Title page for ETD etd-07082005-043614

Type of Document Dissertation
Author Woelke, Pawel Benedykt
Author's Email Address pwoelk1@lsu.edu
URN etd-07082005-043614
Title Computational Model for Elasto-Plastic and Damage Analysis of Plates and Shells
Degree Doctor of Philosophy (Ph.D.)
Department Civil & Environmental Engineering
Advisory Committee
Advisor Name Title
George Z. Voyiadjis Committee Chair
Piotr Perzyna Committee Member
Steve Cai Committee Member
Su-Seng Pang Committee Member
Suresh Moorthy Committee Member
Tomasz Lodygowski Committee Member
Blaise Bourdin Dean's Representative
  • transverse shear strains
  • plates and shells
  • damage in shells
  • plastic shells with mixed hardening
  • large rotations
  • shear and membrane locking
Date of Defense 2005-06-06
Availability unrestricted
Shells and plates are very important for various engineering applications. Analysis and design of these structures is therefore continuously of interest to the scientific and engineering community. Accurate and conservative assessments of the maximum load carried by the structure, as well as the equilibrium path in both elastic and inelastic range are of paramount importance.

Elastic behaviour of shells has been very closely investigated, mostly by means of the finite element method. Inelastic analysis on the other hand, especially accounting for damage effects, has received much less attention from the researchers.

A computational model for finite element, elasto-plastic and damage analysis of homogenous and isotropic shells is presented here. The formulation of the model proceeds in several stages, described in the following chapters. First, a theory for thick spherical shells is developed, 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 finite element analysis. A simple C0 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 which makes this formulation computationally very efficient.

The elasto-plastic behavior of thick shells and plates is represented by means of the non-layered model, with an Updated Lagrangian method used to describe a small strain geometric non-linearity. In the treatment of material non-linearities an Iliushin?s yield function expressed in terms of stress resultants is adopted, with isotropic and kinematic hardening rules.

Finally, the damage effects modeled through the evolution of porosity are incorporated into the yield function, giving a generalized and convenient yield surface expressed in terms of the stress resultants. Since the elastic stiffness matrix is derived explicitly, and a non-layered model is employed in which integration through the thickness is not necessary, the current stiffness matrix is also given explicitly and numerical integration is not performed at any stage during the analysis. This makes this model consistent mathematically, accurate for a variety of applications and very inexpensive from the point of view of computer power.

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