Sharp corner functions for mindlin plates

O. G. McGee, J. W. Kim, A. W. Laissa

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called "corner functions," for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalJournal of Applied Mechanics, Transactions ASME
Volume72
Issue number1
DOIs
StatePublished - Jan 2005

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