Finite Element Applications Research Articles

Modal study of bi direction FGM plate

Abstract This study deals with free vibration analysis of bi direction FGM square plate. The mechanical parameters are assumed to be varied in the thickness as well as axially direction (x-axis and z-axis direction). Power law distribution is used to gradation of mechanical constants. Natural frequencies and mode shapes are computed under different boundary conditions. Clamped, simply supported, free and combination of all possible end conditions are considered. The finite element application software COMSOL-5.5 is used in the present study. The results obtained by COMSOL-5.5 software are validated with previous published research work. Effects of power law indices and end conditions on natural frequencies of the plate are explored. The natural frequencies are found to be higher in case of clamped end conditions under power law.

Homotopy perturbation technique for improving solutions of large quadratic eigenvalue problems: Application to friction-induced vibration

This paper puts forward a projection technique for accurately calculating solutions of large Quadratic Eigenvalue Problem. The aim here is to stabilize the complex eigensolutions whilst reducing residual errors, especially when considering significant damping contribution or asymmetric stiffness matrices. Hence, more confident results can be obtained in the frequency band of interest. To achieve this, high order modes, calculated using the homotopy perturbation technique, are introduced in the projection step of the classical method. This numerical proposal is a generalization of the classical projection, based only on normal modes of the associated undamped problem. To evaluate the efficiency of the suggested method, a finite element application dedicated to a friction-induced vibration problem is investigated.

MATLAB automated higher-order tetrahedral mesh generator for CAD geometries and a finite element application with the subparametric mappings

In this article MATLAB code is proposed for three-dimensional CAD geometries to produce automatic higher-order (HO) tetrahedral mesh. The HO mesh generator HOtetramesh proposed here is based up on a MATLAB PDE toolbox mesh generator function generateMesh . The input for this code is identical with that for input for the PDE toolbox mesh generator and the tetrahedral element with the necessary order. An HO tetrahedral mesh is generated as the output with the node coordinates, connectivity matrix, boundary edges and boundary nodes. The proposed mesh generator could be used efficiently to produce high-quality meshes in 3D finite element applications. A numerical example is provided with the complete detail for the demonstration of the proposed automated HO tetrahedral mesh generator over a 3D geometry by the subparametric finite element approach. This methodology can be used easily and reliably to address several problems in science and engineering.

Electromagneto-mechanical numerical analysis and experiment of transformer influenced by DC bias considering core magnetostriction

Abnormal vibration may cause the internal failure of transformers. In particular, the nonlinear saturation vibration of the iron core under direct current (DC) magnetic bias will lead to serious structural damage. In this paper, the dynamic process of transformer deformation under magnetic bias is completed by studying the magnetostrictive effect of ferromagnetic materials and analyzing the strain of the iron core. First, the silicon steel magnetostriction model is proposed and the computing processing is analyzed which explains the directivity characteristics of oriented silicon steel. Next, a coupled transformer model of the electromagnetic field and mechanical strain are built based on the piezomagnetic effect. Then, a dry transformer is performed in finite element (FE) application and after that, the displacements of test points are calculated by using measured magnetostriction curves and the FE model. Finally, vibration test is done to analyze the DC bias characteristics. The result of both calculation and measurements reveal that the magnetostriction of silicon material is the key factor of core vibration. It leads to the DC bias of transformer core remarkably and the magnetostriction of core material must be considered for transformer design and its applications.

Finite Element Application in Reservoir Deformation Analysis (Pilot Phase 2)

Finite element method (FEM) is a numerical technique for solving Engineering problem and Mathematical Physics. Useful problems with complicated geometries, Loading, and material properties where analytical solutions may not be obtained. Some of the complicated problems involving load is a cylindrical Reservoir structures where crude oil is stored in a Tank Farm. This paper demonstrates the use of Finite Element Analysis in above surface cylindrical Reservoir Engineering Structure. The reservoir which has sixteen (16) monitoring station was monitored using reflectorless Total station. This paper is the second phase of our pilot model and we hope to developed this second phase further to cover nine studs. The studs covered ranges from northern part of the Reservoir to the southern parts to further test the application of FEM triangular shaded (Truss) elements.

A comprehensive assessment of bus rollover crashes: integration of multibody dynamic and finite element simulation methods

Rollover crashes have the highest fatality rate and exhibit complex and unpredictable mechanisms in terms of vehicle-ground and vehicle-occupant interactions. The objective of this study is to evaluate the tilt table and modified dolly rollover (MDR) crash tests in terms of how these crash tests can represent those interactions and compare their results with two real-world rollover crashes. An application of combined dynamic and finite element (FE) simulations was presented to assess the cutaway bus rollover crash. First, the numerical models were validated against the experimental MDR test. Then, two real-world rollover crashes were simulated in PC-Crash to find the kinematics of the bus prior to the first vehicle-to-roof impact phase. Next, the impact phase of these real-world crashes was simulated using LS-DYNA and the results were compared with the two rollover crash tests. The FE simulations were conducted using a 2-point belted 50th Hybrid III FE model. The results of this study indicate that the common impact mechanism among these rollover scenarios was the impact between the bus’s roof corner (roof connection to the sidewall) and ground which caused lateral deformation patterns. Furthermore, unlike passenger cars where the vertical roof deformation can cause severe injuries in rollover crashes, the intrusion of the bus’s passenger compartment was not identified as a main source of injury. In addition, the highest head, neck, and chest injury risk were predicted during the MDR simulation where the ATD was partially ejected through the side window. Lastly, possible future works and limitations were explained.

Development of element-by-element kernel algorithms in unstructured finite-element solvers for many-core wide-SIMD CPUs: Application to earthquake simulation

Acceleration of the element-by-element (EBE) kernel in matrix-vector products is essential for high-performance in unstructured implicit finite-element applications. However, the EBE kernel is not straightforward to attain high performance due to random data access with data recurrence. In this paper, we develop methods to circumvent these data races for high performance on many-core CPU architectures with wide SIMD units. The developed EBE kernel attains 16.3% and 16.0% of FP32 peak on Intel Xeon Phi (Knights Landing) based Oakforest-PACS and Intel Xeon Platinum (Cascade Lake) based Oakbridge-CX, respectively. This leads to 2.88-fold speedup over the baseline kernel and 2.03-fold speedup of the whole finite-element application on Oakforest-PACS. Examples of finite-element earthquake simulations using the developed EBE kernel algorithms are shown. These insights are expected to enable high performance on other unstructured finite-element solvers on large-scale many-core wide-SIMD CPU based systems.

Dimensional considerations on the mechanical properties of 3D printed polymer parts

Additive manufacturing offers a useful and accessible tool for prototyping and manufacturing small volume functional parts. Polylactic acid (PLA) and thermoplastic polyurethane (TPU) are amongst the most commonly used materials. Characterising 3D printed PLA and TPU is potentially important for both designing and finite element modelling of functional parts. This work explores the mechanical properties of additively manufactured PLA/TPU specimens with consideration to design parameters including size, and infill percentage. PLA/TPU specimens are 3D-printed in selected ISO standard geometries with 20%, 60%, 100% infill percentage. Tensile and compression test results suggest that traditional ISO testing standards might be insufficient in characterising 3D printed materials for finite element modelling or application purposes. Infill percentage in combination to design size, may significantly affect the mechanical performance of 3D printed parts. Dimensional variation may cause inhomogeneity in mechanical properties between large and small cross section areas of the same part. The effect was reduced in small cross section parts where reducing the nominal infill had less effect on the resulting specimens. The results suggest that for 3D printed functional parts with significant dimensional differences between sections, the material properties are not necessarily homogeneous. This consideration may be significant for designers using 3D printing for applications, which include mechanical loading.

Hysteresis Model for Fiber Elements in Effective Damaged Zone of Square-Section Steel Piers Considering Local Instability Effect of Steel Plates

AbstractThe local instability of steel plates is the predominant seismic failure mode for steel bridge piers. However, the application of shell-based finite-element (FE) models in an engineering de...

General Homogenised Formulation for Thick Viscoelastic Layered Structures for Finite Element Applications

Viscoelastic layered surface treatments are widely used for passive control of vibration and noise, especially in passenger vehicles and buildings. When the viscoelastic layer is thick, the structural models must account for shear effects. In this work, a homogenised formulation for thick N-layered viscoelastic structures for finite element applications is presented, which allows for avoiding computationally expensive models based on solids. This is achieved by substituting the flexural stiffness in the governing thin beam or plate equation by a frequency dependent equivalent flexural stiffness that takes shear and the properties of the different layers into account. The formulation is applied to Free Layer Damping (FLD) and Constrained Layer Damping (CLD) beams and plates and its ability to accurately compute the eigenpairs and dynamic response is tested by implementing it in a finite element model and comparing the obtained results to those given by the standard for the application—Oberst for the FLD case and RKU for the CLD one—and to a solid model, which is used as reference. For the cases studied, the homogenised formulation is nearly as precise as the model based on solids, but requires less computational effort, and provides better results than the standard model.

Finite element application of ERBS extraction

In this paper we explore ERBS extraction in application to a heat conduction problem. Two types of basis functions are considered: B-spline and expo-rational B-spline (ERBS) combined with Bernstein polynomials. The first one is a global basis defined on a subdomain whose size is related to the spline degree, while the second one is a strictly local basis under the local geometry. While all the coefficients of the B-spline tensor product surface affect each element of the patch, local surfaces of the blending surface conserve both local manipulation and smoothness of the global surface.We show the conversion between these bases by using an ERBS extraction. The extraction operator allows us to convert the control points of the surface evaluated by B-splines to control points of the ERBS surface and vice versa. This approach is demonstrated on an example of the finite element solution approximation of the heat equation.

Efficient modeling of filled rubber assuming stress-induced microscopic restructurization

The mechanical response of filled rubber depends on load history, strain rate and state, temperature and even direction of previous loading. Although there is a plurality of both physical and phenomenological models, only few are able to reproduce this rich spectrum of effects. Moreover, many of them suffer from physical or mathematical inconsistencies. We present a model, which is based on physical ideas and plausible assumptions about the material’s microstructure, while being designed for high efficiency and robustness in finite element applications. It is shown by fits to extensive experimental data that it reproduces almost the full phenomenology of filled rubbers, both at low and high strains, for different deformation states and rates, holding times, and at different temperatures. The main modeling paradigm is the stress-induced breakdown and reorganization of microscopic structures which defines the time-dependent behavior of the material and allows to reproduce logarithmic relaxation effects. Moreover, its nine fit parameters evolve in a physically reasonable way under variation of filler and cross-linker content. A static limiting case of the model is derived, reducing the number of parameters and computational effort wherever necessary. Finally, a FE-implementation using computer-generated subroutines is presented and tested against experimental data of a simplified bushing under torsional, radial, cardanic and axial loading.

Automated Generation of Three-Dimensional Complex Muscle Geometries for Use in Personalised Musculoskeletal Models

The geometrical representation of muscles in computational models of the musculoskeletal system typically consists of a series of line segments. These muscle anatomies are based on measurements from a limited number of cadaveric studies that recently have been used as atlases for creating subject-specific models from medical images, so potentially restricting the options for personalisation and assessment of muscle geometrical models. To overcome this methodological limitation, we propose a novel, completely automated technique that, from a surface geometry of a skeletal muscle and its attachment areas, can generate an arbitrary number of lines of action (fibres) composed by a user-defined number of straight-line segments. These fibres can be included in standard musculoskeletal models and used in biomechanical simulations. This methodology was applied to the surfaces of four muscles surrounding the hip joint (iliacus, psoas, gluteus maximus and gluteus medius), segmented on magnetic resonance imaging scans from a cadaveric dataset, for which highly discretised muscle representations were created and used to simulate functional tasks. The fibres’ moment arms were validated against measurements and models of the same muscles from the literature with promising outcomes. The proposed approach is expected to improve the anatomical representation of skeletal muscles in personalised biomechanical models and finite element applications.

The Coarse Mesh Condensation Multiscale Method for parallel computation of heterogeneous linear structures without scale separation

A Coarse Mesh Condensation Multiscale Method (CMCM) is proposed to solve large heterogeneous linear structures without scale separation assumption. The technique aims to approximate the full field solution in heterogeneous structures by performing parallel calculations on subdomains. In the linear case, treated in this paper, direct linear relationships can be established between a reduced number of parameters describing Dirichlet boundary conditions on the subdomains boundaries and the degrees of freedom of a coarse mesh. The problem associated with the coarse mesh can be solved in one iteration and allows reconstructing the fine mesh solution in all subdomains. The accuracy of the method is analyzed through benchmarks involving subdomains crossed by the interfaces. Applications to large industrial finite element applications are presented, including one involving around 1.3 billion degrees of freedom.

Electromagnetic device modeling using a new adaptive wavelet finite element method

Wavelets provide sparse representations of integral and differential operators through a multiresolution approximation. This property is well-suited for adaptive implementation of numerical techniques, which is a common topic among researchers nowadays. The current state of the wavelet theory also allows flexible construction of transforms customized to certain applications, which is an important feature considering that the generalization of wavelet techniques to a large class of real-world numerical simulations is still limited. In this paper, it is proposed an adaptive wavelet finite element method for achieving operator-orthogonality between approximation spaces, a property which eliminates coupling among levels of resolution – a common shortcoming of adaptive methods. The resulting method is easily extended to any given finite element application and requires less computation power when compared to other adaptive techniques. These features are showcased by comparing the proposed technique to the popular h-refinement method using electromagnetic device simulations involving Dirichlet and Neumann boundary conditions, inhomogeneous and non-linear media, and irregular meshes.

On the application of polygonal finite element method for Stokes flow – A comparison between equal order and different order approximation

In this work, we discuss the application of polygonal finite elements to the solution of Stokes equations in two dimensions. The proposed framework is based on the mixed finite element discretization that involves velocity and pressure as independent unknown field variables. We present two approaches: (a) same order of approximation for velocity and pressure with Pressure Stabilization Petrov-Galerkin method (PSPG) and (b) different order of approximation for velocity and pressure. The approximation functions over polygons are rational polynomials based on Wachspress coordinates and for numerical integration of the terms in the bilinear and the linear form, we employ the linear smoothing technique. The relative performance between the approaches, the convergence properties and the accuracy is presented for two dimensional numerical examples, which shows that the proposed framework yields accurate results and converges at optimal convergence rate.

Development of vertical incident sound insulation simulation technology using finite element method and application to lightweight core

Development of vertical incident sound insulation simulation technology using finite element method and application to lightweight core

Application of finite elements of various dimensions in strength calculations of thin-wall constructions of agro-industrial complex

The article presents a comparative analysis of the effectiveness of the use of finite elements of various dimensions in the study of the stress-strain state (SSS) of objects of the agro-industrial complex (AIC). To determine the strength parameters of the AIC objects, which can be attributed to the class of thinwalled, it is proposed to use a two-dimensional finite element in the form of a fragment of the middle surface of a triangular shape with nodes at its vertices. To improve the compatibility of a two-dimensional finite element at the boundaries of adjacent elements, it is proposed to use the Lagrange multipliers introduced in additional nodes located in the middle of the sides of the triangular fragment as additional unknowns. It is proposed to use a three-dimensional finite element in the form of a prism with triangular bases to study the SSS of agricultural objects of medium thickness and thick-walled. To improve the compatibility of the prismatic element, Lagrange multipliers in the middle of the sides of the upper and lower bases are also used. On the example of calculating a fragment of a cylindrical pipeline rigidly clamped at the ends loaded with internal pressure, the effectiveness of the developed two-dimensional and three-dimensional finite elements with Lagrange multipliers was proved. The validity of the use of a twodimensional element for researching the SSS of agricultural objects belonging to the class of thin-walled was proved.

Computational Engineering

This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications.

Strengthening of Traditional Mud Houses on Response to Earthquake

Earthquake is an unexpected natural disaster that is unforeseeable and several earthquakes have been faced in Bangladesh with a magnitude of more than 6 in Richter scale in recent years. Non engineered houses are very common in rural area. Mudhouse is a typical house pattern among the non-engineered houses. The earthquake effect in conventional mud houses is a great concern. These houses are susceptible to earthquake damage due to some attributes of materials consisting of less stiffness, brittleness and poor bonding between the units. The present study deals with the strengthening of such houses using timber reinforcement with definite proportion contemplating the mud wall sizes and strengthening the walls by allowing some additional materials as reinforcements. Arrangements of reinforcement were followed in such a way that they would not require skilled labour and much cost. A finite element application STAAD-Pro was adopted to execute the required analysis of unreinforced and reinforced models considering both single story and double story. A series of analyses incorporating linear static and linear dynamic analyses were conducted to comprehend the actual response of models. Investigations from analyses depict that timber reinforcements impart greater stiffness and strength against overturning which increases the frequency of the structure and diminishes the lateral displacements to a good extent. The output from analyses includes lateral displacements, frequency, time-dependent displacements and time-dependent acceleration which depict the positive behaviour of reinforced mud houses. Such an arrangement of reinforcement can be a good choice to subside the detrimental effect of the earthquake.