Super-convergent mass matrix using an inverse approach for beam element with only displacement DOF

In this paper, a super-convergent mass matrix is developed by using inverse method for a family of beam elements which have displacement as nodal degrees of freedom with no slope. This element has six degrees of freedom which four of them are in axial direction on corner nodes and two of them are in lateral direction on two ends of the element. In this aspect, these beam elements are similar to plane stress elements and can beapplied for any cracked structures and composite beams. An inverse approach can be used to develop the element formulation by minimizing the element discritization error. This leads to the definition of the element formulation with no need to specify any shape functions. The objective in this paper is to set up an admissible parametric mass matrix for a new beam element. The unknown parameters will be defined by minimizing the discritization error in the finite element formulation. As a result, convergence rate of eigenvalue solution for new mass matrix is from 6th order while for consistent and lumped mass matrices, it is from 4th and 1th order.

Keywords:

inverse method , 6 DOF beam , mass matrix , discritization error