A primary method of analysis in mechanical and structural engineering is to divide a structure or object into very small sections (the smaller, the more accurate) and then to observe changes in position and temperature based on the applications of physical or thermal forces. The intelligent use of computers has made one of the primary methods, Finite Element Analyis (FEA), even more powerful and useful. The aim of this book is to provide a modern continuum mechanics and mathematical framework to study shell physical behaviors, and to formulate and evaluate FEA procedures. These shell structures are found abundantly in engineering designs, and are being analysed with finite elements in a seemingly routine manner. This monograph explains that fundamental physical aspects of shell behaviors must be understood in order to perform a reliable and effective shell analysis. In particular, it shows how citial it is that the diversity and the peculiarity of shell behavior when the thickness of the structure is decreased be considered.

Klappentext

The authors present 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. A state of the art monograph by leading experts.

Inhalt

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.