Efficient dynamic finite element method for 3D objects with uniform cross-section

An efficient implicit dynamic finite element method (FEM) for elastic 3D objects with uniform crosssections was developed. In this method, the finite element mesh is generated in such a way that the object to be analysed is at first sliced into layers with the same thickness along its generatrix and then each layer is discretized into finite elements of the same pattern. This way of discretization makes the mass, viscosity, and stiffness matrices into the repetitive block tridiagonal matrices. The repetitive block tridiagonal matrix has the characteristic, that the sequence of matrices which appears in the Gaussian elimination for the repetitive block tridiagonal matrix is a rapid convergent sequence. The process of the Gaussian elimination can be terminated when the sequence converges. The rest of the sequence is not necessary to be stored. The present method can save the computational time and memory by utilising this characteristic of the repetitive block tridiagonal matrix. A few examples of analyses including whole Hopkinson-bar analysis were performed to demonstrate the effectiveness of the present method. The present method is applicable not only to the elasto-dynamics but also to many other problems, such as thermal problems, electrical problems, and plastic problems without geometric non-linearity