Simple Deformation and Vibration by FEA

Simple Fields of Physics by FEA Understanding Elasticity the Easy Way Elastic deformation is of enormous importance in mechanical engineering and has long been a prominent item in technical education. The theory profits from major developments during the 1800s. Stress and strain do not transform as directly as vectors, and the subject is somewhat counter-intuitive. A century ago one had to resort to graphical devices, such as the Mohr circle, to handle elasticity concepts. Most textbooks still use this antiquated technique. With the advent of the PC it became possible to transform stress and strain analytically and to plot results in informative ways. In addition, elastic deformation could then be studied by means of finite element analysis, which dramatically extended the range of applications. The present volume contains other enhancements with respect to ordinary textbooks. Problems of torsion and warping are solved by PDEs, even for hollow shafts. There is also a treatise on thermoelastic defor-mation. Many examples are in three dimensions. Finally, wave motion is studied by a slight extension of the PDE formalism. The latter is sufficient for solving problems of forced as well as free vibration. Eigenstates can thus be illustrated for objects in 2D and 3D. This book assumes no previous knowledge of FEA. In the first chapters it introduces the graphics facilities of FlexPDE® and then demonstrates how Laplace and Poisson equations may be solved. The free student version of this program is sufficient throughout.