Introduction to Solid Mechanics and Finite Element Analysis Using Mathematica
Edition: 1
Copyright: 2011
Pages: 506
Edition: 1
Copyright: 2011
Pages: 508
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Introduction to Solid Mechanics and Finite Element Analysis Using Mathematica provides a foundation in the mathematics and mechanics underlying the behavior of deformable objects under load. Covering key topics such as linear algebra, stress, deformation, and strain, it builds toward the application of Finite Element Analysis (FEA) as a powerful computational tool. By combining theory with practical modeling in Mathematica, the book equips readers to both use FEA effectively and understand the solid mechanics principles that guide reliable applications.
Chapter 1 introductory Linear Algebra
1.1. Linear Vector Spaces
1.2 Linear Maps between Vector Spaces (Matrices, Tensors)
1.3 Vector Calculus
Chapter 2 Stress
2.1 The Stress Tensor (Matrix)
2.2 Stress Measures and Stress Invariants
2.3 Stress-Based Failure Criteria
2.4 Mohr's Circle for Plane Stress
2.5 Other Measures of Stress
Chapter 3 Deformation and Strain
3.1 Description of Motion
3.2. The Deformation Gradient
3.3. Strain Measures
3.4. Instantaneous Measures of Deformation: The Velocity Gradient
3.5. Material-lime Derivative
Chapter 4 Mass Balance and Equilibrium Equations
4.1. Eulerian versus Lagrangian Formulations
4.2. Mass Balance [Continuity Equation]
4.3. Differential Equations of Equilibrium
Chapter 5 Linear Elastic Materials Constitutive Equations
5.1. Classifications of Materials Mechanical Response
5.2. Linear Elastic Materials
5.3. Hyperelastic Materials [Large Elastic Deformations)
Chapter 6 The Bean Approximations
6.1. Euler Bernoulli's Beam Under Bending
6.2. Timoshenko Beam Under Bending
6.3. Linear Elastic Beam Under Axial Loading
6.4 Examples
6.5 Final Notes
Chapter 7 Energy, Elastic Entergy, and Virtual Work
7.1. Potential (Deformation) Energy in Single Degrees of Freedom Springs
7.2. Deformation Energy Inside a Continuum
7.3. Expressions for the Elastic Strain Energy Function
7.4 The Principle of Virtual Work
7.5 Some Applicatoins of the Principles of Virtual Work
7.6 The Principle of Minimum Potential Energy for Conservatism Systems
Chapter 8 Approximate Methods
8.1 The Rayleigh Ritz Method
8.2 The Galerkin and Other Approximate Methods
8.3 The Strong Form versus the Weak Form
Chapter 9 Introduction to Finite Element Analysis
9.1 Finite Element Analysis Approximation in One Dimension
9.2. Finite Element Analysis in Two and Three Dimensions
9.3. lsoparametric Elements and Numerical Integration
9.4. Comparison of Different Elements Behaviour Under Bending
Dr. Samer Adeeb, PhD, PEng, is Professor and Chair of the Department of Civil and Environmental Engineering at the University of Alberta, where he has been a faculty member since 2007. He holds a PhD in Structural Engineering from the University of Calgary, an MSc in Mathematics from the University of Alberta, and a BSc in Civil Engineering (Structures) from Ain Shams University in Cairo. His research spans structural engineering, pipelines, and biomechanics, with a focus on topics such as pipeline stability, spinal biomechanics, and bone growth analysis.
Introduction to Solid Mechanics and Finite Element Analysis Using Mathematica provides a foundation in the mathematics and mechanics underlying the behavior of deformable objects under load. Covering key topics such as linear algebra, stress, deformation, and strain, it builds toward the application of Finite Element Analysis (FEA) as a powerful computational tool. By combining theory with practical modeling in Mathematica, the book equips readers to both use FEA effectively and understand the solid mechanics principles that guide reliable applications.
Chapter 1 introductory Linear Algebra
1.1. Linear Vector Spaces
1.2 Linear Maps between Vector Spaces (Matrices, Tensors)
1.3 Vector Calculus
Chapter 2 Stress
2.1 The Stress Tensor (Matrix)
2.2 Stress Measures and Stress Invariants
2.3 Stress-Based Failure Criteria
2.4 Mohr's Circle for Plane Stress
2.5 Other Measures of Stress
Chapter 3 Deformation and Strain
3.1 Description of Motion
3.2. The Deformation Gradient
3.3. Strain Measures
3.4. Instantaneous Measures of Deformation: The Velocity Gradient
3.5. Material-lime Derivative
Chapter 4 Mass Balance and Equilibrium Equations
4.1. Eulerian versus Lagrangian Formulations
4.2. Mass Balance [Continuity Equation]
4.3. Differential Equations of Equilibrium
Chapter 5 Linear Elastic Materials Constitutive Equations
5.1. Classifications of Materials Mechanical Response
5.2. Linear Elastic Materials
5.3. Hyperelastic Materials [Large Elastic Deformations)
Chapter 6 The Bean Approximations
6.1. Euler Bernoulli's Beam Under Bending
6.2. Timoshenko Beam Under Bending
6.3. Linear Elastic Beam Under Axial Loading
6.4 Examples
6.5 Final Notes
Chapter 7 Energy, Elastic Entergy, and Virtual Work
7.1. Potential (Deformation) Energy in Single Degrees of Freedom Springs
7.2. Deformation Energy Inside a Continuum
7.3. Expressions for the Elastic Strain Energy Function
7.4 The Principle of Virtual Work
7.5 Some Applicatoins of the Principles of Virtual Work
7.6 The Principle of Minimum Potential Energy for Conservatism Systems
Chapter 8 Approximate Methods
8.1 The Rayleigh Ritz Method
8.2 The Galerkin and Other Approximate Methods
8.3 The Strong Form versus the Weak Form
Chapter 9 Introduction to Finite Element Analysis
9.1 Finite Element Analysis Approximation in One Dimension
9.2. Finite Element Analysis in Two and Three Dimensions
9.3. lsoparametric Elements and Numerical Integration
9.4. Comparison of Different Elements Behaviour Under Bending
Dr. Samer Adeeb, PhD, PEng, is Professor and Chair of the Department of Civil and Environmental Engineering at the University of Alberta, where he has been a faculty member since 2007. He holds a PhD in Structural Engineering from the University of Calgary, an MSc in Mathematics from the University of Alberta, and a BSc in Civil Engineering (Structures) from Ain Shams University in Cairo. His research spans structural engineering, pipelines, and biomechanics, with a focus on topics such as pipeline stability, spinal biomechanics, and bone growth analysis.