Criteria and Methods of Structural Optimization

I: Criteria of Structural Optimization.- 1 Aims, Basic Concepts and Assumptions.
- 1.1 The aims and scope of optimization.
- 1.2 Basic concepts and definitions.
- 1.3 Preliminary assumptions.- 2 Optimization for Minimum Potential Energy, Maximum Rigidity and Minimum Deformability.
- 2.1 The optimality criterion.
- 2.2 Wasiuty?ski's theorems.
- 2.3 Deformability of a structure and the free surface.
- 2.4 The necessary and sufficient conditions of minimum deformability.
- 2.5 Optimization of plane bar structures.
- 2.6 Optimization of plates.
- 2.7 Optimization of spatial lattice bar structures.- 3 Uniform Strength Design.
- 3.1 Strength hypotheses.
- 3.2 The criterion of uniform strength.
- 3.3 Uniform-strength design of structures under multiple loading conditions.
- 3.4 Uniform-strength design of bar structures.
- 3.5 Uniform-strength design of beams with cross-sections defined up to m parameters.
- 3.6 Uniform-strength design of plates.- 4 Optimization for Minimum Volume, Weight or Cost.
- 4.1 The criterion of optimization.
- 4.2 Optimum elastic design.
- 4.3 Examples of optimum elastic design.
- 4.4 Optimum limit design.
- 4.5 Examples of optimum limit design.
- 4.6 Probabilistic approach to optimum design.-
II: Methods of Structural Optimization.- 5 Introduction to Mathematical Methods of Optimization.
- 5.1 Problem formulation in optimum structural design.
- 5.2 Classical extremum theory.
- 5.3 Convex regions and convex functions.- 6 Linear Programming.
- 6.1 The linear programming problem.
- 6.2 Constrained extrema of a linear function.
- 6.3 The graphical method of linear programming.
- 6.4 Determination of an initial basic feasible solution.
- 6.5 The simplex method.
- 6.6 Duality in linear programming.
- 6.7 Other important methods of linear programming.
- 6.8 Linear discrete programming.
- 6.9 Examples of linear programming in optimum structural design.- 7 Non-linear Programming.
- 7.1 Problem statement.
- 7.2 Kuhn-Tucker conditions.
- 7.3 Quadratic programming.
- 7.4 Duality in quadratic programming.
- 7.5 Beale's method.
- 7.6 Wolfe's method.
- 7.7 Geometric programming: unconstrained problem.
- 7.8 Geometric programming: constrained problem.
- 7.9 Non-linear integer programming.
- 7.10 Unconstrained optimization: direct search methods.
- 7.11 Unconstrained optimization: descent methods.
- 7.12 Constrained optimization: direct methods.
- 7.13 Constrained optimization: indirect methods.
- 7.14 Choosing a method.
- 7.15 Applications of non-linear programming methods to structural optimization.- 8 Dynamic Programming.
- 8.1 Introduction.
- 8.2 Multi-stage decision process.
- 8.3 Bellman's principle of optimality.
- 8.4 The variant method of dynamic programming.
- 8.5 Applications of dynamic programming to structural optimization.
- 8.6 Final to initial value problem conversion.
- 8.7 Continuous dynamic programming.- 9 Stochastic Programming.
- 9.1 Linear stochastic programming.
- 9.2 Non-linear stochastic programming.
- 9.3 Reliability-based structural optimization: a stochastic programming approach.- 10 Classical Variational Methods. Examples of Application to Optimum Structural Design.
- 10.1 Introductory remarks and fundamental concepts.
- 10.2 Necessary conditions for an extremum of a functional.
- 10.3 Variational problems with side conditions.
- 10.4 Sufficient conditions for a minimum of a functional.
- 10.5 Direct methods in the calculus of variations.
- 10.6 Examples of application of the calculus of variations to structural optimization.- 11 Non-classical Variational Methods of Optimization.
- 11.1 Assumptions and problem formulations.
- 11.2 Optimality conditions: necessary and sufficient.
- 11.3 Trukhaev-Khomenyuk operator equations.
- 11.4 Elimination of inequality constraints.
- 11.5 Minimax formulation for non-classical variational problems.
- 11.6 Approximate methods for non-classical variational problems.- 12 Mathematical Theory of Extremum Problems.
- 12.1 Introduction.
- 12.2 Cones and dual cones.
- 12.3 Necessary extremum conditions.
- 12.4 Directions of decrease.
- 12.5 Feasible directions.
- 12.6 Tangent directions.
- 12.7 Calculation of dual cones.
- 12.8 The Lagrange multiplier rule and the Kuhn-Tucker theorem.
- 12.9 Optimal control problems. Local maximum principle. Pontryagin maximum principle.
- 12.10 Sufficient extremum conditions.- 13 Iterative and Experimental Methods of Shape Optimization of Structures.
- 13.1 Iterative and experimental approaches to shape optimization.
- 13.2 Types of iterations.
- 13.3 Iteration vs. imitation and the trial and error method.
- 13.4 Designing a column for uniform strain.
- 13.5 Designing an arch bridge for uniform strain.
- 13.6 Determination of an optimum profile of the junction between a beam and a column by means of photo-elastic modelling.
- 13.7 Determination of the optimum shape of plane structures.
- 13.8 Shape optimization of shells.-
III: Bibliographical Survey and Bibliography.- 14 Survey of the Literature of Structural Optimization.
- 14.1 Scope and aim of the survey.
- 14.2 Survey works and general studies on structural optimization.
- 14.3 Optimization of beams.
- 14.4 Optimization of plates.
- 14.5 Optimization of trusses.
- 14.6 Optimization of columns, arches and frames.
- 14.7 Optimization of shells, hanging structures and lattice structures.- Bibliography of Structural Optimization.- Author index.