Front Cover; Optimization in Mechanics: Problems and Methods; Copyright Page; Introduction; Table of Contents; Chapter 1. EXAMPLES; l.A Structures discretized by finite element techniques; 1.1 Structural analysis; 1.2 Optimization of discretized structures; 1.3 Objective function and constraints; 1.4 Statement of a general mass minimization problem; 1.5 Admissible regions. Restraint sets; 1.6 Example. A three bar framework; l.B Vibrating discrete structures. Vibrating beams. Rotating shafts; 1.7 Discrete structures; 1.8 Vibrations of beams; 1.9 Non-dimensional quantities; 1.10 Rotating shafts.

1.11 Relevant problemsl. C Plastic design of frames and plates. Mass and safety factor; 1.12 Frames; 1.13 Plates; l.D Tripod. Stability constraints ; 1.14 Presentation; 1.15 Reduction; 1.16 Solution; 1.17 An associated problem; l.E Conclusion; Chapter 2. BASIC MATHEMATICAL CONCEPTS WITH ILLUSTRATIONS TAKEN FROM ACTUAL STRUCTURES; 2.A Sets. Functions. Conditions for minima; 2.1 Space R -- 2.2 Infinite dimensional spaces; 2.3 Open sets. Closed sets; 2.4 Differentials; 2.5 Conditions for minima or maxima; 2.6 Minimization and maximization with equality constraints. Lagrange multipliers.

2.7 Euler theorems and Lagrange multipliers2.B Convexity; 2.8 Convex sets; 2.9 Structures subjected to several loadings; 2.10 Convex functions. Concave functions; 2.11 Minimization and maximization of convex or concave functions; 2.12 Generalizations of convexity and concavity; 2.13 Gradients and differentials of natural vibration frequencies; 2.14 Quasiconcavity and pseudoconcavity of the fundamental vibration frequencies in finite element theory; 2.15 Quasiconcavity and pseudoconcavity of the fundamental frequencies of vibrating sandwich continuous beams.

Chapter 3. KUHN TUCKER THEOREM. DUALITY3.1 Introduction; 3.2 Farkas lemma; 3.3 Constraint qualification; 3.4 Kuhn Tucker theorem; 3.5 A converse of the Kuhn Tucker theorem; 3.6 Lagrangian. Saddle points; 3.7 Duality; 3.8 Solution to primal problem via dual problem; Chapter 4. ASSOCIATED PROBLEMS; 4.A Theorems; 4.1 Statements of the problem; 4.2 General theorems; 4.3 Use of equivalent problems; 4.4 Solving a problem when the solutions of an associated problem are known; 4.B Examples; 4.6 Problems associated with already solved problems.

4.7 Strength maximization and mass minimization of an elastic columnChapter 5. MATHEMATICAL PROGRAMMING NUMERICAL METHODS; 5.A. Unconstrained optimization; 5.1 Iterative methods; 5.2 Minimization on a given search line; 5.3 Relaxation method; 5.4 Descent directions; 5.5 Gradient methods; 5.6 Conjugate gradient methods; 5.7 Newton method. Quasi-Newton methods; 5.B. Constrained optimization; 5.8 Assumptions; 5.9 Reduction of a problem ^ t o a sequence of linear problems; 5.10 Gradient projection method; 5.11 Other projection methods; 5.12 Penalty methods.