Static and Dynamic Analyses of Plates and Shells: Theory, Software and Applications

Static and Dynamic Analyses of Plates and Shells: Theory, Software and Applications

by Hou-Cheng Huang

Paperback(Softcover reprint of the original 1st ed. 1989)

$96.76 $99.00 Save 2% Current price is $96.76, Original price is $99. You Save 2%.
View All Available Formats & Editions

Product Details

ISBN-13: 9781447116714
Publisher: Springer London
Publication date: 12/31/2013
Edition description: Softcover reprint of the original 1st ed. 1989
Pages: 194
Product dimensions: 6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

1 Introduction.- 1.1 Changing Trends in Shell Analysis.- 1.2 Reliability of Finite Element Analysis.- 1.3 Shell Element Formulations.- 1.4 Objective and Layout.- 2 Degenerations of Three-Dimensional Theory.- 2.1 Introduction.- 2.2 Three-Dimensional Theory.- 2.3 Plate Theory.- 2.3.1 Thin Plate Theory (Kirchhoff hypothesis).- 2.3.2 Thick Plate Theory (Mindlin-Reissner Hypothesis).- 2.4 Three-Dimensional Degenerated Curved Shell.- 2.4.1 Definition of Strains.- 2.4.2 Definition of Stresses.- 2.4.3 The Total Potential Energy.- 3 Defects of Mindlin Plate and Degenerated Shell Elements.- 3.1 Introduction.- 3.2 Formulation of Mindlin Plate Bending Elements.- 3.2.1 Formulation of Mindlin Isoparametric Bending Elements.- 3.2.2 Finite Element Representations of Boundary Conditions.- 3.3 Formulation of Degenerated Shell Elements.- 3.3.1 Coordinate Systems.- 3.3.2 Element Geometry.- 3.3.3 Displacement Field.- 3.4 Defects of Mindlin Plate and Degenerated Shell Elements.- 3.4.1 Locking Phenomena.- 3.4.2 Reduced and Selective Integration.- 3.4.3 Alternative Methods Avoiding the Locking Problems.- 4 Assumed Strain Finite Element Plate Formulations.- 4.1 Introduction.- 4.2 Essence of Shear Locking.- 4.3 Reinterpretation of Selectively Integrated Elements.- 4.4 Elimination of Shear Locking.- 4.4.1 Assumed Transverse Shear Strain Fields.- 4.4.2 Location of the Sampling Points for the Shear Strains.- 4.4.3 The Evaluation of the Stiffness Matrix.- 5 Linear Benchmark Tests for Plate Elements.- 5.1 Introduction.- 5.2 Eigen-Analyses of the Stiffness Matrices.- 5.3 Patch Tests.- 5.3.1 Patch Tests for Bending.- 5.3.2 Patch Tests for Twisting.- 5.3.3 Patch Tests for Shear.- 5.4 Locking Tests.- 5.5 Long Cantilever.- 5.6 Convergence Tests.- 5.6.1 Simply Supported Square Plates under Uniform Load.- 5.6.2 Clamped Square Plate under Uniform Load.- 5.6.3 Clamped Circular Plates.- 5.7 Skew Plates.- 5.7.1 Razzaque’s 60° Skew Plate.- 5.7.2 Morley’s 30° Skew Plate.- 5.8 Stress Resultant Study.- 6 Assumed Strain Finite Element Shell Formulations.- 6.1 Introduction.- 6.2 Shear Locking, Membrane Locking and Selective Integration.- 6.2.1 Shear Locking in Shells.- 6.2.2 Essence of Membrane Locking.- 6.3 Elimination of Shear Locking.- 6.4 Elimination of Membrane Locking.- 6.4.1 Orthogonal Curvilinear Coordinate System (r, s, t or ri).- 6.4.2 Assumed Membrane Strains.- 6.5 Assumed Strain Degenerated Shell Elements.- 6.5.1 Location of Sampling Points for the Membrane Strains.- 6.5.2 The Evaluation of the Stiffness Matrix.- 6.6 Discussion.- 7 Linear Benchmark Tests for Shell Elements.- 7.1 Introduction.- 7.2 Eigen-Analysis of the Stiffness Matrices.- 7.3 Patch Tests.- 7.3.1 Bending, Twisting and Shear Patch Tests.- 7.3.2 Plane Stress Patch Tests.- 7.4 Locking Tests.- 7.4.1 Shear Locking Tests.- 7.4.2 Membrane Locking Tests.- 7.5 Conclusions.- 8 Formulations and Applications for Elasto-Plastic Shell Analyses.- 8.1 Introduction.- 8.2 Laminated Plate and Shell Model.- 8.3 Shear Correction Factors.- 8.4 The Anisotropic Yield Criterion.- 8.4.1 Generalised Huber-Mises Yield Criterion.- 8.4.2 Determination of Anisotropic Parameters.- 8.4.3 Relation between Elasto-Plastic Stresses and Strains.- 8.4.4 Tangent Stiffness Matrix.- 8.5 Numerical Examples.- 8.5.1 Clamped Square Plate.- 8.5.2 Clamped Quadratic Shell.- 9 Formulations and Applications for Elasto-Plastic Dynamic Shell Analyses.- 9.1 Introduction.- 9.2 Dynamic Equilibrium Equations.- 9.3 Modelling of Mass Matrix.- 9.3.1 Consistent Mass Matrix.- 9.3.2 Lumped Mass Matrix.- 9.4 Newmark’s Time Stepping Scheme.- 9.5 Numerical Examples.- 9.5.1 Rectangular Plate.- 9.5.2 Simply Supported Square Plate.- 9.5.3 Clamped Circular Plate.- 9.5.4 Spherical Shell Caps.- Appendix 1 Software Description for Elasto-Plastic Static Analysis.- A1.1 Introduction.- A1.2 Glossary of Variable Names.- A1.2.1 Main Arrays.- A1.2.2 Main Variables.- A1.3 Program Overview.- A1.4 File Handling.- A1.4.1 Subroutine INPUT.- A1.4.2 User Instructions.- A1.4.3 Files.- A1.5 Documented Example — Clamped Quadratic Shell.- A1.5.1 Input Data File.- A1.5.2 Output Data File.- A1.6 Stiffness Evaluation Module.- A1.6.1 Subroutine for Evaluation of Stiffness Matrix.- A1.6.2 Evaluation of Strain-Displacement Matrix.- A1.6.3 Subroutine BSAMP.- A1.6.4 Subroutine FUNC.- A1.6.5 Subroutine FRAME.- A1.6.6 Subroutine SFR1.- A1.6.7 Subroutine SFR3.- A1.6.8 Subroutine TBMAT.- A1.6.9 Subroutine XDIC.- Appendix 2 Software Descriptions for Elasto-Plastic Transient Analysis.- A2.1 Introduction.- A2.2 Glossary of Variable Names.- A2.2.1 Main Arrays.- A2.2.2 Main Variables.- A2.3 Program Overview.- A2.4 File Handling.- A2.4.1 Subroutine INPUTD.- A2.4.2 Subroutine INTIME.- A2.4.3 User Instructions.- A2.4.4 Files.- A2.5 Documented Example — Thin Spherical Cap.- A2.5.1 Input Data File.- A2.5.2 Output Data File.- Author Index.

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews