用最小势能原理求解半空间弹性地基及地基梁问题

The solution for the system of half-space elastic foundation and elastic foundation beam with the principle of minimum potential energy

将地基梁和地基之间的接触分布力视为地基的外力,并将接触分布力进行离散化,依次加载到地基上,利用弹性力学中的叠加原理,推导出了地基中储存的弹性势能公式,建立了地基和地基梁体系的势能表达式,并利用势能最小原理求解出了地基的位移.所建立的势能公式可作为研究建筑结构与地基共同作用原理的理论基础.

The contact stress between foundation and foundation beam was regarded as external force to foundation in this paper.The contact stress is discrete,and exerting on elastic foundation sequentially.The potential energy function of foundation was derived by using superposition theorem.The potential energy functions were given for the whole system of foundation and foundation beam.The displacement and stress state can be calculated with the principle of minimum potential energy.The potential energy function formulas presented in this paper can be used as the theory foundation to study the interaction principle of structure and foundation.