Reanalysis of Structures: A Unified Approach for Linear, Nonlinear, Static and Dynamic Systems

ISBN-13: 9781402081972 / Angielski / Twarda / 2008 / 308 str.

Uri Kirsch

Opis

This book deals with multiple repeated analyses (reanalysis) of structures. Reanalysis is needed in many problems of structural analysis, design and optimization. It is related to a wide range of applications in Aerospace - gineering, Civil Engineering, Mechanical Engineering and Naval Archit- ture. The book was developed while I was teaching graduate courses on analysis, design and optimization of structures, in the United States, C- ada, Europe and Israel. It summarizes many years of research and dev- opments in these areas. The purpose of the book is to collect together the main results of this work and to present them in a unified approach. It meets the need for a general text covering the basic concepts as well as - cent developments on reanalysis of structures. This should prove useful to students, researchers, consultants and practicing engineers involved in structural analysis and design. Other books on structural analysis do not cover most of the topics presented in the book. Early developments on this subject are introduced in a previous book by the author (Design-Oriented Analysis of Structures, Kluwer Academic Publishers, Dordrecht 2002). In general, the structural response cannot be expressed explicitly in terms of the structure properties, and structural analysis involves solution of a set of simultaneous equations. Reanalysis methods are intended to analyze efficiently structures that are modified due to changes in the str- ture properties. The object is to evaluate the structural response (e. g.

Recenzje

From the reviews:

"The author treats the reanalysis of structures as multiple repeated analyses. ... The book introduces effective computational procedures for reanalysis. ... This well-written and well-organized book is a reader-friendly manual in the field of computational structural mechanics. It can be recommended for graduate, postgraduate and doctoral students." (Igor Andrianov, Zentralblatt MATH, Vol. 1141, 2008)

Spis treści

Contents 1 Static Analysis 1.1 Linear Analysis of Framed Structures 1.2 Linear Analysis of Continuum Structures 1.3 Solution of the Linear Equilibrium Equations 1.3.1 Matrix Factorization 1.3.2 Iterative Solution Procedures 1.4 Nonlinear Analysis 1.4.1 Geometric Nonlinearity 1.4.2 Material Nonlinearity 1.4.3 Time Varying Loads 1.4.4 Buckling Analysis 1.4.5 Solution of the Nonlinear Equations References 2 Vibration Analysis 2.1 Free Vibration 2.1.1 Properties of the Eigenproblem 2.1.2 The Standard Eigenproblem and the Rayleigh Quotient 2.2 Solution of the Eigenproblem 2.2.1 Static Condensation 2.2.2 Solution Methods 2.3 Vector Iteration Methods 2.3.1 Inverse Vector Iteration 2.3.2 Vector Iteration with Shifts 2.3.3 Matrix Deflation and Gram-Schmidt Orthogonalization 2.4 Transformation Methods 2.5 Polynomial Iterations 2.6 Rayleigh-Ritz Analysis 2.6.1 Approximate Eigenproblem Solution 2.6.2 Load-Dependent Ritz Vectors 2.7 The Lanczos Method 2.8 Subspace Iteration References 3 Dynamic Analysis 3.1 Linear Dynamic Analysis 3.1.1 Direct Integration 3.1.2 Mode Superposition 3.1.3 Special Analysis Procedures 3.2 Reduced Basis 3.2.1 Static Analysis 3.2.2 Dynamic Analysis 3.3 Nonlinear Dynamic Analysis 3.3.1 Implicit Integration 3.3.2 Mode Superposition References 4 Reanalysis of Structures 4.1 Design Variables 4.2 Formulation of Static Reanalysis 4.2.1 Linear Static Reanalysis 4.2.2 Nonlinear Static Reanalysis 4.3 Formulation of Vibration Reanalysis 4.3.1 Eigenproblem Reanalysis 4.3.2 Iterative Procedures 4.4 Formulation of Dynamic Reanalysis 4.4.1 Linear Dynamic Reanalysis 4.4.2 Nonlinear Dynamic Reanalysis 4.5 Reanalysis Methods 4.5.1 Direct Methods 4.5.2 Approximate Methods 4.5.3 The Combined Approximations Approach References 5 Static Reanalysis 5.1 Determination of the Basis Vectors 5.1.1 The Binomial Series 5.1.2 Calculation of the Basis Vectors 5.1.3 Convergence of the Series 5.2 Linear Reanalysis 5.2.1 Coupled Basis Vectors 5.2.2 Uncoupled Basis Vectors 5.3 Topological Changes 5.3.1 Number of DOF is Decreased 5.3.2 Number of DOF is Increased 5.4 Nonlinear Analysis and Reanalysis 5.4.1 Problem Formulation 5.4.2 Solution by Combined Approximations 5.4.3 Procedures for Analysis and Reanalysis References 6 Vibration Reanalysis 6.1 The Reduced Eigenproblem 6.1.1 Problem Formulation 6.1.2 Determination of the Basis Vectors 6.2 Improved Basis Vectors 6.2.1 Gram-Schmidt Orthogonalizations of the Modes 6.2.2 Shifts of the Basis Vectors 6.2.3 Gram-Schmidt Orthogonalizations of the Basis Vectors 6.3 General Solution Procedure 6.4 Numerical Examples 6.5 Reanalysis by Iterative Procedures References 7 Dynamic Reanalysis 7.1 Linear Dynamic Reanalysis 7.1.1 Solution by Direct Integration 7.1.2 Solution by Mode Superposition 7.2 Nonlinear Dynamic Reanalysis 7.2.1 Solution by Implicit Integration 7.2.2 Solution by Mode Superposition References 8 Direct Reanalysis 8.1 Direct Methods 8.1.1 A Single Rank-One Change 8.1.2 Multiple Rank-One Changes 8.1.3 General Procedure 8.2 Direct Solutions by Combined Approximations. 8.2.1 Multiple Rank-One Changes 8.2.2 Solution Procedure

Blurb

This book deals with various computational procedures for multiple repeated analyses (reanalysis) of structures, and presents them in a unified approach. It meets the need for a general text covering the basic concepts and methods as well as recent developments in this area. Reanalysis is common to numerous analysis and design tasks such as nonlinear analysis, structural optimization, damage analysis, and probabilistic analysis. The book discusses various analysis models, including linear and nonlinear analysis, static and dynamic analysis, and design sensitivity analysis. It demonstrates how various concepts and methods are integrated to achieve effective solution procedures. The approach presented has several advantages in terms of generality, efficiency of the calculations, accuracy of the results and ease of implementation. Efficiency and accuracy considerations are discussed and illustrated. To clarify the presentation, many illustrative examples and numerical results are demonstrated. The text is related to a wide range of applications in such fields as Mechanical Engineering, Aerospace Engineering, Civil Engineering, and Naval Architecture. This should prove useful to students, researchers, analysts and consultants involved in analysis and design of structures. Previous books on structural analysis do not cover most of the material presented in the book.