Elasto-Plastic and Damage Analysis of Plates and Shells
Elasto-Plastic and Damage Analysis of Plates and Shells

Author: George Z Voyiadjis

Publisher: Springer Science & Business Media

Published: 2008-07-23

Total Pages: 213

ISBN-13: 3540793518

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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.

Elasto-Plastic Behavior of Plates and Shells
Elasto-Plastic Behavior of Plates and Shells

Author:

Publisher:

Published: 1976

Total Pages: 36

ISBN-13:

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For an isotropic solid shell, a yield condition, a strain-hardening rule, and a flow rule have been formulated in terms of the membrane forces and bending moments and the strains and curvatures of the middle surface. The results of the proposed theory are compared to the results of the through-the- thickness integration of the stress-strain relations of the material.

Theory and Analysis of Elastic Plates and Shells, Second Edition
Theory and Analysis of Elastic Plates and Shells, Second Edition

Author: J. N. Reddy

Publisher: CRC Press

Published: 2006-11-20

Total Pages: 584

ISBN-13: 9780849384158

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Because plates and shells are common structural elements in aerospace, automotive, and civil engineering structures, engineers must understand the behavior of such structures through the study of theory and analysis. Compiling this information into a single volume, Theory and Analysis of Elastic Plates and Shells, Second Edition presents a complete, up-to-date, and unified treatment of classical and shear deformation plates and shells, from the basic derivation of theories to analytical and numerical solutions. Revised and updated, this second edition incorporates new information in most chapters, along with some rearrangement of topics to improve the clarity of the overall presentation. The book presents new material on the theory and analysis of shells, featuring an additional chapter devoted to the topic. The author also includes new sections that address Castigliano's theorems, axisymmetric buckling of circular plates, the relationships between the solutions of classical and shear deformation theories, and the nonlinear finite element analysis of plates. The book provides many illustrations of theories, formulations, and solution methods, resulting in an easy-to-understand presentation of the topics. Like the previous edition, this book remains a suitable textbook for a course on plates and shells in aerospace, civil, and mechanical engineering curricula and continues to serve as a reference for industrial and academic structural engineers and scientists.

Plastic Limit Analysis of Plates, Shells and Disks
Plastic Limit Analysis of Plates, Shells and Disks

Author: M.A. Save

Publisher: Elsevier

Published: 1997-12-18

Total Pages: 603

ISBN-13: 0080539114

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This revised and updated edition of a book first published in 1972 has kept the general features of the first edition but as could be expected after two decades there are also substantial differences. For instance optimal design has been completely deleted as the developments in this field have been so great that it warrants a book in itself. The fundamental concepts based on Drucker's postulate rather than those of Prager's assumptions function have been introduced. Problems of cyclic loading have been given some more extensive treatment, both in the general theory and in applications. General indications and references have been added for reinforced concrete plates and shells. A general presentation of the yield condition for both plates and shells has been included and the section on the influence of axial force in plates has been almost re-written. Finally, a chapter has been added exclusively devoted to the numerical approach to limit load and shake-down load evaluation. Like the previous edition the book is directed towards engineering applications. The theory is rigorously developed and is therefore of great use to engineering students in plastic limit analysis. Furthermore, applications to metal and reinforced concrete plates and shells and to metal disks are treated by both analytical and numerical approaches.

Elasto-plastic Analysis of Orthotropic Plates and Shells
Elasto-plastic Analysis of Orthotropic Plates and Shells

Author: Benjamin Whang

Publisher:

Published: 1968

Total Pages: 316

ISBN-13:

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A finite element displacement method is developed for the elasto-plastic analysis of bi-linear strain-hardening orthotropic plates and shells. Two basic approaches in the elasto-plastic analysis, the 'initial stiffness' approach and the 'tangent stiffness' approach are presented and compared. Three separate computer programs have been written; the first two are for the plane stress case. The third program is for the rectangular shallow shells, and it uses elements whose thicknesses are subdivided into equally-spaced layers, each of which is assumed to be in plane stress. (Author).

Advances in the Mechanics of Plates and Shells
Advances in the Mechanics of Plates and Shells

Author: D. Durban

Publisher: Springer Science & Business Media

Published: 2001-02-28

Total Pages: 376

ISBN-13: 0792367855

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The optimal control of flexible structures is an active area of research. The main body of work in this area is concerned with the control of time-dependent displacements and stresses, and assumes linear elastic conditions, namely linear elastic material behavior and small defor- tion. See, e. g. , [1]–[3], the collections of papers [4, 5], and references therein. On the other hand, in the present paper we consider the static optimal control of a structure made of a nonlinear elastic material and und- going large deformation. An important application is the suppression of static or quasi-static elastic deformation in flexible space structures such as parts of satellites by the use of control loads [6]. Solar rad- tion and radiation from other sources induce a temperature field in the structure, which in turn generates an elastic displacement field. The displacements must usually satisfy certain limitations dictated by the allowed working conditions of various orientation-sensitive instruments and antennas in the space vehicle. For example, a parabolic reflector may cease to be effective when undergoing large deflection. The elastic deformation can be reduced by use of control loads, which may be imp- mented via mechanically-based actuators or more modern piezoelectric devices. When the structure under consideration is made of a rubb- like material and is undergoing large deformation, nonlinear material and geometric effects must be taken into account in the analysis.