Spectral analysis of nonlinear elastic shapes

This book concerns the elastic stability of thin-walled structures-- one of the most challenging problems facing structural engineers because of its high degree of nonlinearity-- and introduces the innovative approach of using spectral analysis of the shapes and the stiffness to gain insights into the nonlinear deformations. The methodology greatly facilitates correlating the shape changes with the stiffness changes. Professor Doyle also develops specific computer procedures that complement finite element methods so that the ideas and methods are applicable to general structural problems. Basic validity of the procedures is established using key archetypal problems from buckling/post-buckling of columns, arches, curved plates, and cylindrical shells, all worked out in significant detail. The book is ideal for a wide variety of structural engineers, particularly those in aerospace and civil fields. Researchers in computational mechanics also find a rich source of new ideas for post-processing data from nonlinear analyses. Presents an innovative way of tackling nonlinear elastic stability problems with many new results and insights presented; Adopts a thoroughly modern, computationally based approach using finite elements as its basis as well as for its validations; Reinforces reader understanding with a range of practical problems encompassing arbitrary frame and shell structures; Develops concepts systematically starting with basic deformations of structural members followed by analysis of structures with coupled deformations, progressing seemlessly to the nonlinear analysis of structures and buckling/post-buckling behaviors.

Intro -- Contents -- Notation -- Introduction -- Outline of the Book -- References -- 1 Overview of Shapes and Stiffness -- 1.1 Deformed Shapes of Simple Slender Members -- 1.1.1 Comparison of Types of Loads -- 1.1.2 Deformation Distributions and Degrees of Freedom -- 1.1.3 Thin-Walled Cross Sections -- 1.1.4 3D Continuous Solids -- 1.2 Modeling Continuous Structures -- 1.2.1 Virtual Work Formulation of Equilibrium -- 1.2.2 Euler Method -- 1.2.3 Ritz Method -- 1.3 Structural Stiffness and Its Spectral Properties -- 1.3.1 Discrete Stiffness of Structures

1.3.2 Spectral Properties of the Stiffness Matrix -- 1.4 Spectral Shapes of Slender Members -- 1.4.1 Generating Spectral Shapes -- 1.4.2 Spectral Analysis of Stretching, Bending, and Twisting Actions -- Case I: Axial Stretching -- Case II: Flexure of Beams -- Case III: Twisting of Strips -- 1.4.3 Spectral Form of the Ritz Method -- Explorations -- References -- 2 Shapes with Coupled Deformations -- 2.1 Curved Beams and Arches -- 2.1.1 Strain and Strain Energy -- 2.1.2 Fourier Analysis of Shapes -- Analysis I: Antisymmetric Shapes -- Analysis II: Symmetric Inextensible Shapes

Analysis III: Symmetric Extensible Shapes -- 2.2 Deflec…