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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.
Aiming at the problem that the calculation accuracy of finite element method is restricted by the grid density, a method to find the exact solution to the static and dynamic problems of arbitrary complex bar system is proposed. The method is based on the node analysis method, the node-by-node displacement compatibility equation and the internal force balance equation , The spectral coefficient as unknown, the deformation of the rod and the internal force of the cross section are described by the exact solutions of the corresponding problems.Considering the algebraic signification, the process of constructing the coefficient matrix of the equation is described in detail, which provides the basis for the general programming. The distributed loads in the process of modeling and the processing methods of the joint are discussed and the treatment methods are given.The buckling analysis of plane steel frame and the harmonic response analysis of space pipelines demonstrate that the proposed method has the advantages of high calculation precision and small number of units The characteristics, especially for the need for precise solution of the occasion.