Macrostrip for Variable Section Plates

Abstract

Plate systems often involve variable rigidities because of changes in the cross section or reinforcement. The finite strip method provides an efficient method of analysis for some plate configurations. However, in the conventional finite strip and finite element methods each segment with constant rigidity is discretized as an element, even when the segments are unnecessarily small. This could result in a significant increase in the number of elements. This paper presents a procedure for the derivation of a macrostrip with variable rigidity. The macrostrip can be used for modeling variable section members without increasing the number of elements or degrees of freedom. The formulation is for plate systems with step changes of rigidity and is based on the theory of distributions. Thus, plate systems with step changes of rigidity can be handled directly by this method. Continuous variations can be approximated by a series of step changes. To increase the accuracy, the number of steps can be increased without increasing the number of degrees of freedom. Since the algebra involved in the derivation of the macroelement is rather excessive, a set of subroutines are written for the symbolic package MuMath, to carry out the algebraic manipulations.