On the detection, visualization and characterization of spurious kinematic modes in arbitrary plane structures

Abstract

A direct and computationally efficient numerical method for the detection, visualization and characterization of spurious kinematic modes in arbitrary plane structures is presented. The proposed method is based on a pure kinematic approach. Compared to alternative approaches, like the displacement method, where kinematic modes can be indirectly detected by solving the eigenvalue problem for the related stiffness matrix, the proposed method is direct and computationally less expensive. In contrast to existing kinematic approaches, which are restricted to pin-jointed trusses, the members of the structures here can be both arbitrarily shaped (e.g. line, triangle, rectangle etc.) and arbitrarily connected with each other (e.g. pin-jointed, rigid, shear force and bending connections etc.). Also arbitrary supports can be considered. The method is able to detect and visualize all existing spurious kinematic modes of a structure. Additionally, analytical formulas have been derived which allow an explicit calculation of the position of both all instant centers of rotation and all relative centers of rotation of a structure exhibiting one or more kinematic modes. In order to keep the total number of degrees of freedom as small as possible, only translational and no rotational dofs have been introduced. The proposed method can simply be added as an extra module to existing structural analysis software.