Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions

[+] Author and Article Information
A. I. Soler

The Towne School of Civil and Mechanical Engineering, University of Pennsylvania, Philadelphia, Pa.

J. Appl. Mech 36(4), 757-762 (Dec 01, 1969) (6 pages) doi:10.1115/1.3564767 History: Received January 17, 1969; Revised March 10, 1969; Online September 14, 2011


Governing equations of plane elasticity are examined to define suitable approximate theories. Each dependent variable in the problem is considered as a series expansion in Legendre polynomials; attention is focused on establishment of a logical approach to truncation of the series. Important variables for approximate theories of any order are established from energy considerations, and the desired approximate theories are established by direct reduction of the field equations and also from an energy viewpoint. A new “classical” beam theory is developed capable of treating displacement boundary conditions on lateral surfaces. Higher-order approximate theories are studied to make certain comparisons with exact solutions; the results of these comparisons indicate that the new method yields approximate theories which may be more accurate than previous theories with similar levels of approximation.

Copyright © 1969 by ASME
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