Elastic Postbuckling Analysis Of Structural Systems
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Elastic Postbuckling Analysis of Structural Systems
This book presents a unified computational approach to postbuckling stability analysis of structures using the Total Potential Energy (TPE) framework. It builds upon the secant matrix technique (N1-N2 method) and introduces the Variable Order Secant Matrix (VoSM) method, providing a robust framework for analyzing reticulated, framed, continuum, and thin-walled systems under large deformations. The book derives the geometric nonlinear finite element formulations using Total Lagrangian (TL) and co-rotational TL formats, ensuring accurate postbuckling analysis. It includes benchmark problems and numerical case studies, making it a valuable resource for graduate students, researchers, and faculty involved in structural stability and advanced postbuckling investigations. Additionally, it serves as an indispensable reference for analyzing and designing steel structures.
Buckling and Postbuckling of Beams, Plates, and Shells
This book contains eight chapters treating the stability of all major areas of the flexural theory. It covers the stability of structures under mechanical and thermal loads and all areas of structural, loading and material types. The structural element may be assumed to be made of a homogeneous/isotropic material, or of a functionally graded material. Structures may experience the bifurcation phenomenon, or they may follow the postbuckling path. This volume explains all these aspects in detail. The book is self-contained and the necessary mathematical concepts and numerical methods are presented in such a way that the reader may easily follow the topics based on these basic tools. It is intended for people working or interested in areas of structural stability under mechanical and/or thermal loads. Some basic knowledge in classical mechanics and theory of elasticity is required.
Stability, Bifurcation and Postcritical Behaviour of Elastic Structures
A comprehensive and systematic analysis of elastic structural stability is presented in this volume. Traditional engineering buckling concepts are discussed in the framework of the Liapunov theory of stability by giving an extensive review of the Koiter approach. The perturbation method for both nonlinear algebraic and differential equations is discussed and adopted as the main tool for postbuckling analysis. The formulation of the buckling problem for the most common engineering structures - rods and frames, plates, shells, and thin-walled beams, is performed and the critical load evaluated for problems of interest. In many cases the postbuckling analysis up to the second order is presented. The use of the Ritz-Galerkin and of the finite element methods is examined as a tool for approximate bifurcation analysis. The volume will provide an up-to-date introduction for non-specialists in elastic stability theory and methods, and is intended for graduate and post-graduate students and researchers interested in nonlinear structural analysis problems. Basic prerequisites are kept to a minimum, a familiarity with elementary algebra and calculus is all that is required of readers to make use of this book.