Finite Elements Methods in Mechanics

The book "Finite Elements Methods in Mechanics" offers a comprehensive introduction to the fundamental areas of mechanical engineering, including fluid mechanics, heat conduction, beams, and elasticity. It places particular emphasis on the physical foundations of finite element approximation by addressing the application of finite elements to the analysis of elastic membranes. The detailed derivations of mass, stiffness, and force matrices enable a deep understanding of the underlying concepts. Additionally, various computational methods are presented with numerical examples to illustrate the theoretical concepts. The chapters on fluid mechanics cover both conventional and vortex transport formulations for viscous, incompressible fluid flow and provide an in-depth discussion of solution approaches. The variational and Galerkin formulations for heat conduction, beam, and elasticity problems are also treated extensively. The book includes three computer programs written in a C++ environment to solve specific problems, including the Poisson equation and elastic problems in two and three dimensions.