Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 621

Search results for: geometric nonlinearity

621 Finite Element Analysis of Piezolaminated Structures with Both Geometric and Electroelastic Material Nonlinearities

Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen, , Jing Bai


Piezoelectric laminated smart structures can be subjected to the strong driving electric field, which may result in large displacements and rotations. In one hand, piezoelectric materials usually behave very significant material nonlinear effects under strong electric fields. On the other hand, thin-walled structures undergoing large displacements and rotations exist nonnegligible geometric nonlinearity. In order to give a precise prediction of piezo laminated smart structures under the large electric field, this paper develops a finite element (FE) model accounting for material nonlinearity (piezoelectric part) and geometric nonlinearity based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is first validated by both experimental and numerical examples from the literature. Afterwards, it is applied to simulate for plate and shell structures with multiple piezoelectric patches under the strong applied electric field. From the simulation results, it shows that large discrepancies occur between linear and nonlinear predictions for piezoelectric laminated structures driving at the strong electric field. Therefore, both material and geometric nonlinearities should be taken into account for piezoelectric structures under strong electric.

Keywords: piezoelectric smart structures, finite element analysis, geometric nonlinearity, electroelastic material nonlinearities

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620 Nonlinear Finite Element Modeling of Deep Beam Resting on Linear and Nonlinear Random Soil

Authors: M. Seguini, D. Nedjar


An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.

Keywords: finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability

Procedia PDF Downloads 280
619 Simulation of Piezoelectric Laminated Smart Structure under Strong Electric Field

Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen


Applying strong electric field on piezoelectric actuators, on one hand very significant electroelastic material nonlinear effects will occur, on the other hand piezo plates and shells may undergo large displacements and rotations. In order to give a precise prediction of piezolaminated smart structures under large electric field, this paper develops a finite element (FE) model accounting for both electroelastic material nonlinearity and geometric nonlinearity with large rotations based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is applied to analyze a piezolaminated semicircular shell structure.

Keywords: smart structures, piezolamintes, material nonlinearity, strong electric field

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618 Characterization of Ultrasonic Nonlinearity in Concrete under Cyclic Change of Prestressing Force

Authors: Gyu-Jin Kim, Hyo-Gyoung Kwak


In this research, the effect of prestressing force on the nonlinearity of concrete was investigated by an experimental study. For the measurement of ultrasonic nonlinearity, a prestressed concrete beam was prepared and a nonlinear resonant ultrasound method was adopted. When the prestressing force changes, the stress state of the concrete inside the beam is affected, which leads to the occurrence of micro-cracks and changes in mechanical properties. Therefore, it is necessary to introduce nonlinear ultrasonic technology which sensitively reflects microstructural changes. Repetitive prestressing load history, including maximum levels of 45%, 60% and 75%, depending on the compressive strength, is designed to evaluate the impact of loading levels on the nonlinearity. With the experimental results, the possibility of ultrasonic nonlinearity as a trial indicator of stress was evaluated.

Keywords: micro crack, nonlinear ultrasonic resonant spectroscopy, prestressed concrete beam, prestressing force, ultrasonic nonlinearity

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617 Quantification of Site Nonlinearity Based on HHT Analysis of Seismic Recordings

Authors: Ruichong Zhang


This study proposes a recording-based approach to characterize and quantify earthquake-induced site nonlinearity, exemplified as soil nonlinearity and/or liquefaction. Alternative to Fourier spectral analysis (FSA), the paper introduces time-frequency analysis of earthquake ground motion recordings with the aid of so-called Hilbert-Huang transform (HHT), and offers justification for the HHT in addressing the nonlinear features shown in the recordings. With the use of the 2001 Nisqually earthquake recordings, this study shows that the proposed approach is effective in characterizing site nonlinearity and quantifying the influences in seismic ground responses.

Keywords: site nonlinearity, site amplification, site damping, Hilbert-Huang Transform (HHT), liquefaction, 2001 Nisqually Earthquake

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616 Comparative Performance Analysis of Nonlinearity Cancellation Techniques for MOS-C Realization in Integrator Circuits

Authors: Hasan Çiçekli, Ahmet Gökçen, Uğur Çam


In this paper, a comparative performance analysis of mostly used four nonlinearity cancellation techniques used to realize the passive resistor by MOS transistors is presented. The comparison is done by using an integrator circuit which is employing sequentially Op-amp, OTRA and ICCII as active element. All of the circuits are implemented by MOS-C realization and simulated by PSPICE program using 0.35 µm process TSMC MOSIS model parameters. With MOS-C realization, the circuits became electronically tunable and fully integrable which is very important in IC design. The output waveforms, frequency responses, THD analysis results and features of the nonlinearity cancellation techniques are also given.

Keywords: integrator circuits, MOS-C realization, nonlinearity cancellation, tuneable resistors

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615 Nonlinear Static Analysis of Laminated Composite Hollow Beams with Super-Elliptic Cross-Sections

Authors: G. Akgun, I. Algul, H. Kurtaran


In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

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614 Numerical Study of Blackness Factor Effect on Dark Solitons

Authors: Khelil Khadidja


In this paper, blackness of dark solitons is considered. The exact combination between nonlinearity and dispersion is responsible of solitons stability. Dark solitons get born when dispersion is abnormal and balanced by nonlinearity, at the opposite of brillant solitons which is born by normal dispersion and nonlinearity together. Thanks to their stability, dark solitons are suitable for transmission by optical fibers. Dark solitons which are a solution of Nonlinear Schrodinger equation are simulated with Matlab to discuss the influence of coefficient of blackness. Results show that there is a direct proportion between the coefficient of blackness and the intensity of dark soliton. Those gray solitons are stable and convenient for transmission.

Keywords: abnormal dispersion, nonlinearity, optical fiber, soliton

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613 Geometrically Nonlinear Analysis of Initially Stressed Hybrid Laminated Composite Structures

Authors: Moumita Sit, Chaitali Ray


The present article deals with the free vibration analysis of hybrid laminated composite structures with initial stresses developed in the laminates. Generally initial stresses may be developed in the laminates by temperature and moisture effect. In this study, an eight noded isoparametric plate bending element has been used for the finite element analysis of composite plates. A numerical model has been developed to assess the geometric nonlinear response of composite plates based on higher order shear deformation theory (HSDT) considering the Green–Lagrange type nonlinearity. A computer code based on finite element method (FEM) has also been developed in MATLAB to perform the numerical calculations. To validate the accuracy of the proposed numerical model, the results obtained from the present study are compared with those available in published literature. Effects of the side to thickness ratio, different boundary conditions and initial stresses on the natural frequency of composite plates have been studied. The free vibration analysis of a hollow stiffened hybrid laminated panel has also been carried out considering initial stresses and presented as case study.

Keywords: geometric nonlinearity, higher order shear deformation theory (HSDT), hybrid composite laminate, the initial stress

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612 Finite Element Modeling and Nonlinear Analysis for Seismic Assessment of Off-Diagonal Steel Braced RC Frame

Authors: Keyvan Ramin


The geometric nonlinearity of Off-Diagonal Bracing System (ODBS) could be a complementary system to covering and extending the nonlinearity of reinforced concrete material. Finite element modeling is performed for flexural frame, x-braced frame and the ODBS braced frame system at the initial phase. Then the different models are investigated along various analyses. According to the experimental results of flexural and x-braced frame, the verification is done. Analytical assessments are performed in according to three-dimensional finite element modeling. Non-linear static analysis is considered to obtain performance level and seismic behavior, and then the response modification factors calculated from each model’s pushover curve. In the next phase, the evaluation of cracks observed in the finite element models, especially for RC members of all three systems is performed. The finite element assessment is performed on engendered cracks in ODBS braced frame for various time steps. The nonlinear dynamic time history analysis accomplished in different stories models for three records of Elcentro, Naghan, and Tabas earthquake accelerograms. Dynamic analysis is performed after scaling accelerogram on each type of flexural frame, x-braced frame and ODBS braced frame one by one. The base-point on RC frame is considered to investigate proportional displacement under each record. Hysteresis curves are assessed along continuing this study. The equivalent viscous damping for ODBS system is estimated in according to references. Results in each section show the ODBS system has an acceptable seismic behavior and their conclusions have been converged when the ODBS system is utilized in reinforced concrete frame.

Keywords: FEM, seismic behaviour, pushover analysis, geometric nonlinearity, time history analysis, equivalent viscous damping, passive control, crack investigation, hysteresis curve

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611 Islamic Geometric Design: Infinite Point or Creativity through Compass and Digital

Authors: Ridzuan Hussin, Mohd Zaihidee Arshad


The creativity of earlier artists and sculptors in designing geometric is extraordinary provided with only a compass. Indeed, geometric in Islamic art and design are unique and have their own aesthetic values. In order to further understand geometric, self-learning with the approach of hands on would be appropriate. For this study, Islamic themed geometric designed and created, concerning only; i. The Square Repetition Unit and √2, ii. The Hexagonal Repetition Unit and √3 and iii. Double Hexagon. The aim of this research is to evaluate the creativity of Islamic geometric pattern artworks, through Fundamental Arts and Gestalt theory. Data was collected using specific tasks, and this research intends to identify the difference of Islamic geometric between 21 untitled selected geometric artworks (conventional design method), and 25 digital untitled geometric pattern artworks method. The evaluation of creativity, colors, layout, pattern and unity is known to be of utmost importance, although there are differences in the conventional or the digital approach.

Keywords: Islamic geometric design, Gestalt, fundamentals of art, patterns

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610 Aeroelastic Analysis of Engine Nacelle Strake Considering Geometric Nonlinear Behavior

Authors: N. Manoj


The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.

Keywords: aeroelasticity, finite volume, geometric nonlinearity, limit cycle oscillations, strake

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609 Nonlinear Modelling and Analysis of Piezoelectric Smart Thin-Walled Structures in Supersonic Flow

Authors: Shu-Yang Zhang, Shun-Qi Zhang, Zhan-Xi Wang, Xian-Sheng Qin


Thin-walled structures are used more and more widely in modern aircrafts and some other structures in aerospace field nowadays. Accompanied by the wider applications, the vibration of the structures has been a bigger problem. Because of the direct and converse piezoelectric effect, piezoelectric materials combined to host thin-walled structures, named as piezoelectric smart structures, can be an effective way to suppress the vibration. So, an accurate model for piezoelectric thin-walled structures in air flow is necessary and important. In our recent work, an electromechanical coupling nonlinear aerodynamic finite element model of piezoelectric smart thin-walled structures is built based on the Reissner-Mindlin plate theory and first-order piston theory for aerodynamic pressure of supersonic flow. Von Kármán type nonlinearity is considered in the present model. Finally, the model is validated by experimental and numerical results from the literature, which can describe the vibration of the structures in supersonic flow precisely.

Keywords: piezoelectric smart structures, aerodynamic, geometric nonlinearity, finite element analysis

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608 A Nonlinear Dynamical System with Application

Authors: Abdullah Eqal Al Mazrooei


In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system.

Keywords: Lorenz models, nonlinear systems, nonlinear estimator, state-space model

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607 Mapping Method to Solve a Nonlinear Schrodinger Type Equation

Authors: Edamana Vasudevan Krishnan


This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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606 Spatial Interpolation Technique for the Optimisation of Geometric Programming Problems

Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna


Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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605 Analysis of Evolution of Higher Order Solitons by Numerical Simulation

Authors: K. Khadidja


Solitons are stable solution of nonlinear Schrodinger equation. Their stability is due to the exact combination between nonlinearity and dispersion which causes pulse broadening. Higher order solitons are born when nonlinear length is N multiple of dispersive length. Soliton order is determined by the number N itself. In this paper, evolution of higher order solitons is illustrated by simulation using Matlab. Results show that higher order solitons change their shape periodically, the reason why they are bad for transmission comparing to fundamental solitons which are constant. Partial analysis of a soliton of higher order explains that the periodic shape is due to the interplay between nonlinearity and dispersion which are not equal during a period. This class of solitons has many applications such as generation of supercontinuum and the impulse compression on the Femtosecond scale. As a conclusion, the periodicity which is harmful to transmission can be beneficial in other applications.

Keywords: dispersion, nonlinearity, optical fiber, soliton

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604 Spectral Broadening in an InGaAsP Optical Waveguide with χ(3) Nonlinearity Including Two Photon Absorption

Authors: Keigo Matsuura, Isao Tomita


We have studied a method to widen the spectrum of optical pulses that pass through an InGaAsP waveguide for application to broadband optical communication. In particular, we have investigated the competitive effect between spectral broadening arising from nonlinear refraction (optical Kerr effect) and shrinking due to two photon absorption in the InGaAsP waveguide with chi^(3) nonlinearity. The shrunk spectrum recovers broadening by the enhancement effect of the nonlinear refractive index near the bandgap of InGaAsP with a bandgap wavelength of 1490 nm. The broadened spectral width at around 1525 nm (196.7 THz) becomes 10.7 times wider than that at around 1560 nm (192.3 THz) without the enhancement effect, where amplified optical pulses with a pulse width of 2 ps and a peak power of 10 W propagate through a 1-cm-long InGaAsP waveguide with a cross-section of 4 um^2.

Keywords: InGaAsP waveguide, Chi^(3) nonlinearity, spectral broadening, photon absorption

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603 Differentiation of the Functional in an Optimization Problem for Coefficients of Elliptic Equations with Unbounded Nonlinearity

Authors: Aigul Manapova


We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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602 Influence of Nonlinearity of Concrete and Reinforcement Using Micropiles on the Seismic Interaction of Soil-Piles-Bridge

Authors: Mohanad Alfach, Amjad Al Helwani


Post-seismic observations of recent devastating earthquakes have shown that the behavior of the soil-pile-structure shows strong nonlinearity of soil and concrete under intensive seismic loading. Many of pile ruptures recently observed after the strong earthquake due to structural reasons (development of plastic hinges in the piles). The most likely reason for this rupture is the exceeding of maximum bending moment supported by the pile at several points. An analysis of these problems is necessary to take into account the nonlinearity of concrete, the strategy of strengthening the damaged piles and the interaction of these piles with the proposed strengthening by using micropiles. This study aims to investigate the interaction aspects for soil-piles- micropiles-structure using a global approach with a three dimensional finite difference code Flac 3D (Fast lagrangian analysis of continua in 3 dimensions).

Keywords: interaction, piles, micropiles, concrete, seismic, nonlinear, three-dimensional

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601 Geometric Design to Improve the Temperature

Authors: H. Ghodbane, A. A. Taleb, O. Kraa


This paper presents geometric design of induction heating system. The objective of this design is to improve the temperature distribution in the load. The study of such a device requires the use of models or modeling representation, physical, mathematical, and numerical. This modeling is the basis of the understanding, the design, and optimization of these systems. The optimization technique is to find values of variables that maximize or minimize the objective function.

Keywords: optimization, modeling, geometric design system, temperature increase

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600 Geometric Simplification Method of Building Energy Model Based on Building Performance Simulation

Authors: Yan Lyu, Yiqun Pan, Zhizhong Huang


In the design stage of a new building, the energy model of this building is often required for the analysis of the performance on energy efficiency. In practice, a certain degree of geometric simplification should be done in the establishment of building energy models, since the detailed geometric features of a real building are hard to be described perfectly in most energy simulation engine, such as ESP-r, eQuest or EnergyPlus. Actually, the detailed description is not necessary when the result with extremely high accuracy is not demanded. Therefore, this paper analyzed the relationship between the error of the simulation result from building energy models and the geometric simplification of the models. Finally, the following two parameters are selected as the indices to characterize the geometric feature of in building energy simulation: the southward projected area and total side surface area of the building, Based on the parameterization method, the simplification from an arbitrary column building to a typical shape (a cuboid) building can be made for energy modeling. The result in this study indicates that this simplification would only lead to the error that is less than 7% for those buildings with the ratio of southward projection length to total perimeter of the bottom of 0.25~0.35, which can cover most situations.

Keywords: building energy model, simulation, geometric simplification, design, regression

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599 Investigation of Airship Motion Sensitivity to Geometric Parameters

Authors: Han Ding, Wang Xiaoliang, Duan Dengping


During the process of airship design, the layout and the geometric shape of the hull and fins are crucial to the motion characteristics of the airship. In this paper, we obtained the quantification motion sensitivity of the airship to geometric parameters through turning circles and horizontal/vertical zigzag maneuvers by the parameterization of airship shape and building the dynamic model using Lagrangian approach and MATLAB Simulink program. In the dynamics simulation program, the affection of geometric parameters to the mass, center of gravity, moments of inertia, product of inertia, added mass and the aerodynamic forces and moments have been considered.

Keywords: airship, Lagrangian approach, turning circles, horizontal/vertical zigzag maneuvers

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598 Geometric Imperfections in Lattice Structures: A Simulation Strategy to Predict Strength Variability

Authors: Xavier Lorang, Ahmadali Tahmasebimoradi, Chetra Mang, Sylvain Girard


The additive manufacturing processes (e.g. selective laser melting) allow us to produce lattice structures which have less weight, higher impact absorption capacity, and better thermal exchange property compared to the classical structures. Unfortunately, geometric imperfections (defects) in the lattice structures are by-products results of the manufacturing process. These imperfections decrease the lifetime and the strength of the lattice structures and alternate their mechanical responses. The objective of the paper is to present a simulation strategy which allows us to take into account the effect of the geometric imperfections on the mechanical response of the lattice structure. In the first part, an identification method of geometric imperfection parameters of the lattice structure based on point clouds is presented. These point clouds are based on tomography measurements. The point clouds are fed into the platform LATANA (LATtice ANAlysis) developed by IRT-SystemX to characterize the geometric imperfections. This is done by projecting the point clouds of each microbeam along the beam axis onto a 2D surface. Then, by fitting an ellipse to the 2D projections of the points, the geometric imperfections are characterized by introducing three parameters of an ellipse; semi-major/minor axes and angle of rotation. With regard to the calculated parameters of the microbeam geometric imperfections, a statistical analysis is carried out to determine a probability density law based on a statistical hypothesis. The microbeam samples are randomly drawn from the density law and are used to generate lattice structures. In the second part, a finite element model for the lattice structure with the simplified geometric imperfections (ellipse parameters) is presented. This numerical model is used to simulate the generated lattice structures. The propagation of the uncertainties of geometric imperfections is shown through the distribution of the computed mechanical responses of the lattice structures.

Keywords: additive manufacturing, finite element model, geometric imperfections, lattice structures, propagation of uncertainty

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597 Numerical Study on Ultimate Capacity of Bi-Modulus Beam-Column

Authors: Zhiming Ye, Dejiang Wang, Huiling Zhao


Development of the technology demands a higher-level research on the mechanical behavior of materials. Structural members made of bi-modulus materials have different elastic modulus when they are under tension and compression. The stress and strain states of the point effect on the elastic modulus and Poisson ratio of every point in the bi-modulus material body. Accompanied by the uncertainty and nonlinearity of the elastic constitutive relation is the complicated nonlinear problem of the bi-modulus members. In this paper, the small displacement and large displacement finite element method for the bi-modulus members have been proposed. Displacement nonlinearity is considered in the elastic constitutive equation. Mechanical behavior of slender bi-modulus beam-column under different boundary conditions and loading patterns has been simulated by the proposed method. The influence factors on the ultimate bearing capacity of slender beam and columns have been studied. The results show that as the ratio of tensile modulus to compressive modulus increases, the error of the simulation employing the same elastic modulus theory exceeds the engineering permissible error.

Keywords: bi-modulus, ultimate capacity, beam-column, nonlinearity

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596 The Effect of Measurement Distribution on System Identification and Detection of Behavior of Nonlinearities of Data

Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri


In this paper, we considered and applied parametric modeling for some experimental data of dynamical system. In this study, we investigated the different distribution of output measurement from some dynamical systems. Also, with variance processing in experimental data we obtained the region of nonlinearity in experimental data and then identification of output section is applied in different situation and data distribution. Finally, the effect of the spanning the measurement such as variance to identification and limitation of this approach is explained.

Keywords: Gaussian process, nonlinearity distribution, particle filter, system identification

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595 Structural Analysis of the Burkh Anticline in Fars Zone, in the Zagros Fold-Thrust Belt

Authors: A. Afroogh, R. Ramazani Omali, N. Hafezi Moghaddas, A. Nohegar


Burkh anticline is located in Southeast of Zagros fold-thrust belt in the Fars Province. Geometric analyses of the anticline have been carried out to estimate the closure of the Dehram Group in order to evaluate its potential for gas reservoirs. Geometric analyses of the Burkh anticline indicate that the fold geometry is rather similar to that of the detachment folds. Based on the data from the geometric analysis, seven structural cross section the anticlines are drawn and using the cross sections, a structural contour for Dehram Group is constructed. The calculated values for the anticline closure prohibits this structure as it is not an appropriate host to gas reservoirs.

Keywords: Burkh anticline, Zagros fold-thrust belt, geometric analyses, vertical and horizontal closure, Dehram group

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594 Kýklos Dimensional Geometry: Entity Specific Core Measurement System

Authors: Steven D.P Moore


A novel method referred to asKýklos(Ky) dimensional geometry is proposed as an entity specific core geometric dimensional measurement system. Ky geometric measures can constructscaled multi-dimensionalmodels using regular and irregular sets in IRn. This entity specific-derived geometric measurement system shares similar fractal methods in which a ‘fractal transformation operator’ is applied to a set S to produce a union of N copies. The Kýklos’ inputs use 1D geometry as a core measure. One-dimensional inputs include the radius interval of a circle/sphere or the semiminor/semimajor axes intervals of an ellipse or spheroid. These geometric inputs have finite values that can be measured by SI distance units. The outputs for each interval are divided and subdivided 1D subcomponents with a union equal to the interval geometry/length. Setting a limit of subdivision iterations creates a finite value for each 1Dsubcomponent. The uniqueness of this method is captured by allowing the simplest 1D inputs to define entity specific subclass geometric core measurements that can also be used to derive length measures. Current methodologies for celestial based measurement of time, as defined within SI units, fits within this methodology, thus combining spatial and temporal features into geometric core measures. The novel Ky method discussed here offers geometric measures to construct scaled multi-dimensional structures, even models. Ky classes proposed for consideration include celestial even subatomic. The application of this offers incredible possibilities, for example, geometric architecture that can represent scaled celestial models that incorporates planets (spheroids) and celestial motion (elliptical orbits).

Keywords: Kyklos, geometry, measurement, celestial, dimension

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593 Directed-Wald Test for Distinguishing Long Memory and Nonlinearity Time Series: Power and Size Simulation

Authors: Heri Kuswanto, Philipp Sibbertsen, Irhamah


A Wald type test to distinguish between long memory and ESTAR nonlinearity has been developed. The test uses a directed-Wald statistic to overcome the problem of restricted parameters under the alternative. The test is derived from a model specification i.e. allows the transition parameter to appear as a nuisance parameter in the transition function. A simulation study has been conducted and it indicates that the approach leads a test with good size and power properties to distinguish between stationary long memory and ESTAR.

Keywords: directed-Wald test, ESTAR, long memory, distinguish

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592 A New Aggregation Operator for Trapezoidal Fuzzy Numbers Based On the Geometric Means of the Left and Right Line Slopes

Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava


This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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