用边界元反分析构造平面残余应力场  

AN INVERSE APPROACH FOR CONSTRUCTING PLANAR RESIDUAL STRESSES USING BEM

作　　者：钱秀清[1] 姚振汉[1] 曹艳平[2] 

机构地区：[1]清华大学工程力学系,北京100084 [2]特鲁瓦技术大学机械与系统工程系

出　　处：《工程力学》2006年第9期6-11,共6页Engineering Mechanics

基　　金：国家自然科学基金(10472051)

摘　　要：基于固有应变概念,采用边界元方法,提出一种反方法构造连续的满足域内自平衡条件的平面残余应力场。考虑到反分析的稳定性,固有应变场用一系列光滑基函数(如多项式和三角函数)近似;为了识别由剪切固有应变引起的残余应力,求出对应于固有应变的位移特解与面力特解,将域内积分用双重互易边界元法转换为边界积分,保持了边界元法的优势;同时导出了灵敏度矩阵的显式表达,以提高反分析的效率。最后给出了两个算例验证方法的可行性。An inverse approach based on the inherent strain method using BEM is proposed for constructing the planar residual stresses existing in structures that are in self-equilibrium. Considering the stability of the inverse approach, the inherent strain field is approximately expressed as a series of smooth basis functions, such as polynomials and trigonometric functions. In order to identify the residual stress induced by shear inherent strain, the specific solution expressions of displacement and traction corresponding to inherent strain are given, and the domain integral is transformed into boundary integral using the dual reciprocity boundary element method so that the advantage of the BE approach is preserved. The explicit expression of the sensitivity matrix is derived to enhance the efficiency of the inverse approach. Two numerical examples are given to show the applicability of the presented scheme.

关 键 词：平面残余应力 固有应变 反问题 双重互易边界元法 稳定性 

分 类 号：O344.5[理学—固体力学]