结构安定分析的Galerkin边界元方法

SHAKEDOWN ANALYSIS OF STRUCTURES BY SYMMETRIC GALERKIN BOUNDARY ELEMENT METHOD

基于Melan静力安定定理,利用Galerkin边界元方法建立了多组交变载荷作用下结构安定分析的下限计算格式.在给定载荷域的载荷角点所对应载荷作用下,采用Galerkin边界元法计算相应的虚拟弹性应力场,并且利用结构在Galerkin边界元弹塑性增量计算中同一增量步中不同迭代步之间的应力差作为自平衡应力场的基矢量,通过这些基矢量的线性组合构造了自平衡应力场,大大降低了所形成的数学规划问题的未知变量数.并通过复合形法对非线性规划问题直接进行求解,得到了结构在交变载荷作用下的下限安定乘子.计算结果表明,所采用的方法具有较高的精度和计算效率.

The computational formulation of lower bound shakedown analysis of structures under the action of a group of variable loads is established by using symmetric Galerkin boundary element method (SGBEM) in this paper. Because of the adoption of analytical integral scheme and symmetric coefficient matrix, the SGBEM has higher computational precision and efficiency. Especially the stresses directly obtained by the integral formulation of internal points have higher precision than those calculated through displacement finite element method. The self-equilibrium stress field is constructed by linear combination of several basic vectors, which are the stress differences between different iteration steps at the same incremental step using the traditional elasto-plastic incremental method. Because of the adoption of reduced basis technique, the dimensions of the resulting mathematic programming decreased considerably. The lower bound shakedown load mul-tipler of structure is obtained by using the Complex method to solve the nonlinear programming directly. The Complex method represents a cost-effective, numerically stable and reliable tool for the mathematical programming problem of shakedown analysis. The whole procedure turns out to be significantly cost-effective with respect to other approaches, particularly with respect to evolutive step-by-step analysis by commercial finite element codes. The numerical results of the solution procedure adopted herein appear to be satisfactory and rather insensitive to the choice of the initial complex configurations and load increments used to create basic self-equilibrium stress vectors. The computational examples illustrate the validation of the present method.