Reduction of plane thermoelasticity problem in inhomogeneous strip to integral volterra type equation

Abstract

We have developed a method for analytical solving of the plane thermoelasticity problem in terms of stresses for a strip, which is infinite with respect to width. To derive the governing equations, we have used a method of direct integration of differential equilibrium and compatibility equations. Reducing the governing equations to the integral Volterra type equation of the second kind, we have solved it in Fourier transforms by applying a method of simple iteration.

Straipsnyje vystomas analizinio sprendinio metodas nehomogeninio strypo termoelastiškumo uždaviniui strypo itempimams rasti, kai strypo ilgis yra begalinis pločio atžvilgiu. Pagrindines lygtys išvedamos naudojant diferencialines pusiausvyros ir suderinamumo lygtis ir tiesiogini integravima. Suvedus pagrindines lygtis i antrojo tipo Volterra integraline lygti, naudojant Furje transformacija, ji sprendžiama paprastosios iteracijos metodu.

Key words:

• inhomogeneous strip
• plane thermoelasticity problem