曲杆梁格内力影响面的机动分析有限元法

Finite Element Method for Kinematical Analysis of the Internal Force Influence Surface of Curved-Bar Grillage

以米勒-布雷斯劳原理为基础,运用小变形的叠加原理,将曲杆梁格机动分析与有限元静力分析相结合,建立了曲杆梁格内力影响面分析的机动分析有限元法,该方法把内力影响面分析归结为求解在一个等效结点荷载作用下的梁格位移场,并推导了计入横向剪切变形影响的十二自由度空间曲梁单元等效结点荷载计算公式.该方法概念简洁清晰,与静力法及直接求解位移的机动法相比,计算效率大为提高.算例表明了本文理论和所推导公式的正确性.

Based on the Muller-Breslau principle, a finite element method to kinematically analyze the internal force influence surface is established by combining a kinematical method with the finite element static method and using the superposition principle applied to little displacement for curved-bar grillage. With this method, the analysis of internal force influence surface comes down to a matter of solving a displacement field under equivalent nodal loads. Formulas of equivalent nodal loads for the curved-beam element, involving twelve degrees of freedom and taking the effect of transverse shearing deformation into account, have been deduced. Compared with the static method and kinematical method for computing displacement, the method presented here brings high efficiency. And the conception is concise and clear. Examples are also given to demonstrate the correctness of the theory and formulas.