Modelagem de problemas de engenharia: solução de equações diferenciais parciais pelo método dos elementos finitos

Abstract

The present paper approaches main engineering problems solved by finite element method. Engineering problems are mathematically represented to describe physical phenomena and involve the solution of particular case studies. It embraces many different topics such determination of the variability of the stress in a mechanical structure, its strains, flux of heat in a metallic plate, and water flow in a porous media. These and other phenomena that occur frequently in engineering problems can be solved by partial differential equations. These problems are divided in two main types: problems of contour values and of initial value. The analytical solution of these partial deferential equations is in the great majority non applicable, due to the dispersion and the complexity of the properties of the materials, geometry etc. For this reason the use of numerical methods is important in a way to substitute the analytical accurate solution for an approach solution. In this work the method of the finite elements is highlighted as a regular mathematical tool available for the solution of the great variety of problems found in the diverse branches of engineering.