عنوان

Finite element analysis /

0429453078

0429841604

0429841612

9780429453076

9780429841606

9780429841613

1138320730

9781138320734

Finite element analysis /

[Book]

M. Moatamedi and H. Khawaja.

Boca Raton :

CRC Press, Taylor and Francis Group, CRC Press is an imprint of the Taylor and Francis Group, an informa business,

[2018]

1 online resource

" The International Society of Multiphysics, www.Multiphysics. org."

"A Science Publishers book."

Includes bibliographical references (pages 147-150) and index.

Cover; Title Page; Copyright Page; Preface; Table of Contents; 1: Introduction; 1.1 Book Aims and Objectives; 1.2 History and Perspective; 1.2.1 The engineering problem; 1.2.2 The finite element method; 1.3 The Finite Element Mesh: Terminology; 2: Matrix Stiffness Methods; 2.1 The Simple Bar Element; 2.1.1 Stiffness in co-ordinate system parallel to element axes; 2.1.2 Transformation to global co-ordinates; 2.2 Assembly of Bar Elements-The Global Stiffness Matrix; 2.3 Loads and Boundary Conditions; 2.4 A Solution Strategy; 2.5 Numerical Examples; 2.5.1 Uniaxial system 1

Table of Content Introduction Book Aims and Objectives History and Perspective The Finite Element Mesh: Terminology Matrix Stiffness Methods The Simple Bar Element Assembly of Bar Elements -- The Global Stiffness Matrix Loads and Boundary Conditions A Solution Strategy Numerical Examples Error Analysis and Ill-Conditioning Singular Equations: Rigid Body Modes and Mechanisms Symmetry, Anti-symmetry and Asymmetry Thermal Loads The Finite Element Formulation -- One-Dimensional Problems The Fundamental Equations The Shape Function The Finite Element Equations The Element Stiffness Matrix for a 2 Node Bar with Linear Shape Functions The Finite Element Formulation -- Two-Dimensional Problems The Fundamental Equations The Finite Element Formulation for a Continuum A Triangular Element A Quadrilateral Element Numerical Study -- Pin-Jointed Frame with a Shear Web Restrictions on Element Formulation -- Completeness and Compatibility Computational Implementation of the Finite Element Method Solution Methodologies -- Frontal v Banded Solvers Storage of the Stiffness Matrix Numerical Integration -- Gaussian Quadrature Beams, Plates, Shells and Solids Solid Elements A Beam Element Plates and Shells Parametric Element Formulation Isoparametric bar element Isoparametric Four-Node Quadrilateral Element Isoparametric Eight-Node Quadrilateral Element

2.5.2 Uniaxial system 22.5.3 Pin-jointed framework 1; 2.5.4 Redundant pin-jointed framework; 2.6 Error Analysis and Ill-conditioning; 2.6.1 Theory; 2.6.2 Numerical examples; 2.6.2.1 Error analysis of Example 2.5.4; 2.6.2.2 System exhibiting ill-conditioning; 2.6.3 Sources of ill-conditioning; 2.7 Singular Equations: Rigid Body Modes and Mechanisms; 2.8 Symmetry, Antisymmetry and Asymmetry; 2.8.1 Symmetrical loading; 2.8.2 Antisymmetrical loading; 2.8.3 Asymmetrical loading; 2.9 Thermal Loads; 2.9.1 Thermal loads in a bar element

2.9.2 Numerical example of pre-stressing of bolt using thermal loads3: The Finite Element Formulation: One-Dimensional Problems; 3.1 The Fundamental Equations; 3.1.1 The equilibrium equation; 3.1.2 The principle of virtual displacements; 3.2 The Shape Function; 3.3 The Finite Element Equations; 3.3.1 Algebraic form; 3.3.2 Matrix form; 3.4 The Element Stiffness Matrix for a 2-Node Bar with Linear Shape Functions; 3.4.1 Bar of constant Young's modulus and of constant cross-section; 3.4.2 Bar with linear taper; 4: The Finite Element Formulation: Two-Dimensional Problems

4.1 The Fundamental Equations4.1.1 Elasticity of a continuum; 4.1.2 Vector notation; 4.1.3 The stress/strain relationships; 4.1.4 The principle of virtual displacements for the two-dimensional continuum; 4.2 The Finite Element Formulation for a Continuum; 4.3 A Triangular Element; 4.3.1 Shape functions; 4.3.2 The element stiffness matrix; 4.3.3 Body forces; 4.3.4 Surface pressures and tractions; 4.3.5 Numerical example: A single element; 4.4 A Quadrilateral Element; 4.4.1 Shape functions; 4.4.2 The element stiffness matrix; 4.4.3 An application for the element

4.5 Numerical Study: Pin-jointed Frame with a Shear Web4.6 Restrictions on Element Formulations-Completeness and Compatibility; 4.6.1 Attributes of the polynomial form of shape function-number of terms and differentiability; 4.6.2 Completeness-constant strain and rigid body modes; 4.6.3 Compatibility; 4.6.4 Conforming elements; 4.6.5 Convergence; 4.6.6 Non-conforming elements and the patch test; 5: Computational Implementation of the Finite Element Method; 5.1 Solution Methodologies-Frontal v Banded; 5.1.1 Banded solver; 5.1.2 Frontal solver; 5.2 Storage of the Stiffness Matrix

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Finite element analysis has become the most popular technique for studying engineering structures in detail. It is particularly useful whenever the complexity of the geometry or of the loading is such that alternative methods are inappropriate. The finite element method is based on the premise that a complex structure can be broken down into finitely many smaller pieces (elements), the behaviour of each of which is known or can be postulated. These elements might then be assembled in some sense to model the behaviour of the structure. Intuitively this premise seems reasonable, but there are many important questions that need to be answered. In order to answer them it is necessary to apply a degree of mathematical rigour to the development of finite element techniques. The approach that will be taken in this book is to develop the fundamental ideas and methodologies based on an intuitive engineering approach, and then to support them with appropriate mathematical proofs where necessary. It will rapidly become clear that the finite element method is an extremely powerful tool for the analysis of structures (and for other field problems), but that the volume of calculations required to solve all but the most trivial of them is such that the assistance of a computer is necessary. As stated above, many questions arise concerning finite element analysis. Some of these questions are associated with the fundamental mathematical formulations, some with numerical solution techniques, and others with the practical application of the method. In order to answer these questions, the engineer/analyst needs to understand both the nature and limitations of the finite element approximation and the fundamental behaviour of the structure. Misapplication of finite element analysis programs is most likely to arise when the analyst is ignorant of engineering phenomena.

Ingram Content Group

9780429841606

Finite element analysis

9781138320734 (hardback : acid-free paper)

Finite element method.

Finite element method.

MATHEMATICS-- Numerical Analysis.

MAT-- 041000

Moatamedi, M., (Moji)

Khawaja, H., (Hassan A.)

20200822112904.0

rda

[Book]

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