Research Article
Feb 1972
Finite Element Method for Elastic Plastic Plates
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VIEW THE REPLYAuthors: Ted Belytschko and Milan VelebitAuthor Affiliations
Publication: Journal of the Engineering Mechanics Division
Volume 98, Issue 1
Abstract
A finite element method is developed for the analysis of elastic, perfectly plastic sandwich plates. The method is formulated by means of Greenberg's complementary energy rate theorem using constant moment elements. This formulation results in a quadratic programming problem. If it is assumed that no internal unloading takes place, formulation as a linear algebraic system of equations is possible; criteria are presented for checking this assumption. The method has several advantages over stiffness formulations: (1) Elastic-plastic boundary can occur only along element boundaries, and (2) calculation of governing equations requires no integration over elements as moments are constant. Results are presented for clamped and simply supported square plates and agreement with other available results is good. The method may be useful in error analysis for elastic plastic problems when combined with stiffness techniques as it provides complementary bounds on the same functional.
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Published In
Journal of the Engineering Mechanics Division
Volume 98 • Issue 1 • February 1972
Pages: 227 - 242
Copyright
© 1972 American Society of Civil Engineers.
History
Published in print: Feb 1972
Published online: Feb 3, 2021
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Authors
Affiliations
Ted Belytschko
Asst. Prof. of Structural Mech., Univ. of Illinois at Chicago Circle, Chicago, Ill
Milan Velebit
Structural Designer, Illinois Central Railroad, Chicago, Ill., and Grad. Student, Univ. of Illinois at Chicago Circle, Chicago, Ill
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