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The finite element method : a practical course

Author: G R Liu
Publisher: Amsterdam : Elsevier, [2014] ©2014
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Summary:
Written for practicing engineers and students alike, this book emphasizes the role of finite element modeling and simulation in the engineering design process. It provides the necessary theories and techniques of the FEM in a concise and easy-to-understand format and applies the techniques to civil, mechanical, and aerospace problems. Updated throughout for current developments in FEM and FEM software, the book also  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: G R Liu
ISBN: 9780080983561 0080983561 9780080994413 0080994415
OCLC Number: 876884521
Description: 1 online resource (457 pages) : illustrations
Contents: Half Title; Title Page; Copyright; Dedication; Biography; Contents; Preface to the First Edition; 1 Computational Modeling; 1.1 Introduction; 1.2 Physical problems in engineering; 1.3 Computational modeling using FEM; 1.3.1 Modeling of the geometry; 1.3.2 Meshing; 1.3.3 Material or medium properties; 1.3.4 Boundary, initial, and loading conditions; 1.4 Solution procedure; 1.4.1 Discrete system equations; 1.4.2 Equation solvers; 1.5 Results visualization; 2 Briefing on Mechanics for Solids and Structures; 2.1 Introduction; 2.2 Equations for three-dimensional solids; 2.2.1 Stress and strain. 2.2.2 Constitutive equations2.2.3 Dynamic equilibrium equations; 2.2.4 Boundary conditions; 2.3 Equations for two-dimensional solids; 2.3.1 Stress and strain; 2.3.2 Constitutive equations; 2.3.3 Dynamic equilibrium equations; 2.4 Equations for truss members; 2.4.1 Stress and strain; 2.4.2 Constitutive equations; 2.4.3 Dynamic equilibrium equations; Solution; 2.5 Equations for beams; 2.5.1 Stress and strain; 2.5.2 Constitutive equations; 2.5.3 Moments and shear forces; 2.5.4 Dynamic equilibrium equations; 2.6 Equations for plates; 2.6.1 Stress and strain; 2.6.2 Constitutive equations. 2.6.3 Moments and shear forces2.6.4 Dynamic equilibrium equations; 2.6.5 Reissner-Mindlin plate; 2.7 Remarks; 2.8 Review questions; 3 Fundamentals for Finite Element Method; 3.1 Introduction; 3.2 Strong and weak forms: problem formulation; 3.3 Hamilton's principle: A weak formulation; 3.3.1 Hamilton's principle; 3.3.2 Minimum total potential energy principle; 3.4 FEM procedure; 3.4.1 Domain discretization; 3.4.2 Displacement interpolation; 3.4.3 Standard procedure for constructing shape functions; 3.4.3.1 On the inverse of the moment matrix; 3.4.3.2 On the compatibility of the shape functions. 3.4.3.3 On other means of construct shape functions3.4.4 Properties of the shape functions; 3.4.5 Formulation of finite element equations in local coordinate system; 3.4.6 Coordinate transformation; 3.4.7 Assembly of global FE equation; 3.4.8 Imposition of displacement constraints; 3.4.9 Solving the global FE equation; 3.5 Static analysis; 3.6 Analysis of free vibration (eigenvalue analysis); 3.7 Transient response; 3.7.1 Central difference algorithm; 3.7.2 Newmark's method (Newmark, 1959); 3.8 Remarks; 3.8.1 Summary of shape function properties. 3.8.2 Sufficient requirements for FEM shape functions3.8.3 Recap of FEM procedure; 3.9 Review questions; 4 FEM for Trusses; 4.1 Introduction; 4.2 FEM equations; 4.2.1 Shape function construction; 4.2.2 Strain matrix; 4.2.3 Element matrices in the local coordinate system; 4.2.4 Element matrices in the global coordinate system; 4.2.4.1 Spatial trusses; 4.2.4.2 Planar trusses; 4.2.5 Boundary conditions; 4.2.6 Recovering stress and strain; 4.3 Worked examples; Exact solution; FEM solution; 4.3.1 Properties of the FEM; 4.3.1.1 Reproduction property of the FEM.
Responsibility: G.R. Liu, School of Aerospace Systems, University of Cincinnati, USA, S.S. Quek, Institute of High Performance Computing, Singapore.

Abstract:

Suitable for practicing engineers and students alike, this book emphasizes the role of finite element modeling and simulation in the engineering design process. It provides the necessary theories and  Read more...

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