Eigenvalue analysis of compatible and incompatible rectangular four‐node quadrilateral elements | Zendy

Hacker W. L. | Zendy; Schreyer H. L. | Zendy

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Eigenvalue analysis of compatible and incompatible rectangular four‐node quadrilateral elements

Author(s) -

Hacker W. L.,

Schreyer H. L.

Publication year - 1989

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.1620280315

Subject(s) - quadrilateral , eigenvalues and eigenvectors , hourglass , direct stiffness method , stiffness matrix , element (criminal law) , stiffness , finite element method , mathematics , mathematical analysis , convergence (economics) , node (physics) , structural engineering , monotonic function , matrix (chemical analysis) , bending stiffness , beam (structure) , geometry , engineering , physics , materials science , quantum mechanics , astronomy , political science , law , economics , composite material , economic growth

Exact analytical expressions for the eigenvalues of the elastic stiffness matrix are obtained for the four‐node, rectangular, quadrilateral element. A procedure is given for identifying alternative hourglass modes and eigenvalues which render the element incompatible but with non‐monotonic convergence assured. A convergence study confirms that for the special case of when the hourglass modes coincide with beam bending the element can serve as a beam element. Analytical expressions are given for the resulting element stiffness matrix.

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