The Mechanics of Solids and Structures - Hierarchical Modeling and the Finite Element Solution

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.

Texte du rabat

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.

Résumé

In the recent decades, computational procedures have been applied to an increasing extent in engineering and the physical sciences. Mostly, two separate fields have been considered, namely, the analysis of solids and structures and the analysis of fluid flows. These continuous advances in analyses are of much interest to physicists, mathematicians and in particular, engineers. Also, computational fluid and solid mechanics are no longer treated as entirely separate fields of applications, but instead, coupled fluid and solid analysis is being pursued. The objective of the Book Series is to publish monographs, textbooks, and proceedings of conferences of archival value, on any subject of computational fluid dynamics, computational solid and structural mechanics, and computational multi-physics dynamics. The publications are written by and for physicists, mathematicians and engineers and are to emphasize the modeling, analysis and solution of problems in engineering.

Contenu

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.