极限下限分析的正交基无单元Galerkin法  

LOWER BOUND LIMIT ANALYSIS BY USING THE ELEMENT-FREE GALERKIN METHOD WITH ORTHOGONAL BASIS

作　　者：陈莘莘[1] 刘应华[1] 岑章志[1] 

机构地区：[1]清华大学工程力学系,北京100084

出　　处：《力学学报》2007年第5期633-640,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(19902007);全国优秀博士论文专项基金(200025)资助项目.

摘　　要：基于极限分析的下限定理,建立了用正交基无单元Galerkin法进行理想弹塑性结构极限分析的整套求解算法.下限分析所需的虚拟弹性应力场可由正交基无单元Galerkin法直接得到,所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟.这些自平衡应力场基矢量可由弹塑性增量分析中的平衡迭代得到.通过对自平衡应力场子空间的不断修正,整个问题的求解将化为一系列非线性数学规划子问题,并通过复合形法进行求解.算例表明该方法有效地克服了维数障碍问题,使计算效率得到了充分的提高,是切实可行的.　The limit analysis of structures is a very useful in plasticity,which can determine the load-carrying capacity of structures and provide a theoretical foundation necessary for engineering design.The elasto-plastic incremental analysis is more general and yields more information often at higher computational effort.But, in many practical engineering problems,only limit loads and collapse modes are important,and the stress and strain field histories are not required.In order to avoid the complicated computations of elasto-plastic incremental analysis,the limit analysis is an appealing direct method for determining the load-carrying capacity. Based on the lower bound theorem of limit analysis,a solution procedure for limit analysis of structures made of elasto-perfectly plastic material is presented firstly making use of element free Galerkin（EFG）method with orthogonal basis.The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration.In addition,the orthogonal basis functions are constructed in the moving least squares（MLS）approximation so that the matrix inversion at each quadrature point is avoided.The elastic stress field for lower bound limit analysis can be computed directly by using the EFG method with orthogonal basis.The self-equilibrium stress field is expressed by linear combination of several self-equilibrium stress basis vectors with parameters to be determined.These self-equilibrium stress basis vectors are determined by an equilibrium iteration procedure during the elasto-plastic incremental analysis. Through modifying the self-equilibrium stress subspace continuously,the whole solution process of the problem is reduced to several sub-problems of nonlinear programming.The complex method is used to solve these nonlinear programming sub-problems and determine the maximal load amplifier.Numerical examples show that the present method overcomes the dimension obstacle and improves the computational effi

关 键 词：无单元Galerkin法 正交基 极限分析 非线性规划 复合形法 

分 类 号：TB125[理学—工程力学]