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Optimization of Finite Dimensional Structures





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ISBN 9781439820032
Published July 2, 2010 by CRC Press
439 Pages 183 B/W Illustrations

 
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Book Description

Originally developed for mechanical and aeronautical engineering, structural optimization is not so easily applied to civil and architectural engineering, as structures in these fields are not mass products, but more often unique structures planned in accordance with specific design requirements. The shape and geometry of such structures are determined by a designer or an architect in view of nonstructural performance that includes aesthetics. Until now, books in this area gave little help to engineers working in cooperation with designers, as they covered conceptual material with little consideration of civil engineering applications, or they required a solid background in applied mathematics and continuum mechanics, an area not usually studied by practicing engineers and students in civil engineering.

Optimization of Finite Dimensional Structures introduces methodologies and applications that are closely related to design problems encountered in structural optimization, to serve as a bridge between the communities of structural optimization in mechanical engineering and the researchers and engineers in civil engineering. This unparalleled, self-contained work:

  • Provides readers with the basics of optimization of frame structures, such as trusses, building frames, and long-span structures, with descriptions of various applications to real-world problems
  • Summarizes the historical development of methodologies and theorems on optimization of frame structures
  • Introduces many recently developed highly efficient optimization techniques presented with illustrative examples
  • Describes traditional problems with constraints on limit loads, member stresses, compliance, and eigenvalues of vibration, all in detail
  • Offers a unique look at optimization results for spatial trusses and latticed domes

Mathematical preliminaries and methodologies are summarized in the book’s appendix, so that readers can attend to the details when needed without having to wade through tedious mathematics in the explanatory main chapters. Instead, small examples that can be solved by hand or by using a simple program are presented in these chapters, making the book readily accessible and highly useful for both classroom use and professional self-study.

Table of Contents

Various Formulations of Structural Optimization
Overview of structural optimization
History of structural optimization
Structural optimization problem
Plastic design
Stress constraints
Fully-stressed design
Optimality criteria approach
Compliance constraint
Frequency constraints
Configuration optimization of trusses
Multiobjective structural optimization
Heuristic approach
Simultaneous analysis and design
Design Sensitivity Analysis
Overview of design sensitivity analysis
Static responses
Eigenvalues of free vibration
Linear buckling load
Transient responses
Nonlinear responses
Shape sensitivity analysis of trusses
Topology Optimization of Trusses
Introduction
Michell truss
Topology optimization problem
Optimization methods
Stress constraints
Mixed integer programming for topology optimization with discrete variables
Genetic algorithm for truss topology optimization
Random search method using exact reanalysis
Multiple eigenvalue constraints
Application of data mining
Configuration Optimization of Trusses
Introduction
General formulation and methodologies of configuration optimization
Generation of a link mechanism
Optimization of Building Frames
Overview of optimization of building frames
Local and global searches of approximate optimal designs
Parametric optimization of frames
Local search for multiobjective optimization of frames
Multiobjective seismic design of building frames
Optimization of Spatial Trusses and Frames
Introduction
Seismic optimization of spatial trusses
Heuristic approaches to optimization of a spatial frame
Shape optimization considering the designer’s preference
Shape optimization of a single-layer latticed shell
Configuration optimization of an arch-type truss with local geometrical constraints
Seismic design for spatially varying ground motions
Substructure approach to seismic optimization
Appendix
Mathematical preliminaries
Rayleigh’s principle
Singular value decomposition
Directional derivative and subgradient
Optimization methods
Single-point-search heuristics
Multiobjective programming
Constraint approach
Linear weighted sum approach
Goal programming
Parametric structural optimization problem
Bezier surface
Adjoint curve
Response spectrum approach
CQC method
Design response spectrum
Sensitivity analysis of mean maximum response
List of available standard sections of beams and columns

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