Author | Banichuk, N. V. author |
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Title | Problems and Methods of Optimal Structural Design [electronic resource] / by N. V. Banichuk ; edited by Edward J. Haug |
Imprint | Boston, MA : Springer US : Imprint: Springer, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-3676-1 |
Descript | XXI, 313 p. online resource |
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