【摘要】 提出了弹性力学平面问题的局部边界积分方程方法．这种方法是一种无网格方法，它采用移动最小二乘近似试函数，且只包含中心在所考虑节点的局部边界上的边界积分．它易于施加本质边界条件．所得系统矩阵是一个带状稀疏矩阵．它组合了伽辽金有限元法、整体边界元法和无单元伽辽金法的优点．该方法可以容易推广到求解非线性问题以及非均匀介质的力学问题。 计算了两个弹性力学平面问题的例子，给出了位移和能量的索波列夫模，所得计算结果证明：该方法是一种具有收敛快、精度高、简便有效的通用方法．更多还原

【Abstract】 The basic concept and numerical implementation of a local boundary integral equation formulation for solving the elasticity problem have been presented in the present paper. It is a new truly meshless method, because the numerical implementation of the method leads to an efficient meshless discrete model. The concept of a companion solution is introduced, such that the traction terms would not appear in the integrals over the local boundary after the modified integral kernel is used for all nodes whose local boundary ■ falls within the global boundary ■ of the given problem; it uses the moving least square approximations, and involves only boundary integration over a local boundary centered at the node in question. It poses no difficulties in satisfying essential boundary conditions, and leads to a banded and sparse system matrix. The undependence of the solution on the size of the integral local boundary provides a great nexibility in dealing with the numerical model of the elastic plane problems under various boundary conditions with arbitrary shapes. Convergence studies in the numerical examples show that the present method possesses an excellent rate of convergence and reasonably accurate results for both the unknown displacement and strain energy, as the original approximated trial solutions have nice continuity and smoothness. The numerical results also show that using both linear and quadratic bases as well as spline and Gaussian weight functions in approximation functions can give quite accurate numerical results. Compared with the conventional boundary element method based on the global boundary integral equations, the present method is advantageous in the following aspects: i) No boundary and domain element needed to be constructed in the present method, while it is necessary to discretize both the entire domain and its boundary for the conventional boundary element method in general. The volume and boundary integrals in the present method are evaluated only over small regular sub-domains and along their regular local boundary ■ surrounding the source point. ii) In the present method the unknown displacements and tractions at any point can be easily evaluated from the approximated trial solution only over the nodes within the domain of definition of this point; while this process involves an integration through all of the boundary points at the global boundary in the conventional boundary element method. iii) Non-smooth boundary points(corners) cause no problems in the present method, while special attention is needed in the conventional boundary element method to deal with these corner points. iv) It is not necessary in general to keep the unknown traction on the boundary as an independent variable for the present method, while the unknown traction has to be kept as an independent variable in the conventional BEM. v) The stiffness matrix is banded in the present method instead of being fully populated as in the conventional BEM. Besides, the present formulation possesses flexibility in adapting tile density of the nodal points at any place of the problem domain such that the resolution and fidelity of the solution can be improved easily. This is especially useful in developing intelligent, adaptive algorithms based on error indicators for engineering applications更多还原