Reduction and Recovering Method for MDOF Plane Stress Problems to an SDOF System

Abstract

The work in this paper proposes a new method for reducing MDOF (Multi Degree of Freedom) system of plane stress elements in FEM into its equivalent SDOF (Single Degree of Freedom) system and recovering back the results of dynamic analysis from the equivalent SDOF to its MDOF system. The aim of the current works is to reduce the computation time required for dynamic analysis; while the dynamic characteristic of plane stress structure can be evaluated easily by its equivalent SDOF model within negligible error. In present Strain Reduction Method, displacements of all nodal points in the plane stress structure except an arbitrary representative node are transformed into lower order and magnitude of their corresponding element strain fields. Hence, the equilibrium dynamic equation consists of only strain fields instead of displacement fields, except for the arbitrary representative node. Therefore, during the dynamic equations condensation process, higher derivatives of the strain fields which were initially transformed from nodal displacements can be neglected, leaving the representative node as an SDOF system. Finally, several examples are shown to verify the soundness of the present proposed method in reducing MDOF system of plane stress FEM model into the equivalent SDOF system and recovering back the results within tolerable errors.