Explicit stiffness matrices for triangular, plate bending finite elements

Harrison, Robert Leeds

Explicit stiffness matrices for triangular, plate bending finite elements

Doctoral Thesis

1973

Publisher

University of Cape Town

Department

Department of Civil Engineering

Faculty

Faculty of Engineering and the Built Environment

Abstract

Explicit stiffness matrices are available for rectangular plate bending elements, rectangular plane stress and plane strain elements and triangular plane stress and plane strain elements. Triangular plate bending elements can at present only be formed by using a numeric algorithm. The explicit version of a stiffness matrix is not only far more simple to program in a computer routine but its execution (as will be shown) requires approximately one twelfth of the time of a numeric version. Rectangular plate bending elements do not have a compliant shape (see definition) so their use is limited to plates which in many cases can be solved by other methods. Judging from the number of attempts to find a successful triangular plate bending element, the simplicity of a triangular shape appeals to most investigators. In the present investigation only triangular elements with a node on each corner and three degrees of freedom at each node will be considered. Some investigators have included extra nodes on the edges and/or at the centroid of the triangle. This is done in order to overcome difficulties experienced in choosing a suitable displacement function for a nine degree of freedom triangle. Except for comparison of results (table 4) such elements will not be considered. An explicit stiffness matrix for a small deflection theory, elastic, isotropic, triangular plate bending element will be developed.

Keywords

Civil Engineering

Reference:

Collections

PhD / Doctoral

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