Titlebook: Michell Structures; Tomasz Lewiński,Tomasz Sokó?,Cezary Graczykowski Book 2019 Springer Nature Switzerland AG 2019 Michell Structures.Trus

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978-3-030-06988-9Springer Nature Switzerland AG 2019

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Industrial Applications, to the given load. The exact solutions to the Michell theory have been an inspiration for developing new numerical methods of Topology Optimization, which nowadays does contribute to essential changes in the design methods in many domains of engineering.

Inclement

Theory of Michell Structures. Single Load Case,The Michell structures are solutions to the problems of optimum design put forward and discussed in Sects.?. and . provided that the nodes of the trusses may be placed at arbitrary point of the design domain being a subdomain of the plane or of the Euclidean space. The present chapter introduces the reader to the main topic of the book.

Omniscient

Extensions of the Michell Theory,The present chapter concerns the extension of the Michell problems towards the multi-load cases and reveals the impact of the Michell theory on the other problems of topology optimization, especially those concerning the optimum material design.

Manifest

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Selected Problems of Statics,e in which state of stress . satisfies the conditions . and which a given load transmits to a given segment of the boundary of the design domain; . represents .th eigenvalue of a symmetric matrix .. The solution to this problem depends essentially on the ratio . but does not depend on other material

Obstruction

Optimum Design of Structures of Finite Number of Bars. Single Load Variant, minimal compliance leads to an auxiliary problem, which naturally appears in the problem of minimization of truss volume under the condition of stresses in bars being bounded from both sides. This auxiliary problem is a problem of linear programming, which makes it possible to construct optimal str

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,Selected Classes of Spatial Michell’s Structures,optimality condition (.) referring to the spatial setting (.) differs from the plane setting (.), since in the plane problem, the number of the bounds is equal to the number of the adjoint principal strains and in some regimes the following equalities can be fulfilled ., ., while in the spatial prob