Shear and Volumetric Locking Effect on the Performance of Harmonic Solid Ring Finite Elements

Abstract

Harmonic solid ring finite elements are commonly used in the analysis of axisymmetric structures subjected to non-axisymmetric as well as axisymmetric loadings. Depending on the material and/or geometrical properties of axisymmetric problems the finite element analysis may produce erroneous solutions due to approximations assumed in the formulation. Volumetric and shear locking are the some troublesome behaviors of some finite elements. In this study, finite element formulations of 4-noded (Ring4) and 9-noded (Ring9) ring elements are developed considering constant and linear shear locking effect for the element types, respectively, by incorporating selectively reduced integration technique. A computer program is coded in Matlab for the purpose and the performances of both elements are explored in terms of locking issue as well as accuracy. For this purpose several axisymmetric problems are solved such as hollow thick cylinder and circular plate problems. Numerical results indicate that while Ring9 does not suffer from volumetric locking for high values of Poisson's ratios Ring4 suffers. Besides, while Ring4 with full integration displays shear locking effects Ring4 with selectively reduced integration eliminates the locking. The finite element formulations are explained in detail and the results of numerical examples are presented comparatively in graphical and tabular formats.

Efficient Finite Element Models for Calculation of the No-load losses of the Transformer

“…Finite element methods are versatile and most commonly used numerical method among researchers and practitioners to solve complex problems in engineering and science [18]. FEM is a numerical technique which commonly used for the simulation of differential and integral equations.…”