| The traditional displacement-based beam-column finite element , whose interpolation functions can not effectively represent the interior displacement of element, has essential drawback for variable cross-section beam. One general method to solve this problem is to use more elements but the computational cost will become high rapidly. The force-based beam-column finite element , which uses force interpolation functions that do not depend on cross-section, has many merits. This element can not get the consistent mass matrix directly because no explicit displacement interpolation functions are adopted. The lumped mass matrix is needed for the explicit finite element integration method. The rotational component of the lumped mass matrix is usually neglected, which can cause great error sometimes. So it is necessary to study the methods of formulation of consistent mass matrix and lumped mass matrix for beam-column element. The main contents of this study consist of the following:1. Based on the principle of virtual work, the element stiffness matrix consisdering shear deformation is derived. Several examples are used to validate the accuracy of the stiffness matrix.2. The consistent mass matrix of force-based beam-column finite element consisdering moment of inertia is formulated. The accuracy and efficiency of the mass matrix is verified by examples.3. The optimal rotational component is presented for element lumped mass matrix of Euler beam element corresponding to different boundary conditions. More accurate natural frequency of vibration can be obtained through the presented lumped mass matrix. |
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