Introduction to finite element analysis for engineers. ([2018])

• Record Type: Book
• Further Information: Note: Saad A. Ragab and Hassan E. Fayed.
• Authors: Ragab, Saad; Fayed, Hassan E
• Contents: Cover; Half title; Title; Copyright; Dedication; Contents; Preface; Chapter 1 Introduction; 1.1 Computational Sciences and Mechanics; 1.2 Brief Mathematical Background: Linear Algebra; 1.2.1 Vectors; 1.2.2 Matrices; 1.3 Brief Mathematical Background: Partial Di erential Equations; 1.3.1 Elliptic Equations: Poisson's Equation; 1.3.2 Parabolic Equations: Heat Equation; 1.3.3 Hyperbolic Equations: Wave Equation; Chapter 2 Second-Order Ordinary Di erential Equations; 2.1 Model Problem; 2.1.1 Axial Deformation of a Bar; 2.1.2 One-Dimensional Heat Conduction in Solids; 2.2 A Motivational Example 2.3 The Method of Weighted Residuals2.4 Weak Form; 2.5 Global Basis Functions and Matrix Formulation; 2.6 Finite Element Formulation Using Element Shape Functions; 2.6.1 Linear Element; 2.6.2 Quadratic Element; 2.6.3 Higher-Order Elements and Lagrange Interpolation Functions; 2.7 Thermoelastic E ects in One Dimension; 2.8 Numerical Evaluations of Element Matrices; 2.9 Biomedical Engineering Applications; 2.9.1 Reaction-Di usion: Oxygen Consumption in Flat Tissues; 2.9.2 Reaction-Di usion: Oxygen Consumption in Cylindrical Tissues and Spherical Cells 2.9.3 Pulsatile Blood Flow in Arteries: Womersley Problem2.10 Problems; Chapter 3 Fourth-Order Ordinary Di erential Equations; 3.1 Euler{Bernoulli Beam Theory; 3.2 Weak Form of the Beam Equation; 3.3 Finite Element Method: Beam Element; 3.4 Plane Frames; 3.5 Plane Trusses; 3.6 Principle of Virtual Displacements (Work); 3.7 Principle of Minimum Total Potential Energy; 3.7.1 Rayleigh{Ritz Method; 3.8 Problems; Chapter 4 Elliptic Equations: Equilibrium in Two Dimensions; 4.1 Model Problem; 4.2 Weak Form; 4.3 Mesh Generation and Connectivity Matrix; 4.4 Approximations and Element Shape Functions 4.4.1 Bilinear Triangular Element4.4.2 Bilinear Rectangular Element; 4.5 Element Equations and Matrices; 4.5.1 Matrices for Bilinear Triangular Element; 4.5.2 Matrices for Bilinear Rectangular Element; 4.5.3 Matrices for Natural and Mixed Boundary Conditions; 4.6 Elements Assembly and Global System; 4.7 Applications; 4.7.1 Heat Conduction in Solids; 4.7.2 Fully Developed Laminar Flow in Noncircular Ducts .; 4.7.3 Torsion of Noncircular Sections; 4.8 Isoparametric Elements and Numerical Integration; 4.8.1 Shape Functions of Canonical Elements; 4.8.2 Mapping; 4.8.3 Approximations 4.8.4 Element Matrices4.9 Applications; 4.9.1 Potential Flow around 2D Airfoils, Lift; 4.9.2 Oxygen Transport and Consumption in Krogh Capillary- Tissue Cylinder; 4.10 Problems; Chapter 5 Parabolic Equations: Time-Dependent Di usion Problems; 5.1 Model Problem; 5.2 The Weak Form; 5.3 The Weak Form for an Element; 5.4 Approximations and Element Matrices; 5.5 Temporal Approximation: Time Marching; 5.6 Transient Heat Conduction; 5.7 Biomedical Engineering Applications; 5.7.1 Bioheat: Pennes' Heat Conduction Model; 5.7.2 Unsteady Oxygen Consumption in Spherical and Cylin-drical Domains
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2018
• Extent: 1 online resource (xiv, 551 pages)
• Subjects: 518/.25; Finite element method; Engineering mathematics; Engineering mathematics; Finite element method; MATHEMATICS / Numerical Analysis; Electronic books
• Languages: English
• ISBNs: 9781315405681; 1315405687
• Related ISBNs: 9781138030176; 1138030171; 9781315405704
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.