E-raamat: 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.