基于正交基无单元Galerkin法和非线性规划的安定分析方法

Shakedown analysis by using the element free Galerkin method with orthogonal basis and nonlinear programming

基于安定分析的下限定理,用正交基无单元Galerkin法建立了交变载荷作用下理想弹塑性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的载荷作用下,采用正交基无单元Galerkin法计算相应的虚拟弹性应力场,并且利用结构在正交基无单元Galerkin法弹塑性增量分析中平衡迭代结果计算得到自平衡应力场基矢量,然后由这些基矢量的线性组合模拟自平衡应力场。安定分析问题最终被归结为一系列未知变量较少的非线性数学规划子问题,通过复合形法求解。算例表明该方法的计算结果是令人满意的,并且对初始复合形顶点和用于构造自平衡应力场基矢量的载荷增量是非常不敏感的。

The computational formulation of lower bound shakedown analysis of structures under the action of variable loads is established by using the element free Galerkin （EFG） method with orthogonal basis. The considered structure is made up of elasto-perfectly plastic material. The stress field associated with the corners of the method with orthogonal basis. The self-equili given brium load domain can be computed by stress field is expressed by linear fictitious elastic using the EFG combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are determined by equilibrium iteration procedure during elasto-plastic incremental analysis. Through modifying the self-equilibrium stress subspace continuously, the lower bound shakedown analysis problem is finally reduced to a series of sub-problems of nonlinear programming with relatively few optimization variables. The Complex method is used to solve these nonlinear programming sub-problems. 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 self-equilibrium stress basis vectors.