Inhomogeneous problem for a strip with different boundary conditions

A. P. Kerzhaev^a, I. V. Menshova^ab, A. V. Nikitin<sup>c

a</sup> Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS
^b Bauman Moscow State Technical University
^c Russian University of Cooperation

Abstract: In this paper, an exact solution to an inhomogeneous problem of elasticity theory is constructed for an infinite strip, the lower side of which is rigidly clamped, while the upper side is free. An external load acts along the vertical axis of the strip. The solution method is based on the use of the Papkovich orthogonality relation. The solution is represented in the form of series in Papkovich–Fadle eigenfunctions, the coefficients of which are determined explicitly. Examples of solving the problem are given.

Keywords: inhomogeneous problem, strip, Papkovich–Fadle eigenfunctions, Papkovich orthogonality relation, exact solutions.

Received: 20.09.2023
Revised: 26.12.2023
Accepted: 10.11.2023

DOI: 10.37972/chgpu.2023.56.2.007