Solid Mechanics using the Finte Element Method

Today the fundamentals of solid mechanics may be explained by "numerical" experiments using the finite element method. The explanation is detailed in this book using many examples. After a short review of how the finite element method works (in Chapter 1), Chapter 2 develops some key points of solid mechanics: what is a beam? when and how can a structure be represented by beam elements? what are the basic hypotheses? what kind of information does a beam model provide? A generalized beam element is also presented. Chapter 3 uses the same approach for the discussion on stress concentrations and stress singularities: local effects; influence of geometric discontinuities, such as holes or corners; mesh refinements and/or analytic-numeric approaches. Chapter 4 is devoted to plate modeling: coupling of membrane and bending, folded, stiffened, composite plates. Chapter 5 provides a short presentation of the dynamics of structures with a particular focus on the modal method, the influence of local defaults on the modal response is also analyzed. Commercial software (Ansys) is used to study the examples.