Automatic Generation of Finite Element Matrices

Some of the basic ideas involved in the development of an automatic generator for finite element stiffness and mass matrices are analyzed. Two different programs are presented, one for rectangular elements, the other for isoparametric elements. In both cases polynomial expansions are assumed. In the first case the element matrices can be obtained as a linear combination of dimensionless intrinsic matrices multiplied by factors representing the element dimensions. In this form the derivation has to be done only once for a type of element. In the second case it is easier to compute the element matrices for the specified dimensions. This represents savings in computer memory but requires a new derivation for each element with different dimensions.