Finite Element and Meshless Methods in Computational Mechanics

1. Auflage 2020
ISBN: 978-1-4419-5682-8
Verlag: Springer-Verlag New York Inc.

Buch, Englisch, 500 Seiten, Book, Format (B × H): 155 mm x 235 mm

Reihe: Advances in Mechanics and Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Batra, Romesh C.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Technische Wissenschaften Technik Allgemein Modellierung & Simulation
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Naturwissenschaften Physik Mechanik

Inhaltsverzeichnis

(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.