杆系结构静/动力学计算的直接方法

针对有限单元法计算精度受网格密度制约的问题,提出一种求任意复杂杆系静、动力学问题精确解的方法.该方法基于节点分析法,逐个节点列位移相容方程和内力平衡方程,以谱系数作为未知数,杆件变形和截面内力则采用相应问题的精确解来描述.用代数符号化的方式,对方程系数矩阵的组建过程进行了详细描述,为通用程序编制提供依据.对建模过程中的分布式载荷和铰接接头的处理方法进行了探讨并给出处理方法.通过平面钢架屈曲分析和空间管路谐响应分析,证实所提方法具有计算精度高、划分单元数少的特点,特别适合于需要精确解的场合.

A Direct Approach to Skeletal Structures Statics and Dynamics

Abstract： The precision of finite element method is restricted by mesh density. To solve this problem, an analytical method for arbitrary complex bar system was proposed based on the nodal method. The nodal compatibility equation of displacement and the equilibrium equation of internal force were considered. The spectral coefficients were treated as the unknowns. The deformation and internal section force were described by the exact solutions of corresponding problems. The process of the construction of the coefficient matrix of the equation of the system was illustrated in an algebraic symbolic way, providing basis for general program development. Two special modelling procedures, distributed load and hinge joint, were investigated and given. A plane steel frame buckling analysis and a space pipe line harmonic analysis were launched. The results confirm that the present method is highly precise and requires a small number of elements. The method is well suited for the requirement of analytical solutions.