Elasto-Plastic and Damage Analysis of Plates and Shells

1. Front Matter

   Pages I-XIV

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2. Introduction

   • George Z. Voyiadjis, Pawel Woelke

   Pages 1-6

3. Shell Constitutive Equations

   • George Z. Voyiadjis, Pawel Woelke

   Pages 7-47

4. Shell Element Based on the Refined Theory of Thick Spherical Shells

   • George Z. Voyiadjis, Pawel Woelke

   Pages 49-75

5. Geometrically Non-linear Finite Element Analysis of Thick Plates and Shells

   • George Z. Voyiadjis, Pawel Woelke

   Pages 77-90

6. Elasto-Plastic Geometrically Non-linear Finite Element Analysis of Thick Plates and Shells

   • George Z. Voyiadjis, Pawel Woelke

   Pages 91-117

7. Elasto-Plastic Geometrically Non-linear Finite Element Analysis of Thick Plates and Shells With Damage Due to Microvoids

   • George Z. Voyiadjis, Pawel Woelke

   Pages 119-143

8. Non-linear Post Buckling Finite Element Analysis of Plates and Shells

   • George Z. Voyiadjis, Pawel Woelke

   Pages 145-161

9. Determination of Transverse Shear Stresses and Delamination in Composite Laminates Using Finite Elements

   • George Z. Voyiadjis, Pawel Woelke

   Pages 163-183

10. Numerical Methods and Computational Algorithms

    • George Z. Voyiadjis, Pawel Woelke

    Pages 185-197

11. Back Matter

    Pages 199-200

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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.

• Bauschinger effect
• Damage in shells
• Porosity
• Scalar damage variable
• Thick/ thin plates and shells
• explicit stiffness matrix
• kinetic hardening
• modeling
• numerical methods
• shear and membrane locking
• shell finite element
• stress resultant based yield surface

• Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, USA

  George Z. Voyiadjis

• Applied Science Dept, Weidlinger Associates, Inc, New York, USA

  Pawel Woelke

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