Problems and Methods of Optimal Structural Design

by Nikolai Vladimirovich Banichuk

Overview

The author offers a systematic and careful development of many aspects of structural optimization, particularly for beams and plates. Some of the results are new and some have appeared only in specialized Soviet journals, or as pro­ ceedings of conferences, and are not easily accessible to Western engineers and mathematicians. Some aspects of the theory presented here, such as optimiza­ tion of anisotropic properties of elastic structural elements, have not been considered to any extent by Western research engineers. The author's treatment is "classical", i.e., employing classical analysis. Classical calculus of variations, the complex variables approach, and the Kolosov­ Muskhelishvili theory are the basic techniques used. He derives many results that are of interest to practical structural engineers, such as optimum designs of structural elements submerged in a flowing fluid (which is of obvious interest in aircraft design, in ship building, in designing turbines, etc.). Optimization with incomplete information concerning the loads (which is the case in a great majority of practical design considerations) is treated thoroughly. For example, one can only estimate the weight of the traffic on a bridge, the wind load, the additional loads if a river floods, or possible earthquake loads.

Product Details

ISBN-13:	9781461336785
Publisher:	Springer US
Publication date:	11/19/2011
Series:	Mathematical Concepts and Methods in Science and Engineering , #26
Edition description:	Softcover reprint of the original 1st ed. 1983
Pages:	313
Product dimensions:	5.98(w) x 9.02(h) x 0.03(d)

Table of Contents

1. Formulation of Problems and Research Techniques in Structural Optimization.- 1.1. Formulation of Some Optimal Design Problems.- 1.2. Basic Functional.- 1.3. Principal and Auxiliary Control Functions.- 1.4. Application of Variational Principles of the Theory of Elasticity to Eliminating Differential Relations.- 1.5. Reduction to Problems with Integral Functions.- 1.6. Necessary Conditions for Optimality.- 1.7. Extremal Conditions for Problems with Nonadditive Functional.- 1.8. Problems with Unknown Boundaries.- 1.9. Dual Problems.- 1.10. Application of Numerical Techniques in Solving Problems of Optimal Design.- 2. One-Dimensional Optimization Problems.- 2.1. Optimization Problems for Beams Subjected to Bending.- 2.2. Optimization of Stability for Elastic Beams.- 2.3. Optimal Configuration of Branched Beams.- 2.4. Design of Optimum Curved Beams.- 2.5. Optimization of Nonuniformly Heated and Prestressed Beams.- 3. Optimal Design of Elastic Plates: Control by Varying Coefficients of the Equations.- 3.1. Plates Having the Greatest Rigidity.- 3.2. Numerical Search for Optimal Thickness Distribution of Homogeneous Plates.- 3.3. Optimal Rigidity of Trilayer Plates.- 3.4. Strongest Plates.- 3.5. Optimum Support Conditions for Thin Plates.- 4. Optimization Problems with Unknown Boundaries in the Theory of Elasticity: Control by Varying the Boundary of the Domain.- 4.1. Maximizing the Torsional Rigidity of a Bar.- 4.2. Finding Optimum Shapes of Cross-Sectional Areas for Bars in Torsion.- 4.3. Torsion of Piecewise Homogeneous Bars and Problems of Optimal Reinforcement.- 4.4. Optimization of Stress Concentration for Elastic Plates with Holes.- 4.5. Determining the Shape of Uniformly Stressed Holes.- 4.6. Optimization of the Shapes of Holes in Plates Subjected to Bending.- 5. Optimization of Anisotropic Properties of Elastic Bodies.- 5.1. Optimization Problems for Anisotropic Bodies.- 5.2. An Extremal Problem for Rotation of a Matrix.- 5.3. Optimal Anisotropy for Bars in Torsion.- 5.4. Optimization of Anisotropic Properties of an Elastic Medium in Two-Dimensional Problems of the Theory of Elasticity.- 5.5. Computation of Optimum Anisotropie Properties for Elastic Bodies.- 5.6. Some Comments Concerning the Shapes of Anisotropie Bodies and Problems of Simultaneous Optimization of the Shape and of the Orientation of Axes of Anisotropy.- 6. Optimal Design in Problems of Hydroelasticity.- 6.1. State Equations for Plates That Vibrate in an Ideal Fluid.- 6.2. Optimizing the Frequency of Vibrations.- 6.3. Determining the Reaction of a Fluid When the Flow Field and the Motion of the Plate are Two-Dimensional and the Flow is Solenoidal.- 6.4. Finding the Optimum Shape of a Vibrating Plate.- 6.5. Maximizing the Divergence Velocity of a Plate Subjected to the Flow of an Ideal Fluid.- 6.6. A Scheme in Solenoidal Flow for Investigating Equilibrium Shapes of Elastic Plates and a Problem of Optimization.- 7. Optimal Design under Conditions of Incomplete Information Concerning External Actions and Problems of Multipurpose Optimization.- 7.1. Formulation of Optimization Problems under Conditions of Incomplete Information.- 7.2. Design of Beams Having the Smallest Weight for Certain Classes of Loads and with Constraints of Strength.- 7.3. Optimization of Rigidity for Beams.- 7.4. Design of Plates for Certain Classes of Loads.- 7.5. Optimization of Beams Subjected to Bending and Torsion. Multiple Criteria Optimization Problems.- 7.6. Design of a Circular Plate Having Minimum Weight with Constraints on Rigidity and Natural Frequencies of Vibrations.- 7.7. Construction of Quasi-Optimal Solutions to the Multipurpose Design Problems.