Finite element analysis of structures through unified formulation

Finite element analysis of structures through unified formulation /

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Bibliographic Details
Main Author: Carrera, Erasmo
Corporate Author: Ebooks Corporation
Other Authors: Cinefra, Maria, Petrolo, Marco, Zappino, Enrico
Format: Electronic eBook
Language:English
Published: Chichester, West Sussex : John Wiley & Sons, Inc., 2014.
Subjects:
Finite element method.
Numerical analysis.
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)
Table of Contents:
  • Machine generated contents note: 1. Introduction
  • 1.1. What is in this Book
  • 1.2. Finite Element Method
  • 1.2.1. Approximation of the Domain
  • 1.2.2. Numerical Approximation
  • 1.3. Calculation of the Area of a Surface with a Complex Geometry via the FEM
  • 1.4. Elasticity of a Bar
  • 1.5. Stiffness Matrix of a Single Bar
  • 1.6. Stiffness Matrix of a Bar via the PVD
  • 1.7. Truss Structures and Their Automatic Calculation by Means of the FEM
  • 1.8. Example of a Truss Structure
  • 1.8.1. Element Matrices in the Local Reference System
  • 1.8.2. Element Matrices in the Global Reference System
  • 1.8.3. Global Structure Stiffness Matrix Assembly
  • 1.8.4. Application of Boundary Conditions and the Numerical Solution
  • 1.9. Outline of the Book Contents
  • References
  • 2. Fundamental Equations of 3D Elasticity
  • 2.1. Equilibrium Conditions
  • 2.2. Geometrical Relations
  • 2.3. Hooke's Law
  • 2.4. Displacement Formulation
  • Further Reading
  • 3. From 3D Problems to 2D and ID Problems: Theories for Beams, Plates and Shells
  • 3.1. Typical Structures
  • 3.1.1. Three-Dimensional Structures (Solids)
  • 3.1.2. Two-Dimensional Structures (Plates, Shells and Membranes)
  • 3.1.3. One-Dimensional Structures (Beams and Bars)
  • 3.2. Axiomatic Method
  • 3.2.1. Two-Dimensional Case
  • 3.2.2. One-Dimensional Case
  • 3.3. Asymptotic Method
  • Further Reading
  • 4. Typical FE Governing Equations and Procedures
  • 4.1. Static Response Analysis
  • 4.2. Free Vibration Analysis
  • 4.3. Dynamic Response Analysis
  • References
  • 5. Introduction to the Unified Formulation
  • 5.1. Stiffness Matrix of a Bar and the Related FN
  • 5.2. Case of a Bar Element with Internal Nodes
  • 5.2.1. Case of Bar with Three Nodes
  • 5.2.2. Case of an Arbitrary Defined Number of Nodes
  • 5.3. Combination of the FEM and the Theory of Structure Approximations: A Four-Index FN and the CUF
  • 5.3.1. FN for a 1D Element with a Variable Axial Displacement over the Cross-section
  • 5.3.2. FN for a 1D Structure with a Complete Displacement Field: The Case of a Refined Beam Model
  • 5.4. CUF Assembly Technique
  • 5.5. CUF as a Unique Approach for 1D, 2D and 3D Structures
  • 5.6. Literature Review of the CUF
  • References
  • 6. Displacement Approach via the PVD and FN for 1D, 2D and 3D Elements
  • 6.1. Strong Form of the Equilibrium Equations via the PVD
  • 6.1.1. Two Fundamental Terms of the FN
  • 6.2. Weak Form of the Solid Model Using the PVD
  • 6.3. Weak Form of a Solid Element Using Index Notation
  • 6.4. FN for 1D, 2D and 3D Problems in Unique Form
  • 6.4.1. Three-Dimensional Models
  • 6.4.2. Two-Dimensional Models
  • 6.4.3. One-Dimensional Models
  • 6.5. CUF at a Glance
  • 6.5.1. Choice of N'i,Nj,Fr and Fs
  • References
  • 7. Three-Dimensional FEM Formulation (Solid Elements)
  • 7.1. Eight-Node Element Using Classical Matrix Notation
  • 7.1.1. Stiffness Matrix
  • 7.1.2. Load Vector
  • 7.2. Derivation of the Stiffness Matrix Using the Index Notation
  • 7.2.1. Governing Equations
  • 7.2.2. FE Approximation in the CUF
  • 7.2.3. Stiffness Matrix
  • 7.2.4. Mass Matrix
  • 7.2.5. Loading Vector
  • 7.3. Three-Dimensional Numerical Integration
  • 7.3.1. Three-Dimensional Gauss--Legendre, Quadrature
  • 7.3.2. Isoparametric Formulation
  • 7.3.3. Reduced Integration: Shear Locking, Correction
  • 7.4. Shape Functions
  • References
  • 8. One-Dimensional Models with Nth-Order Displacement; Field, the Taylor Expansion Class
  • 8.1. Classical Models and the Complete Linear Expansion Case
  • 8.1.1. Euler-Bernoulli Beam Model
  • 8.1.2. Timoshenko Beam Theory (TBT)
  • 8.7.3. Complete Linear Expansion Case
  • 8.1.4. Finite Element Based on N = 1
  • 8.2. EBBT, TBT and N = 1 in Unified Form
  • 8.2.1. Unified Formulation of N = 1
  • 8.2.2. EBBT and TBT as Particular Cases of N = 1
  • 8.3. CUF for Higher-Order Models
  • 8.3.1. N = 3 and N = 4
  • 8.3.2. Nth-Order
  • 8.4. Governing Equations, FE Formulation and the FN
  • 8.4.1. Governing Equations
  • 8.4.2. FE Formulation
  • 8.4.3. Stiffness Matrix
  • 8.4.4. Mass Matrix
  • 8.4.5. Loading Vector
  • 8.5. Locking Phenomena
  • 8.5.1. Poisson Locking and its Correction
  • 8.5.2. Shear Locking
  • 8.6. Numerical Applications
  • 8.6.1. Structural Analysis of a Thin-Walled Cylinder
  • 8.6.2. Dynamic Response of Compact and Thin-Walled Structures
  • References
  • 9. One-Dimensional Models with a Physical Volume/Surface-Based Geometry and Pure Displacement Variables, the Lagrange Expansion Class
  • 9.1. Physical Volume/Surface Approach
  • 9.2. Lagrange Polynomials and Isoparametric Formulation
  • 9.2.1. Lagrange Polynomials
  • 9.2.2. Isoparametric Formulation
  • 9.3. LE Displacement Fields and Cross-section Elements
  • 9.3.1. FE Formulation and FN
  • 9.4. Cross-section Multi-elements and Locally Refined Models
  • 9.5. Numerical Examples
  • 9.5.1. Mesh Refinement and Convergence Analysis
  • 9.5.2. Considerations on PL
  • 9.5.3. Thin-Walled Structures and Open Cross-Sections
  • 9.5.4. Solid-like Geometrical BCs
  • 9.6. Component-Wise-Approach for Aerospace and Civil Engineering Applications
  • 9.6.1. CW Approach for Aeronautical Structures
  • 9.6.2. CW Approach for Civil Engineering
  • References
  • 10. Two-Dimensional Plate Models with Nth-Order Displacement Field, the Taylor Expansion Class
  • 10.1. Classical Models and the Complete Linear Expansion
  • 10.1.1. Classical Plate Theory
  • 10.1.2. First-Order Shear Deformation Theory
  • 10.1.3. Complete Linear Expansion Case
  • 10.1.4. FE Based on N = 1
  • 10.2. CPT, FSDT and N = 1 Model in Unified Form
  • 10.2.1. Unified Formulation of the N = 1 Model
  • 10.2.2. CPT and FSDT as Particular Cases of N = 1
  • 10.3. CUF of Nth Order
  • 10.3.1. N = 3 and N = 4
  • 10.4. Governing Equations, the FE Formulation and the FN
  • 10.4.1. Governing Equations
  • 10.4.2. FE Formulation
  • 10.4.3. Stiffness Matrix
  • 10.4.4. Mass Matrix
  • 10.4.5. Loading Vector
  • 10.4.6. Numerical Integration
  • 10.5. Locking Phenomena
  • 10.5.1. Poisson Locking and its Correction
  • 10.5.2. Shear Locking and its Correction
  • 10.6. Numerical Applications
  • References
  • 11. Two-Dimensional Shell Models with Nth-Order Displacement Field, the TE Class
  • 11.1. Geometrical Description
  • 11.2. Classical Models and Unified Formulation
  • 11.3. Geometrical Relations for Cylindrical Shells
  • 11.4. Governing Equations, FE Formulation and the FN
  • 11.4.1. Governing Equations
  • 11.4.2. FE Formulation
  • 11.5. Membrane and Shear Locking Phenomenon
  • 11.5.1. MITC9 Shell Element
  • 11.5.2. Stiffness Matrix
  • 11.6. Numerical Applications
  • References
  • 12. Two-Dimensional Models with Physical Volume/Surface-Based Geometry and Pure Displacement Variables, the LE Class
  • 12.1. Physical Volume/Surface Approach
  • 12.2. LE Model
  • 12.3. Numerical Examples
  • References
  • 13. Discussion on Possible Best Beam, Plate and Shell Diagrams
  • 13.1. MAAA
  • 13.2. Static Analysis of Beams
  • 13.2.1. Influence of the Loading Conditions
  • 13.2.2. Influence of the Cross-section Geometry
  • 13.2.3. Reduced Models vs Accuracy
  • 13.3. Modal Analysis of Beams
  • 13.3.1. Influence of the Cross-section Geometry
  • 13.3.2. Influence of BCs
  • 13.4. Static Analysis of Plates and Shells
  • 13.4.1. Influence of BCs
  • 13.4.2. Influence of the Loading Conditions
  • 13.4.3. Influence of the Loading and Thickness
  • 13.4.4. Influence of the Thickness Ratio on Shells
  • 13.5. BTD
  • References
  • 14. Mixing Variable Kinematic Models
  • 14.1. Coupling Variable Kinematic Models via Shared Stiffness
  • 14.1.1. Application of the Shared Stiffness Method
  • 14.2. Coupling Variable Kinematic Models via the LM Method
  • 14.2.1. Application of the LM Method to Variable Kinematic Models
  • 14.3. Coupling Variable Kinematic Models via the Arlequin Method
  • 14.3.1. Application of the Arlequin Method
  • References
  • 15. Extension to Multilayered Structures
  • 15.1. Multilayered Structures
  • 15.2. Theories for Multilayered Structures
  • 15.2.1. COz Requirements
  • 15.2.2. Refined Theories
  • 75.2.3. Zigzag Theories
  • 15.2.4. Layer-Wise Theories
  • 15.2.5. Mixed Theories
  • 15.3. Unified Formulation for Multilayered Structures
  • 75.3.7. ESLMs
  • 15.3.2. Inclusion of Murakami's ZZ Function
  • 15.3.3. LW Theory and Legendre Expansion
  • 15.3.4. Mixed Models with Displacement and Transverse Stress Variables
  • 15.4. FE Formulation
  • 15.4.1. Assembly at Multilayer Level
  • 15.4.2. Selected Results
  • 15.5. Literature on the CUF Extended to Multilayered Structures
  • References
  • 16. Extension to Multifield Problems
  • 16.1. Mechanical vs Field Loadings
  • 16.2. Need for Second-Generation FEs for Multifield Loadings
  • 16.3. Constitutive Equations for MFPs
  • 16.4. Variational Statements for MFPs
  • 16.4.1. PVD
  • 76.4.2. RMVT
  • 16.5. Use of Variational Statements to Obtain FE equations in Terms of Ě€Fundamental Nuclei'
  • 76.5.7. PVD-Applications
  • 76.5.2. RMVT-Applications
  • 16.6. Selected Results
  • 16.6.1. Mechanical-Electrical Coupling: Static Analysis of an Actuator Plate
  • 16.6.2. Mechanical-Electrical Coupling: Comparison between RMVT Analyses
  • 16.7. Literature on the CUF Extended to MFPs
  • References
  • Appendix A Numerical Integration
  • A.1. Gauss-Legendre Quadrature
  • References
  • Appendix B CUF FE Models: Programming and Implementation Guidelines
  • B.1. Preprocessing and Input Descriptions
  • Contents note continued: B.1.1. General FE Inputs
  • B.1.2. Specific CUF Inputs
  • B.2. FEM Code
  • B.2.1. Stiffness and Mass Matrices
  • B.2.2. Stiffness and Mass Matrix Numerical Examples
  • B.2.3. Constraints and Reduced Models
  • B.2.4. Load Vector
  • B.3. Postprocessing
  • B.3.1. Stresses and Strains
  • References.

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