基于平面壳单元的分阶段成形结构平衡方程

为探讨基于平面壳元的分阶段成形结构终状态的影响因素,建立了包含平面壳元无应力状态量的结构平衡方程.以等参平面壳单元为研究对象,建立了单元内任意一点的无应力状态量与单元高斯积分点处无应力状态量的关系;以单元的无应力状态作为零点计算结构的总势能,并根据最小势能原理,导出了包含平面壳元无应力状态量的结构平衡方程,获得了结构终状态与平面壳元无应力状态量的关系.分析结果表明,当结构体系、外荷载和边界条件一定时,如能保证壳元的无应力状态量一定,则结构的终状态是一定的,与分阶段成形过程无关. 

Equilibrium Equation Derivation of Structures Formed by Stages Based on Plane Shell Element

In order to research the influence factor of the final state of structures formed by stages based on plane shell element, the structural equilibrium equation including the unstressed state amounts was established. The relationship between unstressed state amounts at any point within the isoparametric plane shell element and at Gaussian integral points was founded. The total potential energy of structure was calculated from the zero state when the isoparametric plane shell element is unstressed. From the principle of minimum potential energy, the structural equilibrium equation including unstressed state amounts was derived to make clear the relationship between the final state and unstressed state amounts of plane shell element. The analysis results show that when a structure system, external loads and boundary conditions are given, the final state of a structure formed by stages is definite if the unstressed state amounts of plane shell element are certain.