Static Condensation and Substructuring

Abstract

In the previous chapters we established the relationship (through the system stiffness matrix) between forces applied at the nodal coordinates of the structure and the corresponding nodal displacements. There are instances, such as the use of substructuring for the analysis of large structures, in which it might be advantageous to reduce the number of nodal coordinates. Substructuring requires the reduction of nodal coordinates to allow the independent analysis of portions of the structure (substructuring). The process of reducing the number of free displacements or degrees of freedom is known as static condensation. The same process is also applied to dynamic problems although, in that case, it is only approximate and in general may result in large errors. The static condensation method has recently been modified for applications to dynamic problems. This method is known as the dynamic condensation method (Paz, M. 1997); its application to dynamic problems gives solutions that are virtually exact.