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.