Exact Analysis Of Structures With Periodicity Using U Transformation

This book introduces an analytical method, the U-transformation method, for the exact analysis of structures with the periodic property. The physical meaning of U-transformation is fully explained and the application of this technique to derive exact analytical solutions for a wide variety of structures with the periodic property is thoroughly illustrated. The book also provides useful exact and explicit formulas for many practical engineering problems. Many of these solutions are new results that have just appeared in international journals. The practical engineering structures considered in the book include continuous beams, stiffened plates, trusses, grillages, double layer grids and so on. Contents:Uncoupling of the Dynamic Equation for Cyclic Periodic Structures and U-TransformationAnalytical Solutions for Cyclic Periodic StructuresLinear Periodic Structures — Discrete SystemsLinear Periodic Structures — Continuous SystemsStructures with Periodicity in Two DirectionsExact Solution of the Finite Element EquationNearly Periodic Structures Readership: Graduate students, researchers in structural engineering, and design engineers. Keywords:U-Transformation;Periodic Structures;Periodic Mass-Spring Systems;Mode Subspace;Mode Localization;Stiffened Plates;Othogonal Networks;Diagonal Networks;Grids;Double Layer Grids;Disordered System;Stop Band

By using the U-transformation method, it is possible to uncouple linear simultaneous equations, either algebraic or differential, with cyclic periodicity. This book presents a procedure for applying the U-transformation technique twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact solution. Explicit exact solutions for the static and dynamic analyses for certain engineering structures with doubly periodic properties — such as a continuous truss with any number of spans, cable network and grillwork on supports with periodicity, and grillwork with periodic stiffening members or equidistant line supports — can be found in the book. The availability of these exact solutions not only helps with the checking of the convergence and accuracy of numerical solutions, but also provides a basis for optimization design for these types of structures. The study of the force vibration and mode shape of periodic systems with nonlinear disorder is yet another research area which has attained considerable success by the U-transformation method. This book illustrates the analytical approach and procedure for the problems of localization of the mode shape of nearly periodic systems together with the results. Contents:U-Transformation and Uncoupling of Governing Equations for Systems with Cyclic Bi-PeriodicityBi-Periodic Mass-Spring SystemsBi-Periodic StructuresStructures with Bi-Periodicity in Two DirectionsNearly Periodic Systems with Nonlinear Disorders Readership: Practitioners, researchers and graduate students in mechanical engineering, engineering mechanics, civil engineering, mechanics, and numerical & computational mathematics. Keywords:Double U-Transformation;Cyclic Bi-Periodic Equations;Bi-Periodic Mass-Spring Systems;Bi-Periodic Structures;Localized Modes;Mode Subspace;Cable Network;Grillwork;Grid;Pass Band;Nonlinear Disorder;Stop BandReviews:“This book may be useful to students, postgraduate students, engineers and scientists who analyse periodic structures in different areas of technology and science.”Zentralblatt MATH

This book proposes and validates a number of methods and shortcuts for frugal engineers, which will allow them to significantly reduce the computational costs for analysis and reanalysis and, as a result, for structural design processes. The need for accuracy and speed in analyzing structural systems with ever-tighter design tolerances and larger numbers of elements has been relentlessly driving forward research into methods that are capable of analyzing structures at a reasonable computational cost. The methods presented are of particular value in situations where the analysis needs to be repeated hundreds or even thousands of times, as is the case with the optimal design of structures using different metaheuristic algorithms. Featuring methods that are not only applicable to skeletal structures, but by extension also to continuum models, this book will appeal to researchers and engineers involved in the computer-aided analysis and design of structures, and to software developers in this field. It also serves as a complement to previous books on the optimal analysis of large-scale structures utilizing concepts of symmetry and regularity. Further, its novel application of graph-theoretical methods is of interest to mathematicians.

This book contains the papers presented at two conferences organized by the Wessex Institute of Technology. The first conference is the Seventh International Conference on Computer Simulation in Risk Analysis and Hazard Mitigation, being held in Algarve, Portugal, September 13-15. This biennial conference is the latest in a successful series that began in 1998 and that includes many practical applications, demonstrating how to analyze and manage risk and mitigate hazards. The applications cover man-made as well as natural hazards, the importance of which is becoming increasingly evident in our modern world. These problems have become a priority for all governments, as well as a cause for public concern. The second conference is the Fifth International Conference on Prevention, Assessment, Rehabilitation and Development of Brownfield Sites, also being held in Algarve, September 14-16. The biennial conference was first held in 2002 and covers the challenges the public and private sectors must face in seeking to reuse brownfield sites and to capitalize on the opportunities.

The achievements and biographical details of nearly 1,500 key researchers and practitioners in the fields of computational mechanics, applied mathematics, computer science, artificial intelligence, aerospace, aeronautical, chemical, civil, environmental, mechanical, and structural engineering are included in this directory.