Techno Press
Techno Press

Structural Engineering and Mechanics   Volume 7, Number 2, February 1999, pages 203-216
DOI: http://dx.doi.org/10.12989/sem.1999.7.2.203
 
A simple method of stiffness matrix formulation based on single element test
Mau ST

 
Abstract     [Full Text]
    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.
 
Key Words
    patch test, convergence, element formulation, asymmetric stiffness matrix, higher order performance
 
Address
Mau ST, New Jersey Inst Technol, Newark Coll Engn, Newark, NJ 07102 USA
New Jersey Inst Technol, Newark Coll Engn, Newark, NJ 07102 USA
Univ Houston, Houston, TX 77204 USA
 

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