Finite Element and Meshless Methods in Computational Mechanics
Batra, Romesh C.
2016, Approx. 500 p. 70 illus.
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Only textbook that provides an in-depth analysis of both the finite element and meshless methods, discussing their similarities and differences, and evaluating their relative advantages
Describes the methods for applying each modeling technique to one-, two-, and three-dimensional problems
Discusses the tradeoffs associated with achieving model accuracy and model stability - Provides techniques to verify computed solutions and calculate and measure error
Finite Element and Meshless Methods in Computational Mechanics is intended for use as a primary textbook in advanced undergraduate or graduate courses in computational mechanics or industrial engineering. This book includes a unified presentation of both the finite element and meshless methods and describes in detail their application to computational mechanics. This is the first textbook to provide an in-depth analysis of both numerical simulation methods, discuss their similarities and differences, and evaluate their relative advantages.
- Describes the methods for applying each modeling technique to one-, two-, and three-dimensional problems, while addressing the unique challenges of each type of problem.
- Discusses the tradeoffs associated with achieving model accuracy and model stability.
- Provides techniques to verify computed solutions and caluculate and measure error.
This textbook can also serve as a useful resource for courses in numerical algorithms, continuum mechanics, mathematical techniques in mechanical engineering, geometric modeling, and other advanced topics in engineering and mechanics.
(Prelim.) -Part I: Finite Element Method.- Introduction.- Weak Formuation of a Problem.- Approximate Solution of a Model Problem.- Fourth-Order Differential Equations.- Numerical Integration.- Two-Dimensional Problems.- Three-Dimensional Problems.- Vibrations.- Transient Parabolic Problems.- Linear Elastodynamics.