【作者】 霍同如；

【导师】 杜庆华；

【作者基本信息】 清华大学 ， 固体力学， 1989， 博士

【摘要】 论文研究边界元法在结构形状优化中的应用，主要内容包括： 1．统一地建立了弹性力学平面问题、回转体扭转问题和轴对称问题的多子域边界元格式；为准确计算边界点或近边界点的位移和应力，发展了由一组特解确定奇异积分和几乎奇异积分的方法。 2．提出了灵敏度分析的边值问题提法和变分问题提法，由对弹性力学变分等式求物质导数得出了确定灵敏度的变分方程。 3．将结构分析的边界元法中的一些计算格式，如多子域边界元格式，奇异积分和几乎奇异积分的处理，推广到了边界元法的灵敏度分析；论证了灵敏度的边界元计算中，求导和离散的次序可以交换。 4．研制成功了一种边界元网格自适应划分方案。 5．编制了弹性力学平面问题分析和灵敏度分析的边界元法程序；计算了若干不同类型的算例；综合采用了递归二次规划法和边界元法计算了受拉多边形板，悬臂梁、实体重力坝和空腹重力坝的形状优化。 霍同如 (计算固体力学) 指导教师：杜庆华 教授、博士更多还原

【Abstract】 The paper studies the application of boundary element method in shape optimization of elastic problems. The main achievements includes:1. A unified algorithm of multi-domain boundary element equation is built for planar and axisymmetric elasticity. For more accurate determination of the displacements and stresses at the points on the boundary or near the boundary, a method of introducing particular solutions to determine singular oralmost singular integrals has been developed.2. A general statement of boundary value problem and its variational formulation for sensitivity is presented. By taking material derivatives of variational identity of elasticity, the variational identity for sensitivity has been obtained.3. The algorithms developed in structural analysis, such as, multi-domain boundary element method, the determination of singular or almost singular integrals, have been extended to sensitivity analysis. The property that the order of talcing derivatives and making discretization is reversible in sensitivity analysis has been proved.4. A kind of adaptive boundary element mesh generation scheme is developed.5. Computer programs for analysis and sensitivity analysis of planar elasticity by boundary element method are made, and several computational examples have been performed. By combination usage of recursive quadratic programming and boundary element method, the optimal shapes of a polygon plate in tension, a bending cantilever, a gravity dam and a hollow gravity dam under hydrostatic and gravitational loads have been obtained.更多还原