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Elasto-Plastic and Damage Analysis of Plates and Shells

:	George Z. Voyiadjis, Pawel Woelke
:	Elasto-Plastic and Damage Analysis of Plates and Shells
:	Springer-Verlag
:	9783540793519
:	1
:	CHF 132.50
:

:	Maschinenbau, Fertigungstechnik
:	English

:	208
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Shells and plates are critical structures in numerous engineering applications. Analysis and design of these structures is of continuing interest to the scienti c and engineering communities. Accurate and conservative assessments of the maximum load carried by a structure, as well as the equilibrium path in both the elastic and inelastic range, are of paramount importance to the engineer. The elastic behavior of shells has been closely investigated, mostly by means of the nite element method. Inelastic analysis however, especially accounting for damage effects, has received much less attention from researchers. In this book, we present a computational model for nite element, elasto-plastic, and damage analysis of thin and thick shells. Formulation of the model proceeds in several stages. First, we develop a theory for thick spherical shells, providing a set of shell constitutive equations. These equations incorporate the effects of transverse shear deformation, initial curvature, and radial stresses. The proposed shell equations are conveniently used in nite element analysis. 0 AsimpleC quadrilateral, doubly curved shell element is developed. By means of a quasi-conforming technique, shear and membrane locking are prevented. The element stiffness matrix is given explicitly, making the formulation computationally ef cient. We represent the elasto-plastic behavior of thick shells and plates by means of the non-layered model, using an Updated Lagrangian method to describe a small-strain geometric non-linearity. For the treatment of material non-linearities, we adopt an Iliushin's yield function expressed in terms of stress resultants, with isotropic and kinematic hardening rules.

	Professor Maciej Bieniek	7
	Preface	9
	Contents	11
	Introduction	15
	1.1 Shell Structures	15
	1.2 Motivation and Scope	18
	1.3 Basic Assumptions	19
	References	20
	Shell Constitutive Equations	21
	2.1 Introduction	21
	2.1.1 Thickness of the Shell	22
	2.1.2 Initial Curvature and Radial (Transverse Normal) Stresses	24
	2.2 Plate Constitutive Equations	25
	2.2.1 Stresses and Stress Resultants in a Thin Plate	25
	2.2.2 Equilibrium Equations and Governing Differential Equation of Plate	27
	2.2.3 Transverse Shear and Transverse Normal Stresses in a Plate	29
	2.3 Coordinate Transformation Ò Strains in Spherical Coordinates	31
	2.4 Theoretical Formulation of the Shell Equations	36
	2.4.1 Assumed Out-of-Plane Stress Components	36
	2.4.2 Displacement Field	39
	2.4.3 Stress Components	42
	2.4.4 Stress Couples and Stress Resultants on the Middle Surface	44
	2.4.5 Average Displacements	48
	2.4.6 Equilibrium Equations and Boundary Conditions	52
	2.4.7 The Non-Linear Nature of the Stress Distribution	53
	2.4.8 The Equivalent Formulation for Thick Plates	55
	2.5 Examples	55
	2.5.1 Thick Sphere Subjected to Uniform Pressures	56
	2.5.2 Thick Cylinder Subjected to Uniform Pressures	58
	2.6 Summary	59
	References	60
	Shell Element Based on the Refined Theory of Thick Spherical Shells	63
	3.1 Introduction	63
	3.1.1 Shear Locking	63
	3.1.2 Membrane Locking	66
	3.1.3 Mesh Instabilities	67
	3.2 Finite Element Formulation	68
	3.2.1 Shell Constitutive Equations	68
	3.2.2 Displacements and Boundary Conditions	69
	3.2.3 Element Displacement and Strain Fields – Quasi- Conforming Method	71
	3.2.4 Strain Energy and Stiffness Matrix	76
	3.3 Numerical Examples	78
	3.3.1 The Patch Test	79
	3.3.2 Cantilevered Beam	79
	3.3.3 Morley’s Hemispherical Shell (Morley and Moris, 1978)	80
	3.3.4 Pinched Cylinder with Diaphragms	83
	3.3.5 Scordellis-Lo Roof	84
	3.3.6 P