一种抛物线浅拱线性单元

为研究抛物线浅拱在复杂受力状态下的线性内力及位移,考虑拱的压弯耦合作用,基于力法和浅拱假定,对抛物线拱平衡方程、几何方程和物理方程进行了分析;求得了抛物线拱内力方程通解格式,构建了抛物线浅拱位移形函数。利用最小势能原理,构造了抛物线浅拱单元。算例表明,本文构造的抛物线浅拱单元计算的抛物线拱内力与理论解计算结果符合较好,在划分一个单元时最大相对误差仅为4.03%,可用于抛物线拱分析。

A linear element for parabolic shallow arch

To study the linear internal force and displacement of parabolica shallow arch under complex stress state the equilibrium equations,geometric equations and physical equations were analyzed,based on the assumption of flat arch,by considering the arch bending coupling.The general solution scheme of the parabolic arch internal force equation was obtained and the displacement function of a parabolic shallow arch was constructed.Based on the principle of minimum potential energy,a parabolic shallow arch unit was modelled.The numerical example shows that the calculation precision of the internal force of the parabolic shallow arch unit constructed in this paper is good,and the maximum relative error of one arch unit is only 4.03%,which can be used in the analysis of a parabolic arch.