单元解体法精确求解梁元无应力构形

Accurate Solution for Unstressed Configuration of Beam by Element Disintegration Theory

基于非线性二阶梁柱理论及CR-UL全量求解方法,利用单元解体理论(几何法及零作用法)精确求解平面结构中梁元的完整无应力构形.利用目标构形几何信息及其对应的单元抗力直接求解梁元无应力构形基本参数;采用几何法直接进行坐标转换即得构件单元完整无应力构形;采用零作用法并利用无应力构形基本参数进行逆向计算亦可求解其完整无应力构形;编写程序对提出的两种方法进行了算法及最终结果的验证.结果表明利用几何法可在不建立结构有限元模型的条件下精确高效求解构件的完整无应力构形,利用零作用法亦可精确求解构件完整无应力构形,但需编写完善的几何非线性程序.

In order to solve the unstressed configuration of beams, the accurate computation element disintegration theory, named as geometric method and zero-loads method, was created based on the theory of nonlinear second order beam-column theory and CR-UL total deformation theory. The basic parameters of unstressed configuration of beam were firstly solved by using the geometric information and corresponding element resistance of the objective configuration. The full unstressed configuration of component element was also confirmed by using the geometric method as coordinate transformation. The zero-loads method as converse calculation based on these basic parameters was then proved to be effective. Moreover, a program was compiled to verify the above two methods. The results show that the geometric method for full unstressed configuration of beam elements in this paper could be executed efficiently without the finite element model of full structures, and the zero-loads method could be executed efficiently under the condition of impeccable geometric nonlinear program.