一种基于小变形协调方程的动不定体系精确求解方法

AN EXACT ALGORITHM FOR KINEMATICALLY INDETERMINATE ASSEMBLIES BASED ON COMPATIBILITY EQUATIONS WITH SMALL DEFORMATION ASSUMPTION

对于动不定体系,在荷载作用下往往会经历含有大变位的机构运动,最终到达一个满足受荷不可动判别准则的构型。该文在小变形假设的基础上提出了一种基于体系协调矩阵奇异值分解的动不定体系求解思路,通过在一个计算步内体系的初始构型和临时构型分别建立协调方程,求得相应的预测位移和补偿位移,从而获得每步的真实位移值,实现运动路径的跟踪。经过若干计算步到达受荷不可动的构型后,再进行静力计算,以得到体系的最终平衡状态。算例表明,采用该文的方法,可以在避免迭代的前提下快速、准确地求得体系的最终受力状态。

A kinematically indeterminate assembly will usually undergo mechanism movement involving large displacements under external loads, until reaching a configuration in which it satisfies the criterion for immobility of assemblies. This paper presents an algorithm for the computation of kinematically indeterminate assemblies based on compatibility matrices' singular value decomposition(SVD) with small deformation assumption. In each step, two compatibility equations are established for the initial and temporary configurations, from which the predictor displacements and compensator displacements are respectively obtained. The real mechanism displacements are derived by superposition of the two sets of displacements and the kinematic path is thus tracked.When the assembly arrives at the immovable configuration, the static computation can then be carried out and the final equilibrium state will be gained. Two examples are illustrated, by which the algorithm is proved to be an efficient and accurate way to determine the final state of an assembly without iteration.