By J. N. Reddy

Simply because plates and shells are universal structural parts in aerospace, automobile, and civil engineering buildings, engineers needs to comprehend the habit of such constructions in the course of the examine of idea and research. Compiling this knowledge right into a unmarried quantity, conception and research of Elastic Plates and Shells, moment version offers a whole, up to date, and unified therapy of classical and shear deformation plates and shells, from the elemental derivation of theories to analytical and numerical solutions.

Revised and up-to-date, this moment version contains new info in such a lot chapters, in addition to a few rearrangement of issues to enhance the readability of the final presentation. The ebook offers new fabric at the conception and research of shells, that includes an extra bankruptcy dedicated to the subject. the writer additionally comprises new sections that deal with Castigliano's theorems, axisymmetric buckling of round plates, the relationships among the strategies of classical and shear deformation theories, and the nonlinear finite point research of plates. The booklet presents many illustrations of theories, formulations, and answer equipment, leading to an easy-to-understand presentation of the topics.

Like the former version, this e-book is still an appropriate textbook for a direction on plates and shells in aerospace, civil, and mechanical engineering curricula and maintains to function a reference for commercial and educational structural engineers and scientists.

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**Example text**

If a matrix has m rows and n columns, we will say that it is m by n (m × n), the number of rows always being listed first. The element in the ith row and jth column of a matrix [C] is generally denoted by cij , and we 12 Theory and Analysis of Elastic Plates and Shells will sometimes write [C] = [cij ] to denote this. A square matrix is one that has the same number of rows as columns. , c11 , c22 , · · · , cnn ) are called diagonal elements. The sum of the diagonal elements is called the trace of the matrix.

The energy approach yields not only the equations of motion, but also the force boundary conditions as well as the form of the variables involved in the specification of geometric boundary conditions. In addition, the energy expressions are useful in obtaining approximate solutions by direct variational methods, such as the Ritz and finite element methods. In most of the present study, the principles of virtual work will be used to derive the equations of motion of plates and shells. We begin with the concepts of virtual displacements and virtual forces and work and energy.

24). 6 Constitutive Equations The kinematic relations and the mechanical and thermodynamic principles are applicable to any continuum irrespective of its physical constitution. Here we consider equations characterizing the individual material and its reaction to applied loads. These equations are called the constitutive equations. , constitutive axioms). We will not discuss them here, but will review the linear constitutive relations for solids undergoing small deformations. A material body is said to be homogeneous if the material properties are the same throughout the body.