任意桥梁截面自由扭转常数计算的快速方法

Fast Method of Free Torsion Constant for Arbitrary Bridge Corss Section

计算任意截面的自由扭转常数可采用有限元分析方法,位移法有限元计算出的自由扭转常数比理论值偏大且网格剖分尺寸大小明显影响计算速度。本文从弹性理论圣维南自由扭转问题基本假设出发,针对悬臂梁模型采用基于位移的最小势能原理和基于应力的最小余能原理两种方法,推导势能泛函和余能泛函表达式,并求得泛函的极小值从而推导出相应的有限元方程,得到两种计算自由扭转常数公式。根据推导出的有限元方程,采用三角形单元编写程序进行两种截面的计算并与理论值对比。对比结果表明,采用两种方法计算自由扭转常数并取其平均值作为最终结果相较于采用单一位移法计算其精度大幅提高,两种方法互相参考有利于解决计算结果偏大和计算量过大的问题。

Finite element analysis method can be used to calculate the free torsion constant of the arbitrary section,while it has two problems,first,the calculated value of the free torsion constant based on finite displacement method is bigger than of the theoretical value,second,the size of mesh generation has a big effect on the calculation speed.The article is based on the fundamental assumption of theory of elasticity for the Saint-Venant arbitrary torsion problems,adopting the principles of displacement-based minimum potential energy and capability-based minimum excess energy for the cantilever beams models,deriving the expression of potential energy and complementary energy.At last,it can get the minimum value of expression,thus derive the relative finite element equation and two calculating free torsion constant formulas.Based on the finite element equation,adopting the triangular unit programming and calculating on the two sections,comparing with the theoretical value.It can be found from the comparison result that the precision can be mostly improved by using two methods to calculate the free torsion constant and adopt the mean value as the final result instead of single free torsion constant.Referencing the two methods help to solve the problems of relatively bigger value of calculating results and quantities.