Finite element analysis of structures through unified formulation /

• Κύριος συγγραφέας: Carrera, Erasmo
• Άλλοι συγγραφείς: Cinefra, Maria, Petrolo, Marco, Zappino, Enrico
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Chichester, West Sussex : Wiley, 2014.
• Θέματα: Finite element method.; Numerical analysis.; MATHEMATICS / Numerical Analysis; Electronic books.

"This book deals with the Finite Element Method for the analysis of elastic structures such as beams, plates, shells and solids. The modern approach of Unified Formulation (UF), as proposed by the lead author, deals with the consideration of one-dimensional (beams), two-dimensional (plates and...

Πίνακας περιεχομένων:

• Titlepage; Copyright; About the Authors; Preface; Nomenclature and Acronyms; Symbols; Acronyms; 1 Introduction; 1.1 What is in this Book; 1.2 The Finite Element Method; 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; 1.9 Outline of the Book Contents; Notes; References; 2 Fundamental Equations of 3D Elasticity; 2.1 Equilibrium Conditions
• 2.2 Geometrical Relations2.3 Hooke's Law; 2.4 Displacement Formulation; Notes; Further Reading; 3 From 3D Problems to 2D and 1D Problems: Theories for Beams, Plates and Shells; 3.1 Typical Structures; 3.2 Axiomatic Method; 3.3 Asymptotic Method; Note; 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
• 5.3 Combination of the FEM and the Theory of Structure Approximations: A Four-Index FN and the CUF5.4 CUF Assembly Technique; 5.5 CUF as a Unique Approach for 1D, 2D and 3D Structures; 5.6 Literature Review of the CUF; Notes; References; 6 The Displacement Approach via the PVD and FN for 1D, 2D and 3D Elements; 6.1 Strong Form of the Equilibrium Equations via the PVD; 6.2 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; 6.5 CUF at a Glance; Notes; References
• 7 Three-Dimensional FEM Formulation (Solid Elements)7.1 An Eight-Node Element Using Classical Matrix Notation; 7.2 Derivation of the Stiffness Matrix Using the Index Notation; 7.3 Three-Dimensional Numerical Integration; 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; 8.2 EBBT, TBT and N = 1 in Unified Form; 8.3 CUF for Higher-Order Models; 8.4 Governing Equations, FE Formulation and the FN; 8.5 Locking Phenomena; 8.6 Numerical Applications; References
• 9 One-Dimensional Models with a Physical Volume/Surface-Based Geometry and Pure Displacement Variables, the Lagrange Expansion Class9.1 Physical Volume/Surface Approach; 9.2 Lagrange Polynomials and Isoparametric Formulation; 9.3 LE Displacement Fields and Cross-section Elements; 9.4 Cross-section Multi-elements and Locally Refined Models; 9.5 Numerical Examples; 9.6 The Component-Wise Approach for Aerospace and Civil Engineering Applications; References; 10 Two-Dimensional Plate Models with Nth-Order Displacement Field, the Taylor Expansion Class