涂层结构中温度场的边界元解

涂层结构由于其优良的物理化学性能而备受人们关注，但受其厚度尺寸的影响，涂层材料中物理量的数值计算一直是工程中的难点。边界元法分析涂层结构时，难点在于涂层子域的数值分析，边界量计算既涉及奇异积分又涉及几乎奇异积分。本文基于间接规则化边界积分方程，准确高效地计算奇异边界积分。针对计算边界量及内点物理量时涉及的几乎奇异积分，采用一类非线性变量替换法，有效地改善了被积函数的震荡特性，从而消除了积分核的几乎奇异性。通过采用二次单元逼近几何边界，使得高效准确地计算超薄的涂层结构成为可能。

A NEW MULTISCALE COMPUTATIONAL METHOD FOR MECHANICAL ANALYSIS OF PERIODIC TRUSS MATERIALS

A new multiscale computational method is developed to study the mechanical properties of periodic lattice truss materials. The underlying idea is to construct numerically the multiscale base functions to reflect the heterogeneities of the unit cells and obtain the equivalent stiffness matrix of the unit cells of periodic truss materials. Then the problems only need to be solved on the large–scale meshes and the computational cost can be dramatically reduced. To consider the coupled effect among different directions in the multi-dimensional problems, the coupled additional terms of base functions for the interpolation of the vector fields are introduced. Numerical experiments show that the base functions constructed by the linear boundary conditions sometimes will have a strong boundary effect. While the oscillatory boundary conditions obtained by the oversampling technique and the periodic boundary conditions can greatly reduce the errors induced by the forcible deformations of the unit cells. Especially for the unit cells whose coarse-mesh scales are close to the small scales of heterogeneities, the periodic boundary conditions proposed can improve greatly the accuracy of the results. The advantage of the method developed is that the downscaling computation could be realized easily and the stress and strain in the unit cell can be obtained simultaneously in the multiscale computation. Thus the multiscale method studied here has good potential in the strength analysis of heterogeneous materials.