Application of numerical formulation of finite elements and finite differences in nonlinear transient thermal analysis of structures

Abstract

Among the various branches of research in the structural area, thermal analysis stands out, mainly, in the field of structural problems in fire conditions. Thus, this article aims to make a prediction of the thermal field of the cross section of concrete structural elements exposed to high temperatures. For that, numerical techniques are used to evaluate the physical problem governed by the differential scalar equation of heat diffusion in transient regime and non-linear behavior. The study is guided by two different solution methodologies, characterized by the application of the finite element method and the finite difference method. The main mathematical sentences and premises for each numerical method used are presented and discussed in detail. The numerical results obtained by the developed computer programs are compared with technical standards and numerical solutions available in the literature. In summary, the behavior of the numerical techniques employed in the solution of the problem proved to be close in relation to the reference data, directing the satisfactory performance of the code in the studied application.