Introduction to optimization of structures
This is an exposition of the theory, techniques, and the basic formulation of structural optimization problems. The author considers applications of design optimization criteria involving strength, rigidity, stability and weight. Analytic and numerical techniques are introduced for research in optimal shapes and internal configurations of deformable bodies and structures. Problems of the optimal design of beams, systems of rods, plates and shells, are studied in detail. With regard to applications, this work is oriented towards solutions of real problems, such as reduction of the volume or weight of the material, and improvement of mechanical properties of structures. This book is written for readers specializing in applied mechanics, applied mathematics, and numerical analysis.
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adjoint variables admissible algorithm applied approximation assume axis Banichuk beam bending boundary conditions boundary-value problem calculus of variations coefficients consider constant constraints assigned coordinates corresponding criteria criterion critical load cross-sectional area curve deformation denote derive design variables determine differential equations distribution of thickness dynamic eigenvalues elastic body equal Figure formula function h(x given gradient homogeneous function inequality integral introduce isoperimetric condition iterative Lagrangian multipliers linear loss of stability magnitude material maximum minimum natural frequencies Nauk necessary optimality condition nonlinear programming numerical obtain optimal design optimal design problems optimal shape optimal solution optimization problem plastic plate problem of optimizing properties quantities region relations respect rigidity satisfy sensitivity analysis shape optimization shell Smin solving static statically determinate stress structural optimization surface symmetric theory of elasticity theory of optimal tion torsion truss uniform strength unknown values variation variational principles vector function vibrations weight Young's modulus