Improved modeling capabilites with reduced-order integration

Abstract

Many rectangular isoparametric finite elements contain a modeling error known as parasitic shear. Parasitic shear can be removed by applying the correct reduced-order Gauss quardrature integration rule. When the 1×1 rule is blindly applied another error, spurious zero energy modes, can be introduced. An analysis procedure is presented that identifies the correct Gauss integration rule for eliminating parasitic shear without introducing spurious zero energy modes. Displacement polynomials expressed in transparent notation assists in the identification of error sources. The procedure is developed with the four-node membrane element and then applied to analyze and correct four- and nine-node Mindlin plate bending elements. Eigenvalue analyses and sample problems are presented to demonstrate the improvements produced by the procedure.

Keywords: Displacement, Eigenvalues, Errors, Finite Elements, Gaussian Process, Models