力学教学中应用功的互等定理分析超静定结构约束力

Analysis of Constrained Force on Statically Indeterminate Structure Based on Reciprocal Theorem of Work in Mechanics Teaching

求解超静定结构约束反力是力学知识中的重要内容,当前常用的方法有力法、位移法等,这些方法都是基于变形或力的平衡条件来建立额外的补充方程。本研究提出了一种新的超静定结构约束反力分析思路,基于功的互等定理建立虚功方程,达到求解未知约束反力的目的,结果表明提出的新方法可以应用于超静定结构支座反力的求解。最后,将本文提出的新方法与力法计算过程进行了对比,研究了其计算过程的异同。

Solving the constraining force of statically indeterminate structure is an important content in mechanics.At present,the commonly used methods,such as force method,displacement method and so on,are based on the equilibrium conditions of deformation or force to establish additional supplementary equations.Based on the reciprocal theorem of work,the virtual work equation is established to solve the unknown constraint reaction force of statically indeterminate structure.The calculation results show that the new method can be applied to solve the reaction force of statically indeterminate structures.Finally,the new method is proposed in this paper and the force method are compared to study the similarities and differences of the calculation process.