Implementation of an integro-differential model of a singularly loaded rod by the finite element method

Abstract

This article analyzes an integro-differential equation that models small deformations of an elastically supported console, as well as considers possible use of the finite element method for integro-differential models of a singularly loaded rod. For the proposed model, there is an algorithm for the approximate solution of the equation developed relying on a system of basic functions, the linear combination of which will be the desired approximate solution, while there are also test examples offered for exact solutions of some integro-differential equations and approximate solutions obtained through the finite element method. The examples serve proof to possible transfer of classical projection methods of approximate calculations to the model under study, while employing the developed algorithm of the finite element projection method and conducting a numerical experiment. The numerical experiment showed a reliable and fast convergence. The results obtained within this work allow separating approximate methods depending on the degree of their suitability and effectiveness in problems of unidimensional singular continuum elastic statics.