Papers by Keyword: Boundary Element Method (BEM)

Abstract: Problems of wave propagation in poroelastic bodies and media are considered. The behavior of the poroelastic medium is described by Biot theory for partially saturated material. Mathematical model is written in term of five basic functions – elastic skeleton displacements, pore water pressure and pore air pressure. Boundary element method (BEM) is used with step method of numerical inversion of Laplace transform to obtain the solution. Research is based on direct boundary integral equation of three-dimensional isotropic linear theory of poroelasticity. Green’s matrices and, based on it, boundary integral equations are written for basic differential equations in partial derivatives. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. To approximate the boundary consider its decomposition to a set of quadrangular and triangular 8-node biquadratic elements, where triangular elements are treated as singular quadrangular. Every element is mapped to a reference one. Interpolation nodes for boundary unknowns are a subset of geometrical boundary-element grid nodes. Local approximation follows the Goldshteyn’s generalized displacement-stress matched model: generalized boundary displacements are approximated by bilinear elements whereas generalized tractions are approximated by constant. Integrals in discretized boundary integral equations are calculated using Gaussian quadrature in combination with singularity decreasing and eliminating algorithms.

Abstract: Problems of the poroviscodynamics are considered. Theory of poroviscoelasticity is based on Biot’s equations of fluid saturated porous media under assumption that the skeleton is viscoelastic. Viscoelastic effects of solid skeleton are modeled by mean of elastic-viscoelastic correspondence principle, using such viscoelastic models as a standard linear solid model and model with weakly singular kernel. The fluid is taken as original in Biot’s formulation without viscoelastic effects. Boundary integral equations method is applied to solve three-dimensional boundary-value problems. Boundary-element method with mixed discretization and matched approximation of boundary functions is used. Solution is obtained in Laplace domain, and then Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. An influence of viscoelastic parameters on dynamic responses is studied. Numerical example of the surface waves modelling is considered.

Abstract: This paper presents a three-dimensional direct boundary element approach for solving transient problems of linear anisotropic elasticity and viscoelasticity. In order to take advantage of the correspondence principle between viscoelasticity and elasticity the formulation is given in the Laplace domain. Anisotropic viscoelastic fundamental solutions are obtained using the correspondence principle and anisotropic elastic Green’s functions. The standard linear solid model is used to represent the mechanical behavior of viscoelastic material. Solution in time domain is calculated via numerical inversion by modified Durbin’s method. Numerical example is provided to validate the proposed boundary element formulation.

Abstract: In the paper an application of the particle swarm optimizer (PSO) with cloning improvement to optimization problems is presented. Reinfored structures considered in this work are dynamically loaded and analyzed by the coupled boundary and finite element method (BEM/FEM). The method is applied to optimize location of stiffeners in plates using criteria depended on displacements or stresses. Numerical examples demonstrate that the combination of the PSO with the BEM/FEM is an effective technique for solving computer aided optimal design problems, both with respect to accuracy and computational resources.

Abstract: Using the boundary element method, AZ80 magnesium alloy isothermal forging mould temperature field has be calculated. the outer wall of mold base temperature control at 360 °C, the model of cavity surface minimum temperature at 281.382 °C, the model of cavity on the surface of the highest temperature at 282.319 °C. Mold base outside the cavity wall and the model shows that the maximum temperature at 78.618 °C, the model of the maximum temperature difference between the cavity surface is 0.937 °C.

Abstract: Direct boundary element method formulation for transient dynamic linear piezoelectricity is presented. Integral representations of Laplace transformed dynamic piezoelectric fundamental solutions are used. Laplace domain BEM solutions inverted in real time by the stepping method. Numerical example of transient piezoelectric analysis is presented.

Abstract: To solve the problem that the change of curve slop was not considered in the common corrosion fatigue crack growth, a new corrosion fatigue crack propagation model based on Pairs formula was established in this paper; which corrected parameters C and n of Paris formula at the same time. Based on the fatigue crack propagation experimental data of X70 pipeline steel in hydrogen sulfide corrosive environment, the key parameters of the model were fitted. Based on the new model, a FRANC3D software was used, and the corrosion fatigue crack propagation processes of X70 pipeline steel in corrosive solution were simulated. It was demonstrated that the simulated fatigue crack growth processes obtained by the boundary element method were very close to the test results, and the maximum error is less than 10%. Therefore, boundary element method can be used to predict the life of corrosion fatigue on the project.

Abstract: The author of the article applied the boundary element method (BEM) to determine stresses occurring in a toothed rim of a flexspline. The relevant numerical calculations were conducted using software developed at the Faculty of Transport of the Silesian University of Technology. The numerical analysis conducted for flexsplines entailed the impact exerted by parameters of an indented toothed flexspline rim (number of teeth, addendum modification coefficient) and of a gear tool (gear tool head curve radius, pressure angle) on values of the stresses occurring at the tooth space bottom. Results of the said calculations have been depicted as curves of dependences between stresses at the tooth space bottom in the function of the number of flexspline rim teeth on constant values of the addendum modification coefficient. The cumulative diagrams developed based on the results of the calculations conducted may provide guidelines as to the manner of designing flexsplines for harmonic drives.

Abstract: The formulation developed in this work is based on the coupling of plane elasticity formulation and thin plate formulation for plates (Kirchhoff plates). Both formulations use elastostatic fundamental solutions. Curvature effects are considered as body forces, which generates domain integrals. Domain integrals are transformed into boundary integrals using the radial integration method. Thus, only the boundary is discretized. A radial basis function is used as approximation function in domain integrals. The developed formulation is applied to the dynamic analysis of anisotropic and composite laminate shallow shells under time dependent loads. A computational implementation was performed for the formulation developed and results were compared with results from literature.

Abstract: A two-scale three-dimensional approach for degradation and failure in polycrystalline materials is presented. The method involves the component level and the grain scale. The damage-induced softening at the macroscale is modelled employing an initial stress boundary element approach. The microscopic degradation is explicitly modelled associating Representative Volume Elements (RVEs) to relevant points of the macro continuum and employing a cohesive-frictional 3D grain-boundary formulation to simulate intergranular degradation and failure in the Voronoi morphology. Macro-strains are downscaled as RVEs' periodic boundary conditions, while overall macro-stresses are obtained upscaling the micro-stress field via volume averages. The comparison between effective macro-stresses for the damaged and undamaged RVEs allows to define a macroscopic measure of local material degradation. Some attention is devoted to avoiding pathological damage localization at the macro-scale. The multiscale processing algorithm is described and some preliminary results are illustrated.