Search results for: finite difference modelling

Authors: Zhipeng Feng, Huanhuan Qi, Pingchuan Shen, Fenggang Zang, Yixiong Zhang

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Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×10⁴. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.

Keywords: Vortex induced vibration, limit cycle, CFD, FEM.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

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In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.

Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure

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Authors: A.R.Nezamabadi, M.Mansouri Gavari, S.Mansouri, M.Mansouri Gavari

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This article considers the positional buckling of composite thick plates under thermal loading . For this purpose , the complex finite strip method is used . In analysis of complex finite strip, harmonic complex function in longitudinal direction , cubic functions in transversal direction and parabola distribution of transverse shear strain in thickness of thick plate based on higherorder shear deformation theory are used . In given examples , the effect of angles of stratification , number of layers , dimensions ratio and length – to – thick ratio across critical temperature are considered.

Keywords: Thermal buckling , Thick plate , Complex finite strip , Higher – order shear deformation theory.

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Authors: K. S. Sivakumaran, Bo Chen

Abstract:

The floor beams of steel buildings, cold-formed steel floor joists in particular, often require large web openings, which may affect their shear capacities. A cost effective way to mitigate the detrimental effects of such openings is to weld/fasten reinforcements. A difficulty associated with an experimental investigation to establish suitable reinforcement schemes for openings in shear zone is that moment always coexists with the shear, and thus, it is impossible to create pure shear state in experiments, resulting in moment influenced results. However, Finite Element Method (FEM) based analysis can be conveniently used to investigate the pure shear behaviour of webs including webs with reinforced openings. This paper presents the details associated with the finite element analysis of thick/thin-plates (representing the web of hot-rolled steel beam, and the web of a cold-formed steel member) having a large reinforced opening. The study considered simply-supported rectangular plates subjected to in-plane shear loadings until failure (including post-buckling behaviour). The plate was modelled using geometrically non-linear quadrilateral shell elements, and non-linear stress-strain relationship based on experiments. Total Langrangian with large displacement/small strain formulation was used for such analyses. The model also considered the initial geometric imperfections. This study considered three reinforcement schemes, namely, flat, lip, and angle reinforcements. This paper discusses the modelling considerations and presents the results associated with the various reinforcement schemes under consideration.

Keywords: Cold-formed steel, finite element analysis, opening, reinforcement, shear resistance.

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Authors: Dimitri Perrin, Heather J. Ruskin, Martin Crane

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This study focuses on examining why the range of experience with respect to HIV infection is so diverse, especially in regard to the latency period. An agent-based approach in modelling the infection is used to extract high-level behaviour which cannot be obtained analytically from the set of interaction rules at the cellular level. A prototype model encompasses local variation in baseline properties, contributing to the individual disease experience, and is included in a network which mimics the chain of lymph nodes. The model also accounts for stochastic events such as viral mutations. The size and complexity of the model require major computational effort and parallelisation methods are used.

Keywords: HIV, Immune modelling, Agent-based system, individual response.

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Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Zhou Xiong, Kang Shao Bo, Yang Bo

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To date, high-performance structural steel has been widely used for columns in construction practices due to its significant advantages over conventional steel. However, the same design approach with conventional steel columns is still adopted in the design of high-performance steel columns. As a result, its superior properties cannot be fully considered in design. This paper conducts a test and finite element analysis on the overall stability behaviour of welded Q460GJ steel box columns. In the test, four steel columns with different slenderness and width-to-thickness ratio were compressed under an axial compression testing machine. And finite element models were established in which material nonlinearity and residual stress distributions of test columns were included. Then, comparisons were made between test results and finite element result, it showed that finite element analysis results are agree well with the test result. It means that the test and finite element model are reliable. Then, we compared the test result with the design value calculated by current code, the result showed that Q460GJ steel box columns have the higher overall buckling capacity than the design value. It is necessary to update the design curves for Q460GJ steel columns so that the overall stability capacity of Q460GJ box columns can be designed appropriately.

Keywords: Axial compression, Finite element analysis, Overall stability, Q460GJ steel, Welded box columns.

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Authors: Sumit Tiwari, Rohit Tripathi, G. N. Tiwari

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Present study focused on the utilization of solar energy by the help of photovoltaic greenhouse solar dryer under forced mode. A single slope photovoltaic greenhouse solar dryer has been proposed and thermal modelling has been developed. Various parameters have been calculated by thermal modelling such as greenhouse room temperature, cell temperature, crop temperature and air temperature at exit of greenhouse. Further cell efficiency, thermal efficiency, and overall thermal efficiency have been calculated for a typical day of May and November. It was found that system can generate equivalent thermal energy up to 7.65 kW and 6.66 kW per day for clear day of May and November respectively.

Keywords: Characteristics curve, Photovoltaic, Thermal modelling, Thermal efficiency.

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Authors: A. Javed, K. Djidjeli, J. T. Xing, S. J. Cox

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A method for simulating flow around the solid bodies has been presented using hybrid meshfree and mesh-based schemes. The presented scheme optimizes the computational efficiency by combining the advantages of both meshfree and mesh-based methods. In this approach, a cloud of meshfree nodes has been used in the domain around the solid body. These meshfree nodes have the ability to efficiently adapt to complex geometrical shapes. In the rest of the domain, conventional Cartesian grid has been used beyond the meshfree cloud. Complex geometrical shapes can therefore be dealt efficiently by using meshfree nodal cloud and computational efficiency is maintained through the use of conventional mesh-based scheme on Cartesian grid in the larger part of the domain. Spatial discretization of meshfree nodes has been achieved through local radial basis functions in finite difference mode (RBF-FD). Conventional finite difference scheme has been used in the Cartesian ‘meshed’ domain. Accuracy tests of the hybrid scheme have been conducted to establish the order of accuracy. Numerical tests have been performed by simulating two dimensional steady and unsteady incompressible flows around cylindrical object. Steady flow cases have been run at Reynolds numbers of 10, 20 and 40 and unsteady flow problems have been studied at Reynolds numbers of 100 and 200. Flow Parameters including lift, drag, vortex shedding, and vorticity contours are calculated. Numerical results have been found to be in good agreement with computational and experimental results available in the literature.

Keywords: CFD, Meshfree particle methods, Hybrid grid, Incompressible Navier Strokes equations, RBF-FD.

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Authors: M. Harir, A. Bendiabdellah, A. Chaouch, N. Benouzza

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This paper deals with the modelling and simulation of the squirrel cage induction motor by taking into account all space harmonic components as well as the introduction of the bars skew in the calculation of the linear evolution of the magnetomotive force (MMF) between the slots extremities. The model used is based on multiple coupled circuits and the modified winding function approach (MWFA). The effect of skewing is included in the calculation of motors inductances with an axial asymmetry in the rotor. The simulation results in both time and spectral domains show the effectiveness and merits of the model and the error that may be caused if the skew of the bars are neglected.

Keywords: Modelling, MWFA, Skew effect, Squirrel cage induction motor, Spectral domain.

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.

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Authors: C. Perez, O. Reinoso, N. Garcia, J. M. Sabater, L. Gracia

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For high-speed control of robots, a good knowledge of system modelling is necessary to obtain the desired bandwidth. In this paper, we present a cartesian robot with a pan/tilt unit in end-effector (5 dof). This robot is implemented with powerful direct drive AC induction machines. The dynamic model, parameter identification and model validation of the robot are studied (including actuators). This work considers the cartesian robot coupled and non linear (contrary to normal considerations for this type of robots). The mechanical and control architecture proposed in this paper is efficient for industrial and research application in which high speed, well known model and very high accuracy are required.

Keywords: Robot modelling, parameter identification and validation, AC servo-motors.

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Authors: Yanan Yang, Zhigang Wang, Xiang Chen

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This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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Authors: P. D. Pastuszak

Abstract:

The present work is devoted to thermographic studies of curved composite panels (unidirectional GFRP) with subsurface defects. Various artificial defects, created by inserting PTFE stripe between individual layers of a laminate during manufacturing stage are studied. The analysis is conducted both with the use finite element method and experiments. To simulate transient heat transfer in 3D model with embedded various defect sizes, the ANSYS package is used. Pulsed Thermography combined with optical excitation source provides good results for flat surfaces. Composite structures are mostly used in complex components, e.g., pipes, corners and stiffeners. Local decrease of mechanical properties in these regions can have significant influence on strength decrease of the entire structure. Application of active procedures of thermography to defect detection and evaluation in this type of elements seems to be more appropriate that other NDT techniques. Nevertheless, there are various uncertainties connected with correct interpretation of acquired data. In this paper, important factors concerning Infrared Thermography measurements of curved surfaces in the form of cylindrical panels are considered. In addition, temperature effects on the surface resulting from complex geometry and embedded and real defect are also presented.

Keywords: Active thermography, finite element analysis, composite, curved structures, defects.

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Authors: Ionel D. Craiu, Mihai Nedelcu

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Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: Damage detection, generalized beam theory, inverse finite element method, shape sensing.

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Authors: Swarniv Chandra, Basudev Ghosh

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Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: Monika Neda, Elena Nikonova

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We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).

Keywords: Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.

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Authors: E. Ramprasath, P. Manojkumar, P. Veena

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Proposed paper dealt with the modelling and analysis of induction motor based on the mathematical expression using the graphical programming environment of Laboratory Virtual Instrument Engineering Workbench (LabVIEW). Induction motor modelling with the mathematical expression enables the motor to be simulated with the various required parameters. Owing to the invention of variable speed drives study about the induction motor characteristics became complex. In this simulation motor internal parameter such as stator resistance and reactance, rotor resistance and reactance, phase voltage, frequency and losses will be given as input. By varying the speed of motor corresponding parameters can be obtained they are input power, output power, efficiency, torque induced, slip and current.

Keywords: Induction motor, LabVIEW software, modelling and analysis, electrical and mechanical characteristics of motor.

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Authors: Bhim Kumar Dahal

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Transportation network development in the developing country is in rapid pace. The majority of the network belongs to railway and expressway which passes through diverse topography, landform and geological conditions despite the avoidance principle during route selection. Construction of such networks demand many low to high embankment which required improvement in the foundation soil. This paper is mainly focused on the various advanced ground improvement techniques used to improve the soft soil, modelling approach and its predictability for embankments construction. The ground improvement techniques can be broadly classified in to three groups i.e. densification group, drainage and consolidation group and reinforcement group which are discussed with some case studies.  Various methods were used in modelling of the embankments from simple 1-dimensional to complex 3-dimensional model using variety of constitutive models. However, the reliability of the predictions is not found systematically improved with the level of sophistication.  And sometimes the predictions are deviated more than 60% to the monitored value besides using same level of erudition. This deviation is found mainly due to the selection of constitutive model, assumptions made during different stages, deviation in the selection of model parameters and simplification during physical modelling of the ground condition. This deviation can be reduced by using optimization process, optimization tools and sensitivity analysis of the model parameters which will guide to select the appropriate model parameters.

Keywords: Embankment, ground improvement, modelling, model prediction.

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Authors: Qianhong Zhang, Wenzhuan Zhang

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This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.

Keywords: Difference equations, stability, unstable, global asymptotic behavior.

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Authors: Xi Yang, Bulent Chavdar, Alan Vonseggern, Taylan Altan

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Fracture in hot precision forging of engine valves was investigated in this paper. The entire valve forging procedure was described and the possible cause of the fracture was proposed. Finite Element simulation was conducted for the forging process, with commercial Finite Element code DEFORMTM. The effects of material properties, the effect of strain rate and temperature were considered in the FE simulation. Two fracture criteria were discussed and compared, based on the accuracy and reliability of the FE simulation results. The selected criterion predicted the fracture location and shows the trend of damage increasing with good accuracy, which matches the experimental observation. Additional modification of the punch shapes was proposed to further reduce the tendency of fracture in forging. Finite Element comparison shows a great potential of such application in the mass production.

Keywords: Hot forging, engine valve, fracture, tooling.

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Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

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In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves and circles.

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Authors: Ali M. Al-Shaery

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The purpose of this paper is to address the functions of sustainability dimensions in city information modelling and to present the required sustainability criteria that support establishing a sustainable planning framework for enhancing existing cities and developing future smart cities. The paper is divided into two sections. The first section is based on the examination of a wide and extensive array of cross-disciplinary literature in the last decade and a half to conceptualize the terms ‘sustainable’ and ‘smart city’, and map their associated criteria to city information modelling. The second section is based on analyzing two approaches relating to city information modelling, namely statistical and dynamic approaches, and their suitability in the development of cities’ action plans. The paper argues that the use of statistical approaches to embed sustainability dimensions in city information modelling have limited value. Despite the popularity of such approaches in addressing other dimensions like utility and service management in development and action plans of the world cities, these approaches are unable to address the dynamics across various city sectors with regards to economic, environmental and social criteria. The paper suggests an integrative dynamic and cross-disciplinary planning approach to embedding sustainability dimensions in city information modelling frameworks. Such an approach will pave the way towards optimal planning and implementation of priority actions of projects and investments. The approach can be used to achieve three main goals: (1) better development and action plans for world cities (2) serve the development of an integrative dynamic and cross-disciplinary framework that incorporates economic, environmental and social sustainability criteria and (3) address areas that require further attention in the development of future sustainable and smart cities. The paper presents an innovative approach for city information modelling and a well-argued, balanced hierarchy of sustainability criteria that can contribute to an area of research which is still in its infancy in terms of development and management.

Keywords: Information modelling, smart city, sustainable city, sustainability dimensions, sustainability criteria, city development planning.

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Authors: Shidvash Vakilipour, Masoud Mohammadi, Rouzbeh Riazi, Scott Ormiston, Kimia Amiri, Sahar Barati

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An essential component of a finite volume method (FVM) is the advection scheme that estimates values on the cell faces based on the calculated values on the nodes or cell centers. The most widely used advection schemes are upwind schemes. These schemes have been developed in FVM on different kinds of structured and unstructured grids. In this research, the physical influence scheme (PIS) is developed for a cell-centered FVM that uses an implicit coupled solver. Results are compared with the exponential differencing scheme (EDS) and the skew upwind differencing scheme (SUDS). Accuracy of these schemes is evaluated for a lid-driven cavity flow at Re = 1000, 3200, and 5000 and a backward-facing step flow at Re = 800. Simulations show considerable differences between the results of EDS scheme with benchmarks, especially for the lid-driven cavity flow at high Reynolds numbers. These differences occur due to false diffusion. Comparing SUDS and PIS schemes shows relatively close results for the backward-facing step flow and different results in lid-driven cavity flow. The poor results of SUDS in the lid-driven cavity flow can be related to its lack of sensitivity to the pressure difference between cell face and upwind points, which is critical for the prediction of such vortex dominant flows.

Keywords: Cell-centered finite volume method, physical influence scheme, exponential differencing scheme, skew upwind differencing scheme, false diffusion.

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Authors: Tariq T. Darabseh

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The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.

Keywords: Finite element method, thermal stresses, Green-Lindsay theory, functionally graded material.

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Authors: Ali A. Al-Jazaairry, Tahsin T. Sabbagh

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Presence of cavities in soil predictably induces ground deformation and changes in soil stress, which might influence adjacent existing pile foundations, though the effect of twin cavities on a nearby pile needs to be understood. This research is an attempt to identify the behaviour of piles subjected to axial load and embedded in cavitied clayey soil. A series of finite element modelling were conducted to investigate the performance of piled foundation located in such soils. The validity of the numerical simulation was evaluated by comparing it with available field test and alternative analytical model. The study involved many parameters such as twin cavities size, depth, spacing between cavities, and eccentricity of cavities from the pile axis on the pile performance subjected to axial load. The study involved many cases; in each case, a critical value has been found in which cavities’ presence has shown minimum impact on the behaviour of pile. Load-displacement relationships of the affecting parameters on the pile behaviour were presented to provide helpful information for designing piled foundation situated near twin underground cavities. It was concluded that the presence of the cavities within the soil mass reduces the ultimate capacity of pile. This reduction differs according to the size and location of the cavity.

Keywords: Axial load, clay, finite element, pile, twin cavities, ultimate capacity.

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Authors: Mohamed Tarek Khadir, Damien Fay, Ahmed Boughrira

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Short term electricity demand forecasts are required by power utilities for efficient operation of the power grid. In a competitive market environment, suppliers and large consumers also require short term forecasts in order to estimate their energy requirements in advance. Electricity demand is influenced (among other things) by the day of the week, the time of year and special periods and/or days such as Ramadhan, all of which must be identified prior to modelling. This identification, known as day-type identification, must be included in the modelling stage either by segmenting the data and modelling each day-type separately or by including the day-type as an input. Day-type identification is the main focus of this paper. A Kohonen map is employed to identify the separate day-types in Algerian data.

Keywords: Day type identification, electricity Load, Kohonenmaps, load forecasting.

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Authors: M. Sasajima, M. Watanabe, T. Yamaguchi, Y. Kurosawa, Y. Koike

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Sound pathways in the enclosures of small earphones are very narrow. In such narrow pathways, the speed of sound propagation and the phase of sound waves change because of the air viscosity. We have developed a new finite element method that includes the effects of damping due to air viscosity for modeling the sound pathway. This method is developed as an extension of the existing finite element method for porous sound-absorbing materials. The numerical calculation results using the proposed finite element method are validated against the existing calculation methods.

Keywords: Simulation, FEM, air viscosity, damping.

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Authors: M. Ikhwan Z. Ridzwan, Bidyut Pal, Ulrich N. Hansen

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Finite element method was applied to model damage development in the femoral neck during a sideways fall. The femoral failure was simulated using the maximum principal strain criterion. The evolution of damage was consistent with previous studies. It was initiated by compressive failure at the junction of the superior aspect of the femoral neck and the greater trochanter. It was followed by tensile failure that occurred at the inferior aspect of the femoral neck before a complete transcervical fracture was observed. The estimated failure line was less than 50° from the horizontal plane (Pauwels type II).

Keywords: Femoral Strength, Finite Element Models, Hip Fracture, Progressive Failure, Sideways Fall.

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Authors: R. K. Apalowo, D. Chronopoulos

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A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: Layered Structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element.

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