Jessica Sjah

Abstract:

Smoothed particle hydrodynamics (SPH) was originally created to simulate nonaxisymmetric phenomena in astrophysics. However, this method still has several shortcomings, namely the high computational cost required to model values with high resolution and problems with boundary conditions. The difficulty of modeling boundary conditions occurs because the SPH method is influenced by particle deficiency due to the integral of the kernel function being truncated by boundary conditions. This research aims to answer if SPH modeling with a focus on boundary layer interactions and continuous flow can produce quantifiably accurate values with low computational cost. This research will combine algorithms and coding in the main program of meandering river, continuous flow algorithm, and solid-fluid algorithm with the aim of obtaining quantitatively accurate results on solid-fluid interactions with the continuous flow on a meandering channel using the SPH method. This study uses the Fortran programming language for modeling the SPH (Smoothed Particle Hydrodynamics) numerical method; the model is conducted in the form of a U-shaped meandering open channel in 3D, where the channel walls are soil particles and uses a continuous flow with a limited number of particles.

Keywords: smoothed particle hydrodynamics, computational fluid dynamics, numerical simulation, fluid mechanics

Procedia PDF Downloads 138
3158 Comparison of Water Equivalent Ratio of Several Dosimetric Materials in Proton Therapy Using Monte Carlo Simulations and Experimental Data

Authors: M. R. Akbari , H. Yousefnia, E. Mirrezaei

Abstract:

Range uncertainties of protons are currently a topic of interest in proton therapy. Two of the parameters that are often used to specify proton range are water equivalent thickness (WET) and water equivalent ratio (WER). Since WER values for a specific material is nearly constant at different proton energies, it is a more useful parameter to compare. In this study, WER values were calculated for different proton energies in polymethyl methacrylate (PMMA), polystyrene (PS) and aluminum (Al) using FLUKA and TRIM codes. The results were compared with analytical, experimental and simulated SEICS code data obtained from the literature. In FLUKA simulation, a cylindrical phantom, 1000 mm in height and 300 mm in diameter, filled with the studied materials was simulated. A typical mono-energetic proton pencil beam in a wide range of incident energies usually applied in proton therapy (50 MeV to 225 MeV) impinges normally on the phantom. In order to obtain the WER values for the considered materials, cylindrical detectors, 1 mm in height and 20 mm in diameter, were also simulated along the beam trajectory in the phantom. In TRIM calculations, type of projectile, energy and angle of incidence, type of target material and thickness should be defined. The mode of 'detailed calculation with full damage cascades' was selected for proton transport in the target material. The biggest difference in WER values between the codes was 3.19%, 1.9% and 0.67% for Al, PMMA and PS, respectively. In Al and PMMA, the biggest difference between each code and experimental data was 1.08%, 1.26%, 2.55%, 0.94%, 0.77% and 0.95% for SEICS, FLUKA and SRIM, respectively. FLUKA and SEICS had the greatest agreement (≤0.77% difference in PMMA and ≤1.08% difference in Al, respectively) with the available experimental data in this study. It is concluded that, FLUKA and TRIM codes have capability for Bragg curves simulation and WER values calculation in the studied materials. They can also predict Bragg peak location and range of proton beams with acceptable accuracy.

Keywords: water equivalent ratio, dosimetric materials, proton therapy, Monte Carlo simulations

Procedia PDF Downloads 328
3157 Iterative Dynamic Programming for 4D Flight Trajectory Optimization

Authors: Kawser Ahmed, K. Bousson, Milca F. Coelho

Abstract:

4D flight trajectory optimization is one of the key ingredients to improve flight efficiency and to enhance the air traffic capacity in the current air traffic management (ATM). The present paper explores the iterative dynamic programming (IDP) as a potential numerical optimization method for 4D flight trajectory optimization. IDP is an iterative version of the Dynamic programming (DP) method. Due to the numerical framework, DP is very suitable to deal with nonlinear discrete dynamic systems. The 4D waypoint representation of the flight trajectory is similar to the discretization by a grid system; thus DP is a natural method to deal with the 4D flight trajectory optimization. However, the computational time and space complexity demanded by the DP is enormous due to the immense number of grid points required to find the optimum, which prevents the use of the DP in many practical high dimension problems. On the other hand, the IDP has shown potentials to deal successfully with high dimension optimal control problems even with a few numbers of grid points at each stage, which reduces the computational effort over the traditional DP approach. Although the IDP has been applied successfully in chemical engineering problems, IDP is yet to be validated in 4D flight trajectory optimization problems. In this paper, the IDP has been successfully used to generate minimum length 4D optimal trajectory avoiding any obstacle in its path, such as a no-fly zone or residential areas when flying in low altitude to reduce noise pollution.

Keywords: 4D waypoint navigation, iterative dynamic programming, obstacle avoidance, trajectory optimization

Procedia PDF Downloads 170
3156 Vertical Vibration Mitigation along Railway Lines

Authors: Jürgen Keil, Frank Walther

Abstract:

This article presents two innovative solutions for vertical vibration mitigation barriers including experimental and numerical investigations on the completed barriers. There is a continuing growth of exposure to noise and vibration in people´s daily lives due to the quest for more mobility and flexibility. In previous times neglected, immissions caused by vibrations can lead, for example, to secondary noise or damage in the adjacent buildings. Also people can feel very affected by vibrations. But unlike in new construction, in existing infrastructure and buildings action can be taken almost only on the transmission path of those vibrations. In the following two solutions were shown how vibrations on the transmission path can be mitigated. These are the jet grouting method and a new installation method (patent pending) by means of a prefabricated hollow box which is filled with vibration reducing mats and driven down to depth, are presented. The essential results of the numerical and experimental investigations on the completed wave barriers are included as well. This article is based on the results of a field test with the participation of Keller Holding, which was executed in the context of the European research project RIVAS (Railway Induced Vibration Abatement Solutions), and on a thesis done at the Technical University of Dresden with the involvement of BAUGRUND DRESDEN Ingenieurgesellschaft mbH and the Keller Holding GmbH.

Keywords: jet grouting, rail way lines, vertical vibration mitigation, vibration reducing mats

Procedia PDF Downloads 406
3155 Comparison of Safety Factor Evaluation Methods for Buckling of High Strength Steel Welded Box Section Columns

Authors: Balazs Somodi, Balazs Kovesdi

Abstract:

In the research praxis of civil engineering the statistical evaluation of experimental and numerical investigations is an essential task in order to compare the experimental and numerical resistances of a specific structural problem with the proposed resistances of the standards. However, in the standards and in the international literature there are several different safety factor evaluation methods that can be used to check the necessary safety level (e.g.: 5% quantile level, 2.3% quantile level, 1‰ quantile level, γM partial safety factor, γM* partial safety factor, β reliability index). Moreover, in the international literature different calculation methods could be found even for the same safety factor as well. In the present study the flexural buckling resistance of high strength steel (HSS) welded closed sections are analyzed. The authors investigated the flexural buckling resistances of the analyzed columns by laboratory experiments. In the present study the safety levels of the obtained experimental resistances are calculated based on several safety approaches and compared with the EN 1990. The results of the different safety approaches are compared and evaluated. Based on the evaluation tendencies are identified and the differences between the statistical evaluation methods are explained.

Keywords: flexural buckling, high strength steel, partial safety factor, statistical evaluation

Procedia PDF Downloads 163
3154 Uncertainty Quantification of Fuel Compositions on Premixed Bio-Syngas Combustion at High-Pressure

Authors: Kai Zhang, Xi Jiang

Abstract:

Effect of fuel variabilities on premixed combustion of bio-syngas mixtures is of great importance in bio-syngas utilisation. The uncertainties of concentrations of fuel constituents such as H2, CO and CH4 may lead to unpredictable combustion performances, combustion instabilities and hot spots which may deteriorate and damage the combustion hardware. Numerical modelling and simulations can assist in understanding the behaviour of bio-syngas combustion with pre-defined species concentrations, while the evaluation of variabilities of concentrations is expensive. To be more specific, questions such as ‘what is the burning velocity of bio-syngas at specific equivalence ratio?’ have been answered either experimentally or numerically, while questions such as ‘what is the likelihood of burning velocity when precise concentrations of bio-syngas compositions are unknown, but the concentration ranges are pre-described?’ have not yet been answered. Uncertainty quantification (UQ) methods can be used to tackle such questions and assess the effects of fuel compositions. An efficient probabilistic UQ method based on Polynomial Chaos Expansion (PCE) techniques is employed in this study. The method relies on representing random variables (combustion performances) with orthogonal polynomials such as Legendre or Gaussian polynomials. The constructed PCE via Galerkin Projection provides easy access to global sensitivities such as main, joint and total Sobol indices. In this study, impacts of fuel compositions on combustion (adiabatic flame temperature and laminar flame speed) of bio-syngas fuel mixtures are presented invoking this PCE technique at several equivalence ratios. High-pressure effects on bio-syngas combustion instability are obtained using detailed chemical mechanism - the San Diego Mechanism. Guidance on reducing combustion instability from upstream biomass gasification process is provided by quantifying the significant contributions of composition variations to variance of physicochemical properties of bio-syngas combustion. It was found that flame speed is very sensitive to hydrogen variability in bio-syngas, and reducing hydrogen uncertainty from upstream biomass gasification processes can greatly reduce bio-syngas combustion instability. Variation of methane concentration, although thought to be important, has limited impacts on laminar flame instabilities especially for lean combustion. Further studies on the UQ of percentage concentration of hydrogen in bio-syngas can be conducted to guide the safer use of bio-syngas.

Keywords: bio-syngas combustion, clean energy utilisation, fuel variability, PCE, targeted uncertainty reduction, uncertainty quantification

Procedia PDF Downloads 278
3153 A Study on Prediction Model for Thermally Grown Oxide Layer in Thermal Barrier Coating

Authors: Yongseok Kim, Jeong-Min Lee, Hyunwoo Song, Junghan Yun, Jungin Byun, Jae-Mean Koo, Chang-Sung Seok

Abstract:

Thermal barrier coating(TBC) is applied for gas turbine components to protect the components from extremely high temperature condition. Since metallic substrate cannot endure such severe condition of gas turbines, delamination of TBC can cause failure of the system. Thus, delamination life of TBC is one of the most important issues for designing the components operating at high temperature condition. Thermal stress caused by thermally grown oxide(TGO) layer is known as one of the major failure mechanisms of TBC. Thermal stress by TGO mainly occurs at the interface between TGO layer and ceramic top coat layer, and it is strongly influenced by the thickness and shape of TGO layer. In this study, Isothermal oxidation is conducted on coin-type TBC specimens prepared by APS(air plasma spray) method. After the isothermal oxidation at various temperature and time condition, the thickness and shape(rumpling shape) of the TGO is investigated, and the test data is processed by numerical analysis. Finally, the test data is arranged into a mathematical prediction model with two variables(temperature and exposure time) which can predict the thickness and rumpling shape of TGO.

Keywords: thermal barrier coating, thermally grown oxide, thermal stress, isothermal oxidation, numerical analysis

Procedia PDF Downloads 345
3152 Evaluation of Rheological Properties, Anisotropic Shrinkage, and Heterogeneous Densification of Ceramic Materials during Liquid Phase Sintering by Numerical-Experimental Procedure

Authors: Hamed Yaghoubi, Esmaeil Salahi, Fateme Taati

Abstract:

The effective shear and bulk viscosity, as well as dynamic viscosity, describe the rheological properties of the ceramic body during the liquid phase sintering process. The rheological parameters depend on the physical and thermomechanical characteristics of the material such as relative density, temperature, grain size, and diffusion coefficient and activation energy. The main goal of this research is to acquire a comprehensive understanding of the response of an incompressible viscose ceramic material during liquid phase sintering process such as stress-strain relations, sintering and hydrostatic stress, the prediction of anisotropic shrinkage and heterogeneous densification as a function of sintering time by including the simultaneous influence of gravity field, and frictional force. After raw materials analysis, the standard hard porcelain mixture as a ceramic body was designed and prepared. Three different experimental configurations were designed including midpoint deflection, sinter bending, and free sintering samples. The numerical method for the ceramic specimens during the liquid phase sintering process are implemented in the CREEP user subroutine code in ABAQUS. The numerical-experimental procedure shows the anisotropic behavior, the complete difference in spatial displacement through three directions, the incompressibility for ceramic samples during the sintering process. The anisotropic shrinkage factor has been proposed to investigate the shrinkage anisotropy. It has been shown that the shrinkage along the normal axis of casting sample is about 1.5 times larger than that of casting direction, the gravitational force in pyroplastic deformation intensifies the shrinkage anisotropy more than the free sintering sample. The lowest and greatest equivalent creep strain occurs at the intermediate zone and around the central line of the midpoint distorted sample, respectively. In the sinter bending test sample, the equivalent creep strain approaches to the maximum near the contact area with refractory support. The inhomogeneity in Von-Misses, pressure, and principal stress intensifies the relative density non-uniformity in all samples, except in free sintering one. The symmetrical distribution of stress around the center of free sintering sample, cause to hinder the pyroplastic deformations. Densification results confirmed that the effective bulk viscosity was well-defined with relative density values. The stress analysis confirmed that the sintering stress is more than the hydrostatic stress from start to end of sintering time so, from both theoretically and experimentally point of view, the sintering process occurs completely.

Keywords: anisotropic shrinkage, ceramic material, liquid phase sintering process, rheological properties, numerical-experimental procedure

Procedia PDF Downloads 345
3151 Numerical Simulation on Two Components Particles Flow in Fluidized Bed

Authors: Wang Heng, Zhong Zhaoping, Guo Feihong, Wang Jia, Wang Xiaoyi

Abstract:

Flow of gas and particles in fluidized beds is complex and chaotic, which is difficult to measure and analyze by experiments. Some bed materials with bad fluidized performance always fluidize with fluidized medium. The material and the fluidized medium are different in many properties such as density, size and shape. These factors make the dynamic process more complex and the experiment research more limited. Numerical simulation is an efficient way to describe the process of gas-solid flow in fluidized bed. One of the most popular numerical simulation methods is CFD-DEM, i.e., computational fluid dynamics-discrete element method. The shapes of particles are always simplified as sphere in most researches. Although sphere-shaped particles make the calculation of particle uncomplicated, the effects of different shapes are disregarded. However, in practical applications, the two-component systems in fluidized bed also contain sphere particles and non-sphere particles. Therefore, it is needed to study the two component flow of sphere particles and non-sphere particles. In this paper, the flows of mixing were simulated as the flow of molding biomass particles and quartz in fluidized bad. The integrated model was built on an Eulerian–Lagrangian approach which was improved to suit the non-sphere particles. The constructed methods of cylinder-shaped particles were different when it came to different numerical methods. Each cylinder-shaped particle was constructed as an agglomerate of fictitious small particles in CFD part, which means the small fictitious particles gathered but not combined with each other. The diameter of a fictitious particle d_fic and its solid volume fraction inside a cylinder-shaped particle α_fic, which is called the fictitious volume fraction, are introduced to modify the drag coefficient β by introducing the volume fraction of the cylinder-shaped particles α_cld and sphere-shaped particles α_sph. In a computational cell, the void ε, can be expressed as ε=1-〖α_cld α〗_fic-α_sph. The Ergun equation and the Wen and Yu equation were used to calculate β. While in DEM method, cylinder-shaped particles were built by multi-sphere method, in which small sphere element merged with each other. Soft sphere model was using to get the connect force between particles. The total connect force of cylinder-shaped particle was calculated as the sum of the small sphere particles’ forces. The model (size=1×0.15×0.032 mm3) contained 420000 sphere-shaped particles (diameter=0.8 mm, density=1350 kg/m3) and 60 cylinder-shaped particles (diameter=10 mm, length=10 mm, density=2650 kg/m3). Each cylinder-shaped particle was constructed by 2072 small sphere-shaped particles (d=0.8 mm) in CFD mesh and 768 sphere-shaped particles (d=3 mm) in DEM mesh. The length of CFD and DEM cells are 1 mm and 2 mm. Superficial gas velocity was changed in different models as 1.0 m/s, 1.5 m/s, 2.0m/s. The results of simulation were compared with the experimental results. The movements of particles were regularly as fountain. The effect of superficial gas velocity on cylinder-shaped particles was stronger than that of sphere-shaped particles. The result proved this present work provided a effective approach to simulation the flow of two component particles.

Keywords: computational fluid dynamics, discrete element method, fluidized bed, multiphase flow

Procedia PDF Downloads 331
3150 An Optimal Control Method for Reconstruction of Topography in Dam-Break Flows

Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

Abstract:

Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: erodible beds, finite element method, finite volume method, nonlinear elasticity, shallow water equations, stresses in soil

Procedia PDF Downloads 134
3149 Data-Driven Analysis of Velocity Gradient Dynamics Using Neural Network

Authors: Nishant Parashar, Sawan S. Sinha, Balaji Srinivasan

Abstract:

We perform an investigation of the unclosed terms in the evolution equation of the velocity gradient tensor (VGT) in compressible decaying turbulent flow. Velocity gradients in a compressible turbulent flow field influence several important nonlinear turbulent processes like cascading and intermittency. In an attempt to understand the dynamics of the velocity gradients various researchers have tried to model the unclosed terms in the evolution equation of the VGT. The existing models proposed for these unclosed terms have limited applicability. This is mainly attributable to the complex structure of the higher order gradient terms appearing in the evolution equation of VGT. We investigate these higher order gradients using the data from direct numerical simulation (DNS) of compressible decaying isotropic turbulent flow. The gas kinetic method aided with weighted essentially non-oscillatory scheme (WENO) based flow- reconstruction is employed to generate DNS data. By applying neural-network to the DNS data, we map the structure of the unclosed higher order gradient terms in the evolution of the equation of the VGT with VGT itself. We validate our findings by performing alignment based study of the unclosed higher order gradient terms obtained using the neural network with the strain rate eigenvectors.

Keywords: compressible turbulence, neural network, velocity gradient tensor, direct numerical simulation

Procedia PDF Downloads 172
3148 Demarcating Wetting States in Pressure-Driven Flows by Poiseuille Number

Authors: Anvesh Gaddam, Amit Agrawal, Suhas Joshi, Mark Thompson

Abstract:

An increase in surface area to volume ratio with a decrease in characteristic length scale, leads to a rapid increase in pressure drop across the microchannel. Texturing the microchannel surfaces reduce the effective surface area, thereby decreasing the pressured drop. Surface texturing introduces two wetting states: a metastable Cassie-Baxter state and stable Wenzel state. Predicting wetting transition in textured microchannels is essential for identifying optimal parameters leading to maximum drag reduction. Optical methods allow visualization only in confined areas, therefore, obtaining whole-field information on wetting transition is challenging. In this work, we propose a non-invasive method to capture wetting transitions in textured microchannels under flow conditions. To this end, we tracked the behavior of the Poiseuille number Po = f.Re, (with f the friction factor and Re the Reynolds number), for a range of flow rates (5 < Re < 50), and different wetting states were qualitatively demarcated by observing the inflection points in the f.Re curve. Microchannels with both longitudinal and transverse ribs with a fixed gas fraction (δ, a ratio of shear-free area to total area) and at a different confinement ratios (ε, a ratio of rib height to channel height) were fabricated. The measured pressure drop values for all the flow rates across the textured microchannels were converted into Poiseuille number. Transient behavior of the pressure drop across the textured microchannels revealed the collapse of liquid-gas interface into the gas cavities. Three wetting states were observed at ε = 0.65 for both longitudinal and transverse ribs, whereas, an early transition occurred at Re ~ 35 for longitudinal ribs at ε = 0.5, due to spontaneous flooding of the gas cavities as the liquid-gas interface ruptured at the inlet. In addition, the pressure drop in the Wenzel state was found to be less than the Cassie-Baxter state. Three-dimensional numerical simulations confirmed the initiation of the completely wetted Wenzel state in the textured microchannels. Furthermore, laser confocal microscopy was employed to identify the location of the liquid-gas interface in the Cassie-Baxter state. In conclusion, the present method can overcome the limitations posed by existing techniques, to conveniently capture wetting transition in textured microchannels.

Keywords: drag reduction, Poiseuille number, textured surfaces, wetting transition

Procedia PDF Downloads 166
3147 Depth-Averaged Modelling of Erosion and Sediment Transport in Free-Surface Flows

Authors: Thomas Rowan, Mohammed Seaid

Abstract:

A fast finite volume solver for multi-layered shallow water flows with mass exchange and an erodible bed is developed. This enables the user to solve a number of complex sediment-based problems including (but not limited to), dam-break over an erodible bed, recirculation currents and bed evolution as well as levy and dyke failure. This research develops methodologies crucial to the under-standing of multi-sediment fluvial mechanics and waterway design. In this model mass exchange between the layers is allowed and, in contrast to previous models, sediment and fluid are able to transfer between layers. In the current study we use a two-step finite volume method to avoid the solution of the Riemann problem. Entrainment and deposition rates are calculated for the first time in a model of this nature. In the first step the governing equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed in conservative form and are used to calculate a solution that satisfies the conservation property. This method is found to be considerably faster than other comparative finite volume methods, it also exhibits good shock capturing. For most entrainment and deposition equations a bed level concentration factor is used. This leads to inaccuracies in both near bed level concentration and total scour. To account for diffusion, as no vertical velocities are calculated, a capacity limited diffusion coefficient is used. The additional advantage of this multilayer approach is that there is a variation (from single layer models) in bottom layer fluid velocity: this dramatically reduces erosion, which is often overestimated in simulations of this nature using single layer flows. The model is used to simulate a standard dam break. In the dam break simulation, as expected, the number of fluid layers utilised creates variation in the resultant bed profile, with more layers offering a higher deviation in fluid velocity . These results showed a marked variation in erosion profiles from standard models. The overall the model provides new insight into the problems presented at minimal computational cost.

Keywords: erosion, finite volume method, sediment transport, shallow water equations

Procedia PDF Downloads 220
3146 Model Reference Adaptive Approach for Power System Stabilizer for Damping of Power Oscillations

Authors: Jožef Ritonja, Bojan Grčar, Boštjan Polajžer

Abstract:

In recent years, electricity trade between neighboring countries has become increasingly intense. Increasing power transmission over long distances has resulted in an increase in the oscillations of the transmitted power. The damping of the oscillations can be carried out with the reconfiguration of the network or the replacement of generators, but such solution is not economically reasonable. The only cost-effective solution to improve the damping of power oscillations is to use power system stabilizers. Power system stabilizer represents a part of synchronous generator control system. It utilizes semiconductor’s excitation system connected to the rotor field excitation winding to increase the damping of the power system. The majority of the synchronous generators are equipped with the conventional power system stabilizers with fixed parameters. The control structure of the conventional power system stabilizers and the tuning procedure are based on the linear control theory. Conventional power system stabilizers are simple to realize, but they show non-sufficient damping improvement in the entire operating conditions. This is the reason that advanced control theories are used for development of better power system stabilizers. In this paper, the adaptive control theory for power system stabilizers design and synthesis is studied. The presented work is focused on the use of model reference adaptive control approach. Control signal, which assures that the controlled plant output will follow the reference model output, is generated by the adaptive algorithm. Adaptive gains are obtained as a combination of the "proportional" term and with the σ-term extended "integral" term. The σ-term is introduced to avoid divergence of the integral gains. The necessary condition for asymptotic tracking is derived by means of hyperstability theory. The benefits of the proposed model reference adaptive power system stabilizer were evaluated as objectively as possible by means of a theoretical analysis, numerical simulations and laboratory realizations. Damping of the synchronous generator oscillations in the entire operating range was investigated. Obtained results show the improved damping in the entire operating area and the increase of the power system stability. The results of the presented work will help by the development of the model reference power system stabilizer which should be able to replace the conventional stabilizers in power systems.

Keywords: power system, stability, oscillations, power system stabilizer, model reference adaptive control

Procedia PDF Downloads 141
3145 Overview of Multi-Chip Alternatives for 2.5 and 3D Integrated Circuit Packagings

Authors: Ching-Feng Chen, Ching-Chih Tsai

Abstract:

With the size of the transistor gradually approaching the physical limit, it challenges the persistence of Moore’s Law due to the development of the high numerical aperture (high-NA) lithography equipment and other issues such as short channel effects. In the context of the ever-increasing technical requirements of portable devices and high-performance computing, relying on the law continuation to enhance the chip density will no longer support the prospects of the electronics industry. Weighing the chip’s power consumption-performance-area-cost-cycle time to market (PPACC) is an updated benchmark to drive the evolution of the advanced wafer nanometer (nm). The advent of two and half- and three-dimensional (2.5 and 3D)- Very-Large-Scale Integration (VLSI) packaging based on Through Silicon Via (TSV) technology has updated the traditional die assembly methods and provided the solution. This overview investigates the up-to-date and cutting-edge packaging technologies for 2.5D and 3D integrated circuits (ICs) based on the updated transistor structure and technology nodes. The author concludes that multi-chip solutions for 2.5D and 3D IC packagings are feasible to prolong Moore’s Law.

Keywords: moore’s law, high numerical aperture, power consumption-performance-area-cost-cycle time to market, 2.5 and 3D- very-large-scale integration, packaging, through silicon via

Procedia PDF Downloads 119
3144 Component Test of Martensitic/Ferritic Steels and Nickel-Based Alloys and Their Welded Joints under Creep and Thermo-Mechanical Fatigue Loading

Authors: Daniel Osorio, Andreas Klenk, Stefan Weihe, Andreas Kopp, Frank Rödiger

Abstract:

Future power plants currently face high design requirements due to worsening climate change and environmental restrictions, which demand high operational flexibility, superior thermal performance, minimal emissions, and higher cyclic capability. The aim of the paper is, therefore, to investigate the creep and thermo-mechanical material behavior of improved materials experimentally and welded joints at component scale under near-to-service operating conditions, which are promising for application in highly efficient and flexible future power plants. These materials promise an increase in flexibility and a reduction in manufacturing costs by providing enhanced creep strength and, therefore, the possibility for wall thickness reduction. At the temperature range between 550°C and 625°C, the investigation focuses on the in-phase thermo-mechanical fatigue behavior of dissimilar welded joints of conventional materials (ferritic and martensitic material T24 and T92) to nickel-based alloys (A617B and HR6W) by means of membrane test panels. The temperature and external load are varied in phase during the test, while the internal pressure remains constant. At the temperature range between 650°C and 750°C, it focuses on the creep behavior under multiaxial stress loading of similar and dissimilar welded joints of high temperature resistant nickel-based alloys (A740H, A617B, and HR6W) by means of a thick-walled-component test. In this case, the temperature, the external axial load, and the internal pressure remain constant during testing. Numerical simulations are used for the estimation of the axial component load in order to induce a meaningful damage evolution without causing a total component failure. Metallographic investigations after testing will provide support for understanding the damage mechanism and the influence of the thermo-mechanical load and multiaxiality on the microstructure change and on the creep and TMF- strength.

Keywords: creep, creep-fatigue, component behaviour, weld joints, high temperature material behaviour, nickel-alloys, high temperature resistant steels

Procedia PDF Downloads 124
3143 Structural Optimization, Design, and Fabrication of Dissolvable Microneedle Arrays

Authors: Choupani Andisheh, Temucin Elif Sevval, Bediz Bekir

Abstract:

Due to their various advantages compared to many other drug delivery systems such as hypodermic injections and oral medications, microneedle arrays (MNAs) are a promising drug delivery system. To achieve enhanced performance of the MN, it is crucial to develop numerical models, optimization methods, and simulations. Accordingly, in this work, the optimized design of dissolvable MNAs, as well as their manufacturing, is investigated. For this purpose, a mechanical model of a single MN, having the geometry of an obelisk, is developed using commercial finite element software. The model considers the condition in which the MN is under pressure at the tip caused by the reaction force when penetrating the skin. Then, a multi-objective optimization based on non-dominated sorting genetic algorithm II (NSGA-II) is performed to obtain geometrical properties such as needle width, tip (apex) angle, and base fillet radius. The objective of the optimization study is to reach a painless and effortless penetration into the skin along with minimizing its mechanical failures caused by the maximum stress occurring throughout the structure. Based on the obtained optimal design parameters, master (male) molds are then fabricated from PMMA using a mechanical micromachining process. This fabrication method is selected mainly due to the geometry capability, production speed, production cost, and the variety of materials that can be used. Then to remove any chip residues, the master molds are cleaned using ultrasonic cleaning. These fabricated master molds can then be used repeatedly to fabricate Polydimethylsiloxane (PDMS) production (female) molds through a micro-molding approach. Finally, Polyvinylpyrrolidone (PVP) as a dissolvable polymer is cast into the production molds under vacuum to produce the dissolvable MNAs. This fabrication methodology can also be used to fabricate MNAs that include bioactive cargo. To characterize and demonstrate the performance of the fabricated needles, (i) scanning electron microscope images are taken to show the accuracy of the fabricated geometries, and (ii) in-vitro piercing tests are performed on artificial skin. It is shown that optimized MN geometries can be precisely fabricated using the presented fabrication methodology and the fabricated MNAs effectively pierce the skin without failure.

Keywords: microneedle, microneedle array fabrication, micro-manufacturing structural optimization, finite element analysis

Procedia PDF Downloads 117
3142 Structural Performance of Composite Steel and Concrete Beams

Authors: Jakub Bartus

Abstract:

In general, composite steel and concrete structures present an effective structural solution utilizing full potential of both materials. As they have a numerous advantages on the construction side, they can reduce greatly the overall cost of construction, which is the main objective of the last decade, highlighted by the current economic and social crisis. The study represents not only an analysis of composite beams’ behaviour having web openings but emphasizes the influence of these openings on the total strain distribution at the level of steel bottom flange as well. The major investigation was focused on a change of structural performance with respect to various layouts of openings. Examining this structural modification, an improvement of load carrying capacity of composite beams was a prime object. The study is devided into analytical and numerical part. The analytical part served as an initial step into the design process of composite beam samples, in which optimal dimensions and specific levels of utilization in individual stress states were taken into account. The numerical part covered description of imposed structural issue in a form of a finite element model (FEM) using strut and shell elements accounting for material non-linearities. As an outcome, a number of conclusions were drawn describing and explaining an effect of web opening presence on the structural performance of composite beams.

Keywords: composite beam, web opening, steel flange, totalstrain, finite element analysis

Procedia PDF Downloads 74
3141 Application of Computational Flow Dynamics (CFD) Analysis for Surge Inception and Propagation for Low Head Hydropower Projects

Authors: M. Mohsin Munir, Taimoor Ahmad, Javed Munir, Usman Rashid

Abstract:

Determination of maximum elevation of a flowing fluid due to sudden rejection of load in a hydropower facility is of great interest to hydraulic engineers to ensure safety of the hydraulic structures. Several mathematical models exist that employ one-dimensional modeling for the determination of surge but none of these perfectly simulate real-time circumstances. The paper envisages investigation of surge inception and propagation for a Low Head Hydropower project using Computational Fluid Dynamics (CFD) analysis on FLOW-3D software package. The fluid dynamic model utilizes its analysis for surge by employing Reynolds’ Averaged Navier-Stokes Equations (RANSE). The CFD model is designed for a case study at Taunsa hydropower Project in Pakistan. Various scenarios have run through the model keeping in view upstream boundary conditions. The prototype results were then compared with the results of physical model testing for the same scenarios. The results of the numerical model proved quite accurate coherence with the physical model testing and offers insight into phenomenon which are not apparent in physical model and shall be adopted in future for the similar low head projects limiting delays and cost incurred in the physical model testing.

Keywords: surge, FLOW-3D, numerical model, Taunsa, RANSE

Procedia PDF Downloads 364
3140 Drag Reduction of Base Bleed at Various Flight Conditions

Authors: Man Chul Jeong, Hyoung Jin Lee, Sang Yoon Lee, Ji Hyun Park, Min Wook Chang, In-Seuck Jeung

Abstract:

This study focus on the drag reduction effect of the base bleed at supersonic flow. Base bleed is the method which bleeds the gas on the tail of the flight vehicle and reduces the base drag, which occupies over 50% of the total drag in any flight speed. Thus base bleed can reduce the total drag significantly, and enhance the total flight range. Drag reduction ratio of the base bleed is strongly related to the mass flow rate of the bleeding gas. Thus selecting appropriate mass flow rate is important. However, since the flight vehicle has various flight speed, same mass flow rate of the base bleed can have different drag reduction effect during the flight. Thus, this study investigates the effect of the drag reduction depending on the flight speed by numerical analysis using STAR-CCM+. The analysis model is 155mm diameter projectile with boat-tailed shape base. Angle of the boat-tail is chosen previously for minimum drag coefficient. Numerical analysis is conducted for Mach 2 and Mach 3, with various mass flow rate, or the injection parameter I, of the bleeding gas and the temperature of the bleeding gas, is fixed to 300K. The results showed that I=0.025 has the minimum drag at Mach 2, and I=0.014 has the minimum drag at Mach 3. Thus as the Mach number is higher, the lower mass flow rate of the base bleed has more effect on drag reduction.

Keywords: base bleed, supersonic, drag reduction, recirculation

Procedia PDF Downloads 418
3139 On the End-of-Life Inventory Problem

Authors: Hans Frenk, Sonya Javadi, Semih Onur Sezer

Abstract:

We consider the so-called end of life inventory problem for the supplier of a product in its final phase of the service life cycle. This phase starts when the production of the items stops and continues until the warranty of the last sold item expires. At the beginning of this phase, the supplier places a final order for spare parts to serve customers coming with defective items. At any time during the final phase, the supplier may also decide to switch to an alternative and more cost-effective policy. This alternative policy may be in the form of replacing a defective item with a substitutable product or offering discounts / rebates on new generation products. In this setup, the objective is to find a final order quantity and also a switching time which will minimize the total expected discounted cost. We study this problem under a general cost structure in a continuous-time framework where arrivals of defective items are given by a non-homogeneous Poisson process. We consider four formulations which differ by the nature of the switching time. These formulations are studied in detail and properties of the objective function are derived in each case. Using these properties, we provide exact algorithms for efficient numerical implementations. Numerical examples are provided illustrating the application of these algorithms. In these examples, we also compare the costs associated with these different formulations.

Keywords: End-of-life inventory control, martingales, optimization, service parts

Procedia PDF Downloads 338
3138 The Analysis of Own Signals of PM Electrical Machines – Example of Eccentricity

Authors: Marcin Baranski

Abstract:

This article presents a vibration diagnostic method designed for permanent magnets (PM) traction motors. Those machines are commonly used in traction drives of electrical vehicles. Specific structural properties of machines excited by permanent magnets are used in this method - electromotive force (EMF) generated due to vibrations. This work presents: field-circuit model, results of static tests, results of calculations and simulations.

Keywords: electrical vehicle, permanent magnet, traction drive, vibrations, electrical machine, eccentricity

Procedia PDF Downloads 631
3137 Numerical Modelling of Wind Dispersal Seeds of Bromeliad Tillandsia recurvata L. (L.) Attached to Electric Power Lines

Authors: Bruna P. De Souza, Ricardo C. De Almeida

Abstract:

In some cities in the State of Parana – Brazil and in other countries atmospheric bromeliads (Tillandsia spp - Bromeliaceae) are considered weeds in trees, electric power lines, satellite dishes and other artificial supports. In this study, a numerical model was developed to simulate the seed dispersal of the Tillandsia recurvata species by wind with the objective of evaluating seeds displacement in the city of Ponta Grossa – PR, Brazil, since it is considered that the region is already infested. The model simulates the dispersal of each individual seed integrating parameters from the atmospheric boundary layer (ABL) and the local wind, simulated by the Weather Research Forecasting (WRF) mesoscale atmospheric model for the 2012 to 2015 period. The dispersal model also incorporates the approximate number of bromeliads and source height data collected from most infested electric power lines. The seeds terminal velocity, which is an important input data but was not available in the literature, was measured by an experiment with fifty-one seeds of Tillandsia recurvata. Wind is the main dispersal agent acting on plumed seeds whereas atmospheric turbulence is a determinant factor to transport the seeds to distances beyond 200 meters as well as to introduce random variability in the seed dispersal process. Such variability was added to the model through the application of an Inverse Fast Fourier Transform to wind velocity components energy spectra based on boundary-layer meteorology theory and estimated from micrometeorological parameters produced by the WRF model. Seasonal and annual wind means were obtained from the surface wind data simulated by WRF for Ponta Grossa. The mean wind direction is assumed to be the most probable direction of bromeliad seed trajectory. Moreover, the atmospheric turbulence effect and dispersal distances were analyzed in order to identify likely regions of infestation around Ponta Grossa urban area. It is important to mention that this model could be applied to any species and local as long as seed’s biological data and meteorological data for the region of interest are available.

Keywords: atmospheric turbulence, bromeliad, numerical model, seed dispersal, terminal velocity, wind

Procedia PDF Downloads 143
3136 Investigation of Mangrove Area Effects on Hydrodynamic Conditions of a Tidal Dominant Strait Near the Strait of Hormuz

Authors: Maryam Hajibaba, Mohsen Soltanpour, Mehrnoosh Abbasian, S. Abbas Haghshenas

Abstract:

This paper aims to evaluate the main role of mangroves forests on the unique hydrodynamic characteristics of the Khuran Strait (KS) in the Persian Gulf. Investigation of hydrodynamic conditions of KS is vital to predict and estimate sedimentation and erosion all over the protected areas north of Qeshm Island. KS (or Tang-e-Khuran) is located between Qeshm Island and the Iranian mother land and has a minimum width of approximately two kilometers. Hydrodynamics of the strait is dominated by strong tidal currents of up to 2 m/s. The bathymetry of the area is dynamic and complicated as 1) strong currents do exist in the area which lead to seemingly sand dune movements in the middle and southern parts of the strait, and 2) existence a vast area with mangrove coverage next to the narrowest part of the strait. This is why ordinary modeling schemes with normal mesh resolutions are not capable for high accuracy estimations of current fields in the KS. A comprehensive set of measurements were carried out with several components, to investigate the hydrodynamics and morpho-dynamics of the study area, including 1) vertical current profiling at six stations, 2) directional wave measurements at four stations, 3) water level measurements at six stations, 4) wind measurements at one station, and 5) sediment grab sampling at 100 locations. Additionally, a set of periodic hydrographic surveys was included in the program. The numerical simulation was carried out by using Delft3D – Flow Module. Model calibration was done by comparing water levels and depth averaged velocity of currents against available observational data. The results clearly indicate that observed data and simulations only fit together if a realistic perspective of the mangrove area is well captured by the model bathymetry data. Generating unstructured grid by using RGFGRID and QUICKIN, the flow model was driven with water level time-series at open boundaries. Adopting the available field data, the key role of mangrove area on the hydrodynamics of the study area can be studied. The results show that including the accurate geometry of the mangrove area and consideration of its sponge-like behavior are the key aspects through which a realistic current field can be simulated in the KS.

Keywords: Khuran Strait, Persian Gulf, tide, current, Delft3D

Procedia PDF Downloads 213
3135 Numerical Simulation of Filtration Gas Combustion: Front Propagation Velocity

Authors: Yuri Laevsky, Tatyana Nosova

Abstract:

The phenomenon of filtration gas combustion (FGC) had been discovered experimentally at the beginning of 80’s of the previous century. It has a number of important applications in such areas as chemical technologies, fire-explosion safety, energy-saving technologies, oil production. From the physical point of view, FGC may be defined as the propagation of region of gaseous exothermic reaction in chemically inert porous medium, as the gaseous reactants seep into the region of chemical transformation. The movement of the combustion front has different modes, and this investigation is focused on the low-velocity regime. The main characteristic of the process is the velocity of the combustion front propagation. Computation of this characteristic encounters substantial difficulties because of the strong heterogeneity of the process. The mathematical model of FGC is formed by the energy conservation laws for the temperature of the porous medium and the temperature of gas and the mass conservation law for the relative concentration of the reacting component of the gas mixture. In this case the homogenization of the model is performed with the use of the two-temperature approach when at each point of the continuous medium we specify the solid and gas phases with a Newtonian heat exchange between them. The construction of a computational scheme is based on the principles of mixed finite element method with the usage of a regular mesh. The approximation in time is performed by an explicit–implicit difference scheme. Special attention was given to determination of the combustion front propagation velocity. Straight computation of the velocity as grid derivative leads to extremely unstable algorithm. It is worth to note that the term ‘front propagation velocity’ makes sense for settled motion when some analytical formulae linking velocity and equilibrium temperature are correct. The numerical implementation of one of such formulae leading to the stable computation of instantaneous front velocity has been proposed. The algorithm obtained has been applied in subsequent numerical investigation of the FGC process. This way the dependence of the main characteristics of the process on various physical parameters has been studied. In particular, the influence of the combustible gas mixture consumption on the front propagation velocity has been investigated. It also has been reaffirmed numerically that there is an interval of critical values of the interfacial heat transfer coefficient at which a sort of a breakdown occurs from a slow combustion front propagation to a rapid one. Approximate boundaries of such an interval have been calculated for some specific parameters. All the results obtained are in full agreement with both experimental and theoretical data, confirming the adequacy of the model and the algorithm constructed. The presence of stable techniques to calculate the instantaneous velocity of the combustion wave allows considering the semi-Lagrangian approach to the solution of the problem.

Keywords: filtration gas combustion, low-velocity regime, mixed finite element method, numerical simulation

Procedia PDF Downloads 304
3134 Strain Softening of Soil under Cyclic Loading

Authors: Kobid Panthi, Suttisak Soralump, Suriyon Prempramote

Abstract:

In June 27, 2014 slope movement was observed in upstream side of Khlong Pa Bon Dam, Thailand. The slide did not have any major catastrophic impact on the dam structure but raised a very important question; why did the slide occur after 10 years of operation? Various site investigations (Bore Hole Test, SASW, Echo Sounding, and Geophysical Survey), laboratory analysis and numerical modelling using SIGMA/W and SLOPE/W were conducted to determine the cause of slope movement. It was observed that the dam had undergone the greatest differential drawdown in its operational history in the year 2014 and was termed as the major cause of movement. From the laboratory tests, it was found that the shear strength of clay had decreased with a period of time and was near its residual value. The cyclic movement of water, i.e., reservoir filling and emptying was coined out to be the major cause for the reduction of shear strength. The numerical analysis was carried out using a modified cam clay (MCC) model to determine the strain softening behavior of the clay. The strain accumulation was observed in the slope with each reservoir cycle triggering the slope failure in 2014. It can be inferred that if there was no major drawdown in 2014, the slope would not have failed but eventually would have failed after a long period of time. If there was no major drawdown in 2014, the slope would not have failed. However, even if there hadn’t been a drawdown, it would have failed eventually in the long run.

Keywords: slope movement, strain softening, residual strength, modified cam clay

Procedia PDF Downloads 136