Usage of the symbolic method and exact solutions of harmonic functions in the problem on pressing of the flat stamp in the rectangular plate

TL;DR

This paper presents an exact analytical solution for a plane elasticity problem involving pressing a flat stamp into a rectangular plate, utilizing symbolic methods and harmonic functions to achieve precise results.

Contribution

It introduces a novel approach combining symbolic methods with harmonic function solutions to solve a specific elasticity problem exactly.

Findings

Exact solution derived for the pressing problem in rectangular plates.

Method demonstrates the effectiveness of symbolic functions in elasticity problems.

Provides a framework for solving similar plane deformation problems.

Abstract

In this paper we construct a solution of the two-dimensional problem of the elasticity theory (plane deformation) on pressing of the flat stamp in the rectangular plate by using the symbolic method and the exact solution of the harmonic equation for a rectangle. The substitution of symbolic functions that satisfy the harmonic equation, with relevant solutions of harmonic functions allows obtaining the exact solution of the problem.