This paper applies the improved formulation of the recent singular boundary method to infinite-domain wave problems. The SBM is mathematically simple, easy-to-program, meshless and introduces the concept of source int...
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This paper applies the improved formulation of the recent singular boundary method to infinite-domain wave problems. The SBM is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. In this study, we first derives the source intensity factors of exterior Helmholtz equation by means of the source intensity factors of exterior Laplace equation due to the same order of the singularities between the fundamental solution of Laplace and Helmholtz equations. The source intensity factors of exterior Laplace equation can be determined using the analytical-numerical technique proposed by Chen and Gu [1]. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on four benchmark infinite-domain wave examples.
So far the boundary element method (BEM) has been applied extensively in solving acoustic wave problems, as it involves only surface discretization and solves infinite/semi-infinite problems naturally and exactly. Alt...
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So far the boundary element method (BEM) has been applied extensively in solving acoustic wave problems, as it involves only surface discretization and solves infinite/semi-infinite problems naturally and exactly. Although the BEM reduces the problem dimensionality by one, the conventional method typically gives rise to fully populated and non-symmetric coefficient matrices which result in large storage requirements and prohibitive analysis time. The computational cost of the conventional method is O(N3) with direct solvers, or O(N2) with appropriate iterative solvers, and the storage requirements are O(N2), where N is the degree of freedom. This well-known drawback makes the BEM have difficulties with large models and thus be limited to numerical analyses of small bodies at low frequencies. In order to improve the efficiency, various fast approximate techniques, such as the fast multipole method (FMM), the fast wavelet transforms, the p-FFT method, the H-matrices and the adaptive cross approximation (ACA), have been proposed to accelerate the matrix-vector product in the BEM. Among these methods, the FMM approach seems to be one of the most widely accepted methods in the fast BEM community. Implemented with appropriate iterative solvers, the fast multipole BEM (FMBEM) reduces both the computational cost and storage requirement to O(N) for low-frequency acoustic wave problems, for example.
The simulation of fatigue crack initiation and propagation for particulate reinforced composites and the study of the behaviour of a functionally graded material with interface cracks are facilitated with new Voronoi ...
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The simulation of fatigue crack initiation and propagation for particulate reinforced composites and the study of the behaviour of a functionally graded material with interface cracks are facilitated with new Voronoi cell finite element method (VCFEM), considering the matrix-inclusion interfacial fatigue crack and matrix fatigue crack. In the new element, all possible contacts on the crack edge are considered by remeshing method, when the crack is closing under all possible changing loads. The fatigue crack initiates when the fatigue damage exceeds certain critical damage value, and fatigue crack propagation are simulated by gradual seeking crack propagating directions and new crack tips, using a remeshing method that a damaged node at the crack tip is replaced by a pair of nodes, a new crack tip node is assigned at the crack propagating directions and a more pair of nodes are needed to be added on the crack edge near the crack tip in order to better facilitate the free-traction boundary condition. The comparison of the results of proposed VCFEM and commercial finite element packages MARC. An example has been given for Particle-reinforced metal-matrix composites with 20 elliptical inclusions to simulate the fatigue crack initiation and propagation under plane stress conditions. It appears that this method is a more efficient way to deal with the interfacial damage of composite materials. The results show that the mechanical properties of functionally gradient materials are influenced by the particles' size, topological structure, and interfacial deboning strength. With the interface cracking the overall stiffness of functionally gradient materials is gradually reduced
This presentation is mainly devoted to the research on the regularization of indirect boundary integral equations （IBIEs） for three dimensional problems and establishes the new theory and method of the regularized B...
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This presentation is mainly devoted to the research on the regularization of indirect boundary integral equations （IBIEs） for three dimensional problems and establishes the new theory and method of the regularized BEM. The two special tangential vectors, which are linearly independent and associated with the normal vectors, are constructed, and then a characteristics theorem for the contour integrations of the normal and tangential gradients of some quantities, related with the fundamental solutions for 3D elastic problems, is presented. A limit theorem for the transformation from domain integral equations into boundary integral equations （BIEs） is also proposed. Based on this, together with a novel decomposition technique to the fundamental solution, the regularized BIEs with indirect unknowns, which don't involve the direct calculation of CPV and HFP integrals, are derived for 3D potential problems. Compared with the widely practiced direct regularized BEMs, the presented method has many advantages. First, the C continuity requirement for density function in the direct formulation can be relaxed to the piecewise C continuity in the presented formulation for the respective singular integral to exist. Second, it is more suitable for solving the structures of thin bodies, considering the solution process for boundary or field quantities doesn't involve the HFP integrals and nearly HFP integrals so the Regularization algorithm to the considered singular or nearly singular integrals is more effective. Third, the proposed regularized BIEs can calculate the any displacement gradients and stresses on the boundary, but not limited to the tractions, and also independent of the displacement BIEs. A systematic approach for implementing numerical solutions is produced by adopting the C continuous elements to depict the boundary surface and the discontinuous interpolation function to approximate the boundary quantities. Especially, for the boundary value problems with elliptic
以基面力为状态变量,表征物体的受力状态;以其对偶量位移梯度表征物体的变形状态,介绍了一种新型的基于余能原理的有限变形问题有限元法─基面力元法(Base Force Element Method,BFEM)及其计算性能。该方法的特色是:(1)以基面力矢量为...
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以基面力为状态变量,表征物体的受力状态;以其对偶量位移梯度表征物体的变形状态,介绍了一种新型的基于余能原理的有限变形问题有限元法─基面力元法(Base Force Element Method,BFEM)及其计算性能。该方法的特色是:(1)以基面力矢量为基本未知量;(2)采用并矢运算推导基面力元法的张量表达式;(3)不用引入单元插值函数;(4)模型列式为积分显式,无需进行数值积分;(5)基面力元法列式将平面任意多边形单元、空间任意多面体单元集于一体;(6)可适用于任意坐标系。本文数值算例通过与平面4节点等参元(Q4模型)和平面4节点减缩积分单元(Q4R模型)的对比分析,考查基面力元法的计算性能,结果表明:基于余能原理的基面力元法对网格畸变和单元长宽比的影响不敏感,可以应用于高度几何非线性问题,可进行大荷载步计算,且计算精度较高、收敛性较好,具有较广阔的应用前景。
That the drainage will bring about influence is harmful for engineering property of pile. However, the drainage is not taken into account in the investigation of dynamic behavior of pile in the saturated soil so far. ...
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That the drainage will bring about influence is harmful for engineering property of pile. However, the drainage is not taken into account in the investigation of dynamic behavior of pile in the saturated soil so far. In this paper, Using Green's function of the solid and fluid phases for a two-phase saturated medium in the axisymmetric coordinates, applying Lamb's integral equation with drainage, associating with the continuous conditions and the boundary conditions of pile-soil interaction, the authors via BEM to obtain solutions of the dynamic displacement and the pore pressure for a single pile with drainage in the saturated soil, as well as the flux of drainage. Some figures of the dynamic parameters under drained or/and undrained for dimensionless frequency are plotted respectively. That these results accord with correspond reality justifies that BEM is an effective numerical method used to solve the issue of pile.
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