利用位移互等定理改进的超静定结构位移计算方法

An improved displacement calculation method of statically indeterminate structures based on displacement reciprocal theorem

结构力学中,超静定结构的位移计算常使用单位荷载法,即利用超静定的实际位移状态与虚拟单位力状态相配的传统方法计算位移。该方法用于计算承受复杂荷载的超静定结构时,计算工作量巨大。利用位移互等定理改进的单位荷载法——位移互等算法,将原结构承受的荷载作用于静定的任一力法基本结构上所得的状态,与作用于原结构的虚拟单位力状态相配计算位移。由于荷载转为作用在静定基本结构上,有效降低了计算工作量。该方法在结构力学教学中有一定的实际应用价值,为师生提供了一种可选的新方法,丰富了结构力学的教学内容。

The unit-load method is often used to calculate the displacement of statically indeterminate structure in structural mechanics to find the actual displacement state and the virtual unit-load state and combine both states to solve displacement.However,the enormous workload will arise when this method is used to solve the statically indeterminate structures bearing complex loads.A new unit-load method,which was improved by the displacement reciprocal theorem,put the loads acted on the original structure to any one of its force-method primary structures,and combined this state with the virtual state whose unit-load acted on the original structure to solve displacement.Since the primary structure was statically determined,the workload would be efficiently decreased.Thus,the improved method is valuable in practical application of structural mechanics teaching and provides a new option for teachers and students as an addition of the course contents.