CiNii 図書 - Finite rotation shells : basic equations and finite elements for reissner kinematics

The objective of this book is to provide a comprehensive introduction to ?nite rotation shells and to non-linear shell ?nite elements. It is divided into 5 parts: I. Preliminaries (20 pages), II. Shell equations (104 pages), III. Finite rotations for shells (103 pages), IV. Four-node shell elements (189 pages), and V. Numerical examples (41 pages). Additional numerical examples are presented in Parts III and IV. The bibliography includes 270 entries. The book is intended for both teaching and self-study, and emphasizes fundamental aspects and techniques of the subject. Some familiarity with non-linear mechanics and the ?nite element method is assumed. Shell elements are a subject of active research which results in many publications every year and several conferences and sessions are held r- ularly, among them, two large international conferences: \Computation of Shell and Spatial Structures" and \Shell Structures. Theory and - plications" (SSTA). The literature is voluminous, not easy to follow and evaluate, and the subject is di–cult to comprehend. I hope that this will be facilitated by the book. I would like to express my gratitude to several persons who helped me in my professional life, in this way contributing to the book. I thank Prof. R.L. Taylor from the University of California at Berkeley, Prof. B. Schre er from the University of Padua, and Prof. J.T. Santos from the Instituto Superior Tecnico at Lisbon, for hosting and supporting me when I was a post-doctoral researcher.

Proviosional Table of contents (October 2009) I PRELIMINARIES
1 Introduction
1.1 Subject of this book
1.2 Notation
2 Operations on tensors and their representations
2.1 Cartesian bases
2.2 Normal bases
2.3 Gradients and derivatives
II SHELL EQUATIONS
3 Rotations for 3D Cauchy continuum
3.1 Polar decomposition of deformation gradient
3.2 Rotation Constraint equation
3.3 Interpretation of rotation Q
3.4 Rate form of RC equation
3.5 Rotations calculated from the RC equation
4 3D formulations with rotations
4.1 Governing equations
4.2 4-F formulation for nominal stress
4.3 3-F formulation for nominal stress
4.4 3-F and 2-F formulations for Biot stress
4.5 3-F and 2-F formulations for 2nd Piola-Kirchhoff stress
4.6 2-F formulation with unconstrained rotations
5 Basic geometric definitions for shells
5.1 Coordinates and position vector
5.2 Basic geometric definitions
5.3 Example: Geometrical description of cylinder
6 Shells with Reissner kinematics and drilling rotation
6.1 Kinematics
6.2 Rotation Constraint for shells
6.3 Shell strains
6.4 Virtual work equation for shell
6.5 Local shell equations
6.6 Enhanced shell kinematics
7 Shell-type constitutive equations
7.1 Constitutive equations for 3D shells
7.2 Reduced shell constitutive equations
7.3 Shear correction factor
III FINITE ROTATIONS FOR SHELLS
8 Parametrization of finite rotations
8.1 Basic properties of rotations
8.2 Parametrization of rotations
8.3 Composition of rotations
9 Algorithmic schemes for finite rotations
9.1 Increments of rotation vectors in two tangent planes
9.2 Variation of rotation tensor
9.3 Algorithmic schemes for finite rotations
9.4 Angular velocity and acceleration
IV FOUR-NODE SHELL ELEMENTS
10 Basic relations for 4-node shell elements
10.1 Bilinear isoparametric approximations
10.2 Geometry and bases of shell element
10.3 Jacobian matrices
10.4 Deformation gradient, FTF and QTF products
10.5 Numerical integration of shell elements
10.6 Newton method and tangent operator
11 Plane 4-node elements (without drilling rotation)
11.1 Basic equations
11.2 Displacement element Q4
11.3 Solution of FE equations for problems with additional variables
11.4 Enhanced strain elements based on potential energy
11.5 Mixed Hellinger-Reissner and Hu-Washizu elements
11.6 Modification of FTF product
12 Plane 4-node elements with drilling rotation
12.1 Basic relations for drill RC equation
12.2 Difficulties in approximation of drill RC
12.3 Implementation of drill RC in finite elements
12.4 EADG method for formulations with rotations
12.5 Mixed HW and HR functionals with rotations
12.6 2D+drill elements for bi-linear shape functions
12.7 2D+drill elements for Allman shape functions
12.8 Numerical tests
13 Modification of transverse shear stiffness of shell element
13.1 Treatment of transverse shear stiffness of beams
13.2 Treatment of transverse shear stiffness of shell
14 Warped 4-node shell element
14.1 Definition of warpage
14.2 Warped element with modifications
14.3 Substitute flat element and warpage correction
14.4 Membrane locking of curved shell elements
14.5 Remarks on approximation of curved surfaces by 4-node elements
V NUMERICAL EXAMPLES
15 Numerical tests
15.1 Characteristics of tested shell elements
15.2 Elementary and linear tests
15.3 Nonlinear tests
References
Author index
Subject Index

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