动力分析的块体单元法(英文)

介绍了阶谱块体单元法的基本理论和应用,提出了动力分析的块体单元法表述公式。首先,简要回顾了块体单元法的发展历程,阐释了"覆盖"的新概念,介绍了块体单元法的静力平衡方程组,应用p型有限元法的形函数,将块体的位移场表达成为所谓的广义自由度的函数.然后,给出了广义质量矩阵、广义刚度矩阵和广义阻尼矩阵的具体表达式,通过它们将分布于块体内部的与时间有关的广义弹簧力、广义惯性力和广义阻尼力分别转移到覆盖单元的结点上.随后,基于虚功原理、变形协调条件和本构关系,推导了块体动力系统的控制方程组.最后,研究了一个简单算例,将计算结果和解析解进行了对比,对比结果说明了所提出方法的正确性和有效性.

A dynamic formulation of block element method

The theories and applications of the hierarchical block element method are briefly introduced and a new formulation of the dynamic analysis is developed. Firstly, an overview of the development of the block element method is given. Secondly, the new concept of the covering element is explained and the static equilibrium equations are introduced. Using the shape functions of p-version finite element method, the displacement field of blocks are expressed as the functions of so called general degree of freedoms. Then the general stiffness matrix, mass matrix and damping matrix are listed in details, by which the general time-dependent inertia forces, damping forces and elastic forces distributing over the blocks are respectively transferred to the covering element nodes from in the blocks. And then the governing equations of the block dynamic system are deduced on the basis of the virtual work principle, the deformation compatibility condition and the constitutive relations. At last a numerical example is studied and the comparison between the calculated and analytical displacement response indicates the validity of the proposed method.