A New Nonlinear One-Dimensional Shape Function applied to Simulate a Steady State Heat Transfer Problem

Abstract

Generally linear shape functions are considered for two noded elements as coefficients of higher order polynomial cannot be determined from two nodes. In the present work, attempts have been made to fit a non-linear trigonometric shape function for one dimensional two noded elements. As in case of nonlinearity, the dependent variable varies nonlinearly with the independent one, consideration of linear shape function may lead to erroneous results. Here, a one dimensional heat transfer problem is solved analytically, with the help of linear shape functions and with the help of newly developed nonlinear shape functions. Analysis shows that results obtained by considering nonlinear shape functions have quite good match with that by linear shape functions.