Papers by Keyword: BEM

Abstract: The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a beam. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Bars”) that is very similar to this paper except that the geometry considered in that paper is a bar.

Abstract: The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a bar. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Beams”) that is very similar to this paper except that the geometry considered in that paper is a beam.

Abstract: A procedure based on the Linear Elastic Brittle Interface Model (LEBIM) combined with the Coupled Criterion of Finite Fracture Mechanics (CCFFM) is successfully implemented in a 2D Boundary Element Method (BEM) code. In the original LEBIM formulation, the values of the interface strength, fracture toughness and stiffness are dependent on each other. Therefore, for a large interface stiffness, when the elastic interface tends to a perfect (infinitely stiff) interface, LEBIM is not able to properly characterize the crack propagation. The use of the CCFFM applied to LEBIM, with both the stress and energy criteria imposed as independent fracture conditions, allows to uncouple the interface fracture toughness and strength, obtaining realistic predictions for crack propagation even for stiff interfaces. This code is successfully applied to the problem of debond onset and growth in the pull push test. A benchmark problem is solved, focusing on the convergence of the load-displacement curve and crack-tip solution for h-refinements of BE meshes.

Abstract: The cloaking problem is considered for a 2-D wave scattering model in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The problem is reduced to the inverse extremal problem of choosing the surface impedance. The solvability of the original scattering problem for 2-D Helmholtz equation and of the extremal problem is proved. Optimality system describing the necessary extremum conditions is derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

Abstract: The present paper proposes an analytical method for determining the course (path) of crack propagation. A fatigue crack arises at the tooth root of a cylindrical geared wheel due to loading connected with gear work conditions. The cracking model was built using the adequate NASGRO2/3 formula; moreover, for comparison purposes, Forman and Paris-Erdogan’s laws were utilized. The length of an increase (propagation) in the crack was directly calculated by means of the boundary element method.

Abstract: The influence of the radiator and other components in the noise prediction process of cooling module is difficult to calculate. Firstly, the model including porous media is established. And the large eddy simulation (LES) is used to analyze its impact on the inflow instability and calculate the urbulent kinetic energy and vorticity around the fan. Then the main noise sources are identified by vortex sound theory. The acoustic BEM model is established for discrete and broadband aerodynamic noise prediction of cooling module. And the sound field sound pressure spectrum is analyzed. Finally, the noise test is made to verify the prediction. The results show that the radiator and other components have a huge influence in the flow field and noise prediction and they can not be ignored in the aerodynamic noise calculation process.

Abstract: 3D dynamic boundary-value problems of linear viscoelasticity and poroelasticity are considered. Laplace integral transform and its numerical inversion are used. Classical viscoelastic models, such as Maxwell model, KelvinVoigt model, standard linear solid model, and model with weakly singular kernel (Abel type) are considered. Boundary integral equations (BIE) method is developed to solve three-dimensional boundary-value problems. A numerical modelling of wave propagation is done by means of boundary element approach.

Abstract: The paper contains a brief introduction to the state of the art in poroelasticity models, in BIE & BEM methods application to solve dynamic problems in Laplace domain. Convolution Quadrature Method is formulated, as well as Runge-Kutta convolution quadrature modification and scheme with a key based on the highly oscillatory quadrature principles. Several approaches to Laplace transform inversion, including based on traditional Euler stepping scheme and Runge-Kutta stepping schemes, are numerically compared. A BIE system of direct approach in Laplace domain is used together with the discretization technique based on the collocation method. The boundary is discretized with the quadrilateral 8-node biquadratic elements. Generalized boundary functions are approximated with the help of the Goldshteyn’s displacement-stress matched model. The time-stepping scheme can rely on the application of convolution theorem as well as integration theorem. By means of the developed software the following 3d poroelastodynamic problem were numerically treated: a Heaviside-shaped longitudinal load acting on the face of a column.

Abstract: To describe poroelastic properties, a dynamic model of Biot’s material is used in the frame of the three-dimensional isotropic linear dynamic poroelasticity with four basic functions – displacements of the elastic skeleton and pore pressures. A direct version of the BIE method is developed. The boundary-element scheme is constructed using: regularized BIE’s, a matched element-by-element approximation, adaptive numerical integration in combination with a singularity-reducing algorithm, etc. The computer simulation is done using the boundary-element methodologies of the stepped method.

Abstract: In this paper a sensitivity formulation using the Boundary Element Method (BEM) is presentedfor analysis of structural reliability problems. The sensitivity formulation is based on implicit differentiation method where the first and second order derivatives of the random variables are obtained directly by differentiation of the discretised boundary integral equation. The structural reliability is assessed using the Monte Carlo Method and FORM with BEM sensitivity parameters. A benchmark example is presented to demonstrate the accuracy and efficiency of the BEM for both Monte Carlo and Sensitivity based FORM approaches.