Abstract
From the early days of finite element analysis the numerical static condensation method has been applied to elements with internal nodes to reduce their memory requirements and to simplify their assembly. The static condensation method was first used by Wilson (1965) to eliminate the internal degrees of freedom in a quadrilateral finite element constructed from four triangles. This study applies modern symbolic analysis software to static condensation to reveal additional observations about its benefits and efficiency. It is shown that the stiffness matrix and force vector transformation matrices can be written in closed form for a given element type and used for more efficient post-processing. In addition, it is shown that the classic cubic beam and linear bar element matrices are the symbolic static condensation versions of the three node quintic beam and quadratic bar, respectively. That allows the cubic beam element to be easily post-processed to give cubic moment and quadratic moment and shear diagrams, respectively.
Published Version
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