Introduction to Optimization of StructuresThis 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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Page 78
... solving a system of much simpler problems . By solving these problems we can determine the optimal solution within an arbitrary degree of accuracy . Thus , the zeroth - order approximation satis- fies the following relations : L * ( h ...
... solving a system of much simpler problems . By solving these problems we can determine the optimal solution within an arbitrary degree of accuracy . Thus , the zeroth - order approximation satis- fies the following relations : L * ( h ...
Page 97
... solving the entire optimal design problem from its very beginnings , we need to establish the sensitivity of the solution with respect to variations in the values of the parameters . Generally , an effective solution of the entire ...
... solving the entire optimal design problem from its very beginnings , we need to establish the sensitivity of the solution with respect to variations in the values of the parameters . Generally , an effective solution of the entire ...
Page 179
... solving problems of rigid - plastic analysis . As a result of numerically solving such problems for a given shape of a body , one finds the values of σij , Vi , 2 , and μ . The second type of computation relates to constructions that ...
... solving problems of rigid - plastic analysis . As a result of numerically solving such problems for a given shape of a body , one finds the values of σij , Vi , 2 , and μ . The second type of computation relates to constructions that ...
Contents
Fundamental Concepts and Problems of Optimal Design | 3 |
CHAPTER 2 | 27 |
CHAPTER 3 | 47 |
Copyright | |
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adjoint variables admissible algorithm applied approximation assume Atrek axis Banichuk beam boundary conditions boundary-value problem c₁ calculus of variations coefficients consider constant coordinates corresponding criteria criterion critical load cross-sectional area curve deformation denote derive design variables determine differential equations distribution of thickness dynamic eigenvalues Figure formula function h given gradient h₁ hmin homogeneous function inequality integral isoperimetric condition iterative Lagrangian multipliers linear loss of stability magnitude material maximum minimizing minimum Nauk necessary optimality condition numerical obtain optimal design optimal shape optimal solution optimal structural optimization problem parameter plastic plate problem of optimizing properties quantities region relations respect rigidity satisfy sensitivity analysis shape optimization shell Smin solving static statically determinate stress structural design surface symmetric theory of elasticity theory of optimal tion torsion truss uniform strength unknown values variation variational principles vibrations weight Young's modulus