Structural Optimization: Fundamentals and Applications"This book introduces the fundamental concepts and practical applications of modern structural optimization. It presents, in a unified approach, recent developments in the area. The text addresses both the student and the practising structural engineer. The book discusses in detail alternative problem formulations, the relative merits of different optimization methods and various considerations related to structural design. The emphasis throughout is on approximation concepts, which are essential for the solution of many practical design problems. It demonstrates how various formulations, methods and approximations are integrated to achieve effective design procedures. The advantages as well as the limitations of the different approaches are discussed and illustrated by numerous examples."--Back cover. |
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algorithms assumed B₁ binomial series calculation compatibility conditions compressive stresses computational effort considered convergence convex coordinates cross sections cross-sectional areas derivatives design procedure design space design variables displacement constraints efficient elements example feasible design feasible region first-level problem first-order Taylor series geometrical variables geometry given homogeneous functions indeterminate structure initial design iteration linear programming loading conditions lower bound LP problem LP solution minimization minimum modified modulus of elasticity nonlinear nonlinear programming number of variables objective function obtained OC methods optimal design problem optimal solution optimal topologies optimality criteria optimization methods optimization problem P₁ penalty function plastic problem formulation r₁ recurrence relation redundant forces satisfied scaling shown in Fig solution process solved statically determinate structure statically indeterminate stiffness matrix stress constraints structural optimization subproblems Substituting Taylor series Taylor series expansion true optimum truss shown values X₁ X₂ Y₁ Y₂