A simple method of stiffness matrix formulation based on single element test

Document Type

Article

Publication Date

1-1-1999

Abstract

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

Identifier

0033080027 (Scopus)

Publication Title

Structural Engineering and Mechanics

External Full Text Location

https://doi.org/10.12989/sem.1999.7.2.203

ISSN

12254568

First Page

203

Last Page

216

Issue

2

Volume

7

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