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Introduces the subject systematically and in a unified manner
Describes the application of advanced methods in engineering practice
Gives an overview of nonlinear methods
This book presents a modern continuum mechanics and mathematical framework to study shell physical behaviors, and to formulate and evaluate finite element procedures. With a view towards the synergy that results from physical and mathematical understanding, the book focuses on the fundamentals of shell theories, their mathematical bases and finite element discretizations. The complexity of the physical behaviors of shells is analysed, and the difficulties to obtain uniformly optimal finite element procedures are identified and studied. Some modern finite element methods are presented for linear and nonlinear analyses.
1. Introduction.- 2. Geometrical Preliminaries.- 3. Elements of Functional and Numerical Analysis.- 4. Shell Mathematical Models.- 5. Asymptotic Behaviors of Shell Models.- 6. Displacement-Based Shell Finite Elements.- 7. Influence of the Thickness in the Finite Element Approximation.- 8. Towards the Formulation of Effective General Shell Elements.- 9. On the Nonlinear Analysis of Shells.- A. Tables of symbols.- A.1 Latin symbols.- A.2 Greek symbols.- A.3 Special symbols.- B. Some Useful Mathematical Formulas.- C. Distributions: Basic Definitions and Properties.- References.