Finite elements in structural analysis : theoretical concepts and modeling procedures in statics and dynamics of structures / / Horst Werkle

• Autore: Werkle Horst
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (716 pages)
• Disciplina: 624.17
• Soggetto topico: Structural analysis (Engineering) - Mathematics
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Mathematical Background -- 1.1 Introduction -- 1.2 Matrices and Vectors -- 1.3 Matrix Algebra -- 1.3.1 Addition and Subtraction -- 1.3.2 Multiplication -- 1.3.3 Inverse of a Matrix -- 1.4 Linear Systems of Equations -- 1.4.1 Inhomogeneous and Homogeneous Systems of Equations -- 1.4.2 Existence of Solutions -- 1.4.3 Numerical Solution Methods -- 1.4.4 Norms and Condition Number -- 1.5 Eigenvalue Problems -- 1.5.1 General Eigenvalue Problem -- 1.5.2 Numerical Solution of Eigenvalue Problems -- Exercises -- References -- 2 Basic Equations of the Theory of Elasticity -- 2.1 Types of Structures -- 2.2 One-Dimensional and Two-Dimensional States of Stress -- 2.3 Beams and Plates in Bending -- 2.4 Spatial Structures -- 2.4.1 Generals -- 2.4.2 Beams -- 2.4.3 Solids -- References -- 3 Truss and Beam Structures -- 3.1 Introduction -- 3.1.1 The Finite Element Method in Structural Analysis -- 3.1.2 Nodal Points, Degrees of Freedom, and Finite Elements -- 3.1.3 Computational Method -- 3.2 Introductory Example: Plane Truss System -- 3.2.1 Structural System -- 3.2.2 Element Stiffness Matrix of a Truss Element -- 3.2.3 Coordinate Transformation -- 3.2.4 Global Stiffness Matrix -- 3.2.5 Support Conditions -- 3.2.6 Solution of the System of Equations -- 3.2.7 Support Forces and Element Stresses -- 3.2.8 Flexibility Matrix -- 3.3 Elastic Springs -- 3.3.1 Elastic Support of Nodal Points -- 3.3.2 Spring Elements -- 3.4 Beams in Bending -- 3.4.1 Stiffness Matrix of the Beam Element -- 3.4.2 Element Loads -- 3.4.3 Extension of the Stiffness Matrix of the Beam Element -- 3.4.4 Coordinate Transformation -- 3.4.5 Hinges -- 3.5 Combined Beam and Truss Systems -- 3.6 Spatial Trusses and Beam Structures -- 3.6.1 3D Truss Element -- 3.6.2 3D Beam Element -- 3.6.3 Beam Element with Warping Torsion -- 3.7 Modeling of Beam Structures. ; 3.7.1 Supports -- 3.7.2 Springs -- 3.7.3 Beam Structures -- 3.7.4 Symmetrical Structures -- 3.8 Quality Assurance and Documentation -- 3.8.1 Sources of Error -- 3.8.2 Checking of Beam Structures Computations -- 3.8.3 Documentation of Finite Element Analyses -- Exercises -- References -- 4 Plate, Shell, and Solid Structures -- 4.1 Historical Background -- 4.2 Basic Concepts -- 4.3 Approximation Character of the Finite Element Method -- 4.3.1 One-Dimensional Introductory Example -- 4.3.2 Analytical Solution -- 4.3.3 FEM Approximate Solution with Linear Shape Functions -- 4.3.4 FEM Approximate Solution with Quadratic Shape Functions -- 4.3.5 Properties of the Finite Element Approximate Solution -- 4.4 Rectangular Elements for Plates in Plane Stress -- 4.4.1 Shape Functions -- 4.4.2 Strains and Stresses -- 4.4.3 Stiffness Matrix -- 4.4.4 Element Loads -- 4.4.5 Examples -- 4.5 Finite Elements for Plates in Plane Stress -- 4.5.1 Properties of Finite Elements -- 4.5.2 Displacement-Based Elements with Compatible Shape Functions -- 4.5.3 Nonconforming Elements -- 4.5.4 Hybrid Elements -- 4.5.5 Other Element Types -- 4.5.6 Element Types in Finite Element Software for Structural Analysis -- 4.6 Rectangular Element for Plates in Bending -- 4.6.1 Element Type -- 4.6.2 Shape Functions -- 4.6.3 Deformations and Section Forces -- 4.6.4 Stiffness Matrix -- 4.6.5 Element Loads -- 4.7 Finite Elements for Plates in Bending -- 4.7.1 Displacement-Based Shear Flexible Elements -- 4.7.2 Displacement-Based Shear Rigid Plate Elements -- 4.7.3 Hybrid Plate Elements -- 4.7.4 Other Element Types -- 4.7.5 Element Types in Finite Element Software for Structural Analysis -- 4.8 Finite Elements for Shells -- 4.8.1 Plane Shell Elements as Superimposed Membrane and Bending Elements -- 4.8.2 Curved Shell Elements as "Degenerated" Solid Elements -- 4.8.3 Axisymmetric Shell Elements. ; 4.8.4 Element Types in Finite Element Software for Structural Analysis -- 4.9 Solid Elements -- 4.9.1 Isoparametric Elements -- 4.9.2 Other Element Types -- 4.9.3 Axisymmetric Solid Elements -- 4.9.4 Element Types in Finite-Element Software for Structural Analysis -- 4.10 Transition between Beam, Plate and Solid Elements -- 4.10.1 Generals -- 4.10.2 Transformation of Element Matrices -- 4.10.3 Connections with Displacement Assumptions (RDT) -- 4.10.4 Connections with Stress Assumptions (EST) -- 4.10.5 Engineering Models -- 4.10.6 Other Element Transitions -- 4.11 Modeling of Structural Elements and Buildings -- 4.11.1 Structural Models -- 4.11.2 Singularities of Stresses and Displacements -- 4.11.3 Element Types and Meshing -- 4.11.4 Mesh Generation -- 4.11.5 Modeling of Plates in Plane Stress -- 4.11.6 Modeling of Plates in Bending -- 4.11.7 Foundation Slabs -- 4.11.8 Modeling of Folded Plate and Shell Structures -- 4.11.9 Three-Dimensional Building Models -- 4.11.10 Interpretation of Results -- 4.12 Quality Assurance and Documentation -- 4.12.1 Types of Error -- 4.12.2 Error Estimation and Adaptive Meshing -- 4.12.3 Checking of Surface and Spatial Structure Computations -- 4.12.4 Documentation of Finite Element Analyses of Surface and Spatial Structures -- Exercises -- References -- 5 Dynamic Analysis of Structures -- 5.1 Introduction -- 5.2 Basic Concepts of Dynamics -- 5.2.1 Kinematics -- 5.2.2 Inertial Forces -- 5.2.3 Damping Forces -- 5.3 Equations of Motion -- 5.4 Free Vibrations -- 5.4.1 Undamped Vibrations -- 5.4.2 Damped Vibrations -- 5.5 Forced Vibrations with Harmonic Excitation -- 5.6 Forced Vibrations with General Dynamic Excitation -- 5.6.1 Generals -- 5.6.2 Direct Numerical Integration -- 5.6.3 Modal Analysis -- 5.6.4 Fourier Transformation -- 5.7 Earthquake Excitation -- 5.7.1 Generals -- 5.7.2 Methods of Analysis. ; 5.7.3 Time History Analysis -- 5.7.4 Response Spectrum Analysis -- 5.8 Modeling for Dynamic Analysis -- 5.8.1 Structural Model -- 5.8.2 Finite Element Model -- 5.8.3 Discretization in Time and Frequency Domain -- 5.8.4 Building Models -- 5.8.5 Soil-Structure Interaction -- 5.8.6 Modeling and Validation -- Exercises -- References -- The Book's Homepage -- -- Index.
• Titolo autorizzato: Finite Elements in Structural Analysis
• ISBN: 3-030-49840-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910483005203321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Tracts in Civil Engineering