Michell cantilevers constructed within trapezoidal domains—Part II: virtual displacement fields

Structural and Multidisciplinary Optimization - Tập 32 - Trang 463-471 - 2006
C. Graczykowski1, T. Lewiński2
1Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, Poland
2Faculty of Civil Engineering, Institute of Structural Mechanics, Warsaw University of Technology, Warsaw, Poland

Tóm tắt

The present second part of the paper deals with the virtual displacement fields associated with the optimality conditions $\varepsilon _{I} {\left( {\overline{{\mathbf{u}}} } \right)} = 1,\varepsilon _{{II}} {\left( {\overline{{\mathbf{u}}} } \right)} = - \kappa ,\kappa = {\sigma _{T} } \mathord{\left/ {\vphantom {{\sigma _{T} } {\sigma _{C} }}} \right. \kern-\nulldelimiterspace} {\sigma _{C} }$ , where σ T and σ C represent the allowable values of the tensile and compressive stress, respectively. The displacement fields vanish along a straight segment of a line support and are constructed within an infinite domain bounded by two half-lines. The displacement fields are provided by the integral formulae involving the Lamé fields found in part I of this paper. All the results are expressed in terms of Lommel-like functions. These results make it possible to determine the volumes of the optimal cantilevers designs within the feasible domain considered. Computation of the volumes along with analyses of concrete cantilevers will be the subject of part IV of the present paper.

Tài liệu tham khảo

Chan HSY (1967) Half-plane slip-line fields and Michell structures. Q J Mech Appl Math 20:453–469 Graczykowski C, Lewiński T (2006) Michell cantilevers constructed within trapezoidal domains—Part I: geometry of Hencky nets. Struct Multidisc Optim Hemp WS (1973) Optimum structures. Oxford, Clarendon Press Lewiński T, Zhou M, Rozvany GIN (1994a) Extended exact solutions for least-weight truss layouts—Part I: cantilever with a horizontal axis of symmetry. Int J Mech Sci 36:375–398 Lewiński T, Zhou M, Rozvany GIN (1994b) Extended exact solutions for least-weight truss layouts—Part II: unsymmetric cantilevers. Int J Mech Sci 36:399–419