Introduction to Optimization of Structures, 1st Edition by N. V. Banichuk (auth.)

By N. V. Banichuk (auth.)

This can be an exposition of the speculation, thoughts, and the fundamental formula of structural optimization difficulties. the writer considers functions of layout optimization standards related to power, tension, balance and weight. Analytic and numerical recommendations are brought for study in optimum shapes and inner configurations of deformable our bodies and constructions. difficulties of the optimum layout of beams, platforms of rods, plates and shells, are studied intimately. in regards to purposes, this paintings is orientated in the direction of ideas of genuine difficulties, similar to relief of the amount or weight of the cloth, and development of mechanical houses of constructions. This ebook is written for readers focusing on utilized mechanics, utilized arithmetic, and numerical research.

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L. 8) In concluding this short exposition of various techniques used for eliminating constraints, we observe that the introduction of auxiliary design variables may be accomplished in various (and nonunique) ways. This feature may be utilized in numerical solutions of such problems by improving the convergence of the algorithms. 2 Constraint Formulation Techniques In the theory of optimal design both inequality-equality-type constraints are assigned to the response of a structure. Modern techniques of optimal design permit us to deal with both these types of constraints.

44) attains its minimum, the equality K = - II becomes valid. 43) is transformed into the form J* = max K = -min min II. 42). The (outer) minimum with respect to r must be found among the contours satisfying certain additional geometric conditions assigned to the admissible boundary shapes in specific problems. , the area Q) must remain constant. 4 A different kind of an optimal design problem which permits one to eliminate differential relations and use variational principles occurs in the optimization of eigenvalues in self-adjoint boundary-value problems.

In this minimax approach (otherwise known as the "guaranteed approach") one must assume that a set containing all possible realizable external loads is known and that we need only determine the shape of a structure having minimal weight and satisfying all strength and geometric constraints for all possible loads contained in the realizable set. Such a structural shape will be called optimal if for any structure with a smaller weight, it is possible to select a system of loads belonging to the admissible set such that either some assigned strength or geometric constraint has been violated.

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