EXPANSIONS IN PAPKOVICH—FADLE FUNCTIONS IN THE PROBLEM FOR A HALF-STRIP WITH A CLAMPED END

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Abstract

In this paper, we construct an exact solution to the well-known boundary value problem of the theory of elasticity on the tension of a free half-strip with a rigidly clamped end. The solution is represented by series in Papkovich—Fadle eigenfunctions, the coefficients of which are determined in an explicit form. The solution is based on the Papkovich orthogonality relation and Lagrange expansions. The behavior of stresses near the corner points of the half-strip is investigated. A comparison of the exact solution and numerical one obtained on the basis of the finite element method is given.

About the authors

M. D. Kovalenko

Institute of Applied Mechanics, Russian Academy of Sciences

Email: kov08@inbox.ru
Moscow, Russia

A. P. Kerzhaev

Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences

Moscow, Russia

I. V. Menshova

Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences; Bauman Moscow State Technical University

Moscow, Russia

D. A. Vlasov

Moscow State University of Civil Engineering

Moscow, Russia

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