Problems and Methods of Optimal Structural Design

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.