The first optimal design problem for an elastic column subject to buckling was formulated by Lagrange over 200 years ago. However, rapid development of structural optimization under stability constraints occurred only in the last twenty years. In numerous optimal structural design problems the stability phenomenon becomes one of the most important factors, particularly for slender and thin-walled elements of aerospace structures, ships, precision machines, tall buildings etc. In engineering practice stability constraints appear more often than it might be expected; even when designing a simple beam of constant width and variable depth, the width - if regarded as a design variable - is finally determined by a stability constraint (lateral stability). Mathematically, optimal structural design under stability constraints usually leads to optimization with respect to eigenvalues, but some cases fall even beyond this type of problems. A total of over 70 books has been devoted to structural optimization as yet, but none of them has treated stability constraints in a sufficiently broad and comprehensive manner. The purpose of the present book is to fill this gap. The contents include a discussion of the basic structural stability and structural optimization problems and the pertinent solution methods, followed by a systematic review of solutions obtained for columns, arches, bar systems, plates, shells and thin-walled bars. A unified approach based on Pontryagin's maximum principle is employed inasmuch as possible, at least to problems of columns, arches and plates. Parametric optimization is discussed as well.

Inhalt

1. Elements of the theory of structural stability.- 1.1 Definition of stability.- 1.2 Stability of elastic structures.- 1.3 Elastic-plastic stability.- 1.4 Stability and buckling in creep conditions.- 2. Problems of optimal structural design.- 2.1 Formulation of optimization problems.- 2.2 Design objectives and their criteria.- 2.3 Design variables.- 2.4 Constraints and their criteria.- 2.5 Equation of state.- 2.6 Stability constraints in structural optimization.- 3. Methods of structural optimization.- 3.1 Calculus of variations.- 3.2 Pontryagin's maximum principle.- 3.3 Sensitivity analysis.- 3.4. Parametric optimization, mathematical programming.- 4. Elastic and inelastic columns.- 4.1 Stability of non-prismatic columns.- 4.2 Unified approach to optimization of columns.- 4.3. Unimodal solutions to linearly elastic problems.- 4.4 Multimodal solutions to conservative problems.- 4.5 Non-conservative linearly-elastic problems.- 4.6 Inelastic columns.- 5. Arches.- 5.1 Stability of non-prismatic arches.- 5.2 General statement of the optimization problem.- 5.3 Funicular arches.- 5.4 Extensible arches optimized for in-plane bifurcation and snap-through.- 5.5 Optimal forms of axis of the arch.- 6. Trusses and Frames.- 6.1 Stability of trusses.- 6.2 Optimal design of trusses.- 6.3 Stability of frames.- 6.4 Optimal design of frames.- 7. Plates and Panels.- 7.1 Governing equations of stability of plates.- 7.2 Optimal design of circular and annular plates.- 7.3 Optimal design of rectangular plates.- 7.4 Aeroelastic optimization.- 8. Shells.- 8.1 Stability of shells.- 8.2 Optimal design of cylindrical shells.- 8.3 Optimal design of cylindrical shells via the concept of uniform stability.- 8.4 Optimal design of noncylindrical shells.- 9. Thin-walled bars.- 9.1 Stability ofthin-walled bars.- 9.2 Optimal design of thin-walled columns.- 9.3 Optimal design of thin-walled beams.- 9.4 Aeroelastic problems.- 9.5 Optimal design of structures of thin-walled elements.- 9.6 Final remarks.- References.- I. Monographs, textbooks and proceedings of selected symposia.- 1. Optimal structural design.- 2. Structural stability.- 3. Optimization theory and methods.- II. References to individual chapters.- 1. Elements of the theory of structural stability.- 2. Problems of structural design.- 3. Methods of structural optimization.- 4. Elastic and inelastic columns.- 5. Arches.- 6. Trusses and frames.- 7. Plates and panels.- 8. Shells.- 9. Thin-walled bars.- III. References added in proof.- Author Index.