超静定结构装配应力的一种新解法

A New Method for Assembly Stresses of Statically Indeterminate Structure

以包含误差杆件结构为研究对象,提出了一种新解法研究其装配应力。不同于传统的力法、位移法等方法,利用拉格朗日乘数法建立了广义变分原理以求解含有误差杆件结构装配应力。利用拉格朗日函数,构造无条件广义变分原理的新泛函,求解新泛函的极值问题,从而计算有误差杆件结构的装配应力,给出了杆系内力的通解。计算结果表明该方法的正确性和通用性,该方法为求解有误差杆系的超静定问题提供了一种新思路。

Taking pole structures including manufacturing errors as the research object,a new method for assembly stresses of the structures is proposed.Different from the traditional force method or displacement method,the assembly stresses of pole structures including manufacturing errors are presented by generalized variational principles.Using the Lagrange multiplier function,a new function from unconditional generalized variational principles is investigated.The assembly stresses of pole structures including manufacturing errors can be obtained by solving the extremum problem of the new function.A general solution of internal forces of structures is given.The calculation results demonstrate the accuracy and versatility of the proposed method.This method provides a novel way for the research of statically indeterminate structures including manufacturing errors.