Mathematical Models in the Finite Element Solution -- Fundamental Steps in Structural Mechanics -- The Linear 3-D Elasticity Mathematical Model -- Mathematical Models used in Engineering Structural Analysis -- The Principle of Virtual Work -- The Finite Element Process of Solution -- Hierarchical Modeling Examples -- Modeling for Nonlinear Analysis.

This book presents in one treatise both the basic mathematical models of solid structural mechanics and effective finite element procedures for the solution of these models. The book can be used for teaching, in a modern way, solid and structural mechanics, finite element methods, and for self-study from elementary to quite advanced material. In synthesizing classical mechanics with modern finite element analysis, emphasis is given to the hierarchical nature of the mathematical models of mechanics, from simple to complex, and on choosing the simplest reliable and effective model for analysis. The process of hierarchical modeling and finite element solution is illustrated in examples that show the benefits reached when good hierarchical modeling is performed. To pursue an effective analysis is an art the objective is to predict the future. Performing in the art of analysis is very stimulating and requires constant learning. This book has been written to provide a fundamental basis for that learning process.