Energy Methods and Finite Element Techniques
Stress and Vibration Applications
- 1st Edition - September 28, 2021
- Imprint: Elsevier
- Authors: Muhsin J. Jweeg, Muhannad Al-Waily, Kadhim Kamil Resan
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 8 8 6 6 6 - 6
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 8 8 6 5 1 - 2
Energy Methods and Finite Element Techniques: Stress and Vibration Applications provides readers with a complete understanding of the theory and practice of finite element a… Read more
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Request a sales quoteEnergy Methods and Finite Element Techniques: Stress and Vibration Applications provides readers with a complete understanding of the theory and practice of finite element analysis using energy methods to better understand, predict, and mitigate static stress and vibration in different structural and mechanical configurations. It presents readers with the underlying theory, techniques for implementation, and field-tested applications of these methods using linear ordinary differential equations. Statistical energy analysis and its various applications are covered, and applications discussed include plate problems, bars and beams, plane strain and stress, 3D elasticity problems, vibration problems, and more. Higher order plate and shell elements, steady state heat conduction, and shape function determinations and numerical integration are analyzed as well.
- Introduces the theory, practice, and applications of energy methods and the finite element method for predicting and mitigating structural stress and vibrations
- Outlines modified finite element techniques such as those with different classes of meshes and basic functions
- Discusses statistical energy analysis and its vibration and acoustic applications
Researchers, graduate students, and professional engineers/R&D professionals
- Cover image
- Title page
- Table of Contents
- Copyright
- About the authors
- Preface
- Part I: Energy Method
- Chapter 1. Fundamentals of energy methods
- Abstract
- 1.1 Principles of virtual work (P.V.W.)
- 1.2 Work function and potential energy
- 1.3 Total potential energy
- 1.4 Application of P.V.W. to generate differential equations for axial member
- 1.5 Principles of stationary total potential energy (P.S.T.P.E.) and trigonometric series for beam bending
- 1.6 Principle of virtual complementary energy (P.V.C.E.)
- 1.7 Torsion of a rectangular section bar
- Problems
- Bibliography
- Chapter 2. Direct methods
- Abstract
- 2.1 Galerkin method (G.M.)
- 2.2 Rayleigh ritz method (R.R.M.)
- 2.3 Examples using the P.S.T.P.E. with non-trigonometric coordinate functions
- 2.4 Case studies for bar and beam problems under different loading and support conditions
- Problems
- Chapter 3. Application of energy methods to plate problems
- Abstract
- 3.1 Plate bending
- 3.2 Plate stretching
- 3.3 Buckling of thin plates using energy method
- 3.4 Application of Galerkin’s method G.M. to plate bending
- 3.5 Kantorovich method
- 3.6 Application of Kantorovich’s method to plate bending
- Problems
- Bibliography
- Chapter 4. Energy methods in vibrations
- Abstract
- 4.1 Rayleigh’s method
- 4.2 Rayleigh’s energy theorem (R. Principle)
- 4.3 Rayleigh Ritz method (modified Ritz method)
- 4.4 Plate applications
- 4.5 Application to the governing differential equation of plates
- Problems
- Bibliography
- Part II: Finite Element Method
- Chapter 5. Introduction to finite element method: bar and beam applications
- Abstract
- 5.1 Bar extension
- 5.2 Equivalent nodal forces of the axially distributed loading
- 5.3 Temperature effects—application to axially loaded problems
- 5.4 Application to the beam bending
- 5.5 Inclined bar element
- Problems
- Bibliography
- Chapter 6. Two-dimensional problems: application of plane strain and stress
- Abstract
- 6.1 Two-dimensional modeling: triangular elements
- 6.2 Derivation of the 4-node quadrilateral element, formulation of the element equations
- 6.3 Parallelogramic element
- Problems
- Bibliography
- Chapter 7. Torsion problem
- Abstract
- 7.1 Total potential energy
- 7.2 Iso-parametric formulation of torsion problem: triangular element
- Problems
- Bibliography
- Chapter 8. Axisymmetric elasticity problems
- Abstract
- 8.1 Geometrical description
- 8.2 Three nodes triangular element
- 8.3 Representation of the applied forces as an equivalent nodal forces
- Problems
- Bibliography
- Chapter 9. Application of finite element method to three-dimensional elasticity problems
- Abstract
- 9.1 Three-dimensional elasticity relations
- 9.2 8-Node hexahedral element
- 9.3 Steps of formulation
- 9.4 Example of parallelopiped element
- 9.5 Tetrahedron element
- Problems
- Bibliography
- Chapter 10. Application of finite element to the vibration problems
- Abstract
- 10.1 General
- 10.2 Application to axial vibration of a bar
- 10.3 Equation of motion
- 10.4 Application to transverse vibration of beams
- 10.5 Constant strain element
- 10.6 Quadrilateral elements
- 10.7 Axisymmetric triangular element
- 10.8 Consistent element mass matrix for the 8-nodes solid element
- 10.9 Consistent mass matrix for a tetrahedron element
- Problems
- Bibliography
- Chapter 11. Steady state heat conduction
- Abstract
- 11.1 Steady-state heat flows
- 11.2 Boundary conditions
- 11.3 Derivation of equilibrium equations
- 11.4 Application of three nodes constant strain triangular element
- 11.5 4-Node quadrilateral element
- Problems
- Bibliography
- Chapter 12. Shape function determinations and numerical integration
- Abstract
- 12.1 One-dimensional formulations
- 12.2 Two-dimensional applications
- 12.3 Convergence criteria
- 12.4 Three dimensions of pentahedral element
- 12.5 Numerical integration
- Problems
- Bibliography
- Chapter 13. Higher-order isoparametric formulation
- Abstract
- 13.1 Isoparametric element-thin plate bending element
- 13.2 General shell element
- 13.3 Axisymmetric solid under axisymmetric loading
- 13.4 Laminated composite plates
- Problems
- Bibliography
- Chapter 14. Finite element program structures
- Abstract
- 14.1 Introduction
- 14.2 Structure of the F.E. process, static analysis
- 14.3 Flow chart of the subroutine input’s DATA
- 14.4 Flow chart of the subroutine shape functions and their derivatives
- 14.5 Flow chart of the Jacobian matrix subroutine
- 14.6 Flow chart of the subroutine [BM] matrix
- 14.7 Flow chart of subroutine [DM]
- 14.8 Flow chart of subroutine [DM]×[BM]
- 14.9 Flow chart of the element stiffness matrix subroutine [K] of size (NDFE, NDFE)
- 14.10 Flow chart of the assembly subroutine of the global stiffness matrix [KG]
- 14.11 Global load vector [FG]
- 14.12 Application of BCs flow chart
- 14.13 Flow chart solution subroutine
- 14.14 Calculation of stresses
- 14.15 Element mass matrix
- 14.16 Free vibration
- Bibliography
- Appendix A. Review of typical framed structure 2-node elements
- A.1 Continuous beam element
- A.2 Plane truss element
- A.3 Plane frame element
- A.4 Grid element
- A.5 Space truss element
- A.6 Space frame element
- A.7 Rotating shaft element
- A.8 Torque rod element
- Appendix B. Penalty function
- Summary: Elimination Approach
- Appendix C. Analytical solution of equations of motion
- C.1 Uncoupled equations of motion of undamped problems
- Appendix D. Numerical integration in time-dependent problems
- Index
- Edition: 1
- Published: September 28, 2021
- No. of pages (Paperback): 588
- No. of pages (eBook): 588
- Imprint: Elsevier
- Language: English
- Paperback ISBN: 9780323886666
- eBook ISBN: 9780323886512
MJ
Muhsin J. Jweeg
Muhsin J. Jweeg is a Prof. Dr. of applied mechanics. As a Chartered Engineer, he is a fellow of the Institution of Mechanical Engineers (U.K.) and currently the Vice-Chancellor of Scientific Affairs, Al-Farahidi University, Iraq. Before this position, he was a Dean of the College of Engineering – Al-Nahrain University for Oct 2006-Mar 2013. Prof. Jweeg published many journal papers and three books. He attended many international and national conferences and gained an international prize in India for the best-published paper in IMECH 1995 and many national awards. Several PhD and MSc students graduated under his supervision, most of them working in the field of energy and finite element applications.
Affiliations and expertise
Professor of Applied Mechanics and Dean of Engineering Faculty, Al-Farahidi University, Baghdad, IraqMA
Muhannad Al-Waily
Muhannad Al-Waily is Professor, Al-Kufa University. His research is focused on applied mechanics, vibration analysis, composite materials, crack analysis, and structural health monitoring. He has published dozens of peer-reviewed articles that have been cited by hundreds.
Affiliations and expertise
Professor, Mechanical Engineering Department, Al-Kufa University, IraqKR
Kadhim Kamil Resan
Kadhim Kamil Resan is Senior Lecturer, Al-Mustansiriyah University. He is a member of ISME and ISPO. His research specializes in design of devices, welding, biomaterials, stress relaxation, composite materials, mechanics of materials, fatigue, corrosion, and smart materials.
Affiliations and expertise
Senior Lecturer, Al-Mustansiriyah University, Baghdad, IraqRead Energy Methods and Finite Element Techniques on ScienceDirect