Meshless Local Petrov-Galerkin Method for Stress and Crack Analysis in 3-D Axisymmetric FGM Bodies
Meshless Local Petrov-Galerkin Method for Stress and Crack Analysis in 3-D Axisymmetric FGM Bodies
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DOI：
10.3970/cmes.2005.008.259
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发表时间：
2005-06
影响因子：
2.4
通讯作者：
J. Sládek;V. Sládek;J. Kriváček;Ch. Zhang
中科院分区：
文献类型：
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作者：
J. Sládek;V. Sládek;J. Kriváček;Ch. Zhang
本文提出了一种基于局部Petrov-Galerkin方法的无网格方法，用于分析材料性质连续变化的三维轴对称线弹性体的应力问题。在动力学问题中考虑了惯性效应。单位阶跃函数被用作局部弱形式的测试函数。它导致局部边界积分方程（LBIE）。对于瞬态弹性动力学问题，应用拉普拉斯变换技术，并在拉普拉斯变换域中给出LBIE。三维线弹性固体的几何形状和边界条件的轴对称性将原来的三维边值问题简化为二维问题。子域的几何形状被选择为在所考虑的（x1，x3）-平面中具有圆形横截面的环形。局部积分方程的最终形式仅在弹性静力问题中具有纯轮廓积分性质。在弹性动力学中，由于惯性项，涉及额外的域积分。移动最小二乘（MLS）方法用于LBIE中物理量的近似。关键字：无网格法，局部弱形式，单位阶跃函数，移动最小二乘近似，拉普拉斯变换，功能梯度材料，瞬态弹性动力学，裂纹问题
A meshless method based on the local Petrov-Galerkin approach is presented for stress analysis in three-dimensional (3-d) axisymmetric linear elastic solids with continuously varying material properties. The inertial effects are considered in dynamic problems. A unit step function is used as the test functions in the local weak-form. It is leading to local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace-transform technique is applied and the LBIEs are given in the Laplace-transformed domain. Axial symmetry of the geometry and the boundary conditions for a 3-d linear elastic solid reduces the original 3-d boundary value problem into a 2-d problem. The geometry of subdomains is selected as a toroid with a circular cross section in the considered (x1,x3)-plane. The final form of the local integral equations has a pure contour-integral character only in elastostatic problems. In elastodynamics an additional domain-integral is involved due to inertia terms. The moving least-squares (MLS) method is used for the approximation of physical quantities in LBIEs. keyword: Meshless method, local weak-form, unit step function, moving least-squares approximation, Laplace-transform, functionally graded materials (FGMs), transient elastodynamics, crack problems