Finite Element and Meshless Methods in Computational Mechanics
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Beschreibung
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.
Special Features:
- 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.
The finite element and meshless methods are numerical simulation algorithms used to mathematically model physical phenomena. The finite element method relies on the creation of an underlying simplex structure in the region that is being modeled. By specifying these finite elements, a rough model can be developed that can be used to generate approximate solutions while requiring minimal processor time. The meshless method eliminates these finite elements and instead generates a dynamic model from a particle perspective using a complex matrix of integral equations to define the properties of the region being modeled. Without the limitations of the simplex structure, the model can account for large deformations, advanced materials, complex geometries, nonlinear behavior, and discontinuities. However, this utility results in a significant increase in the computational time that is require to generate a solution.
Application of these techniques extends to all areas of computational physics, engineering, and mechanics.
Although several textbooks exist on the topic of the finite element method and there are some that focus specifically on the meshless method, this is the first textbook to describe both modeling techniques in detail and evaluate their relative advantages.
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
Autor*in
Romesh C. Batra