Abstract
The present paper is the first part of the four-part work on Michell cantilevers transmitting a given point load to a given segment of a straight-line support, the feasible domain being a part of the half-plane contained between two fixed half-lines. The axial stress σ in the optimal cantilevers is assumed to be bounded by −σ C ≤σ≤σ T , where σ C and σ T represent the allowable compressive and tensile stresses, respectively. The work provides generalization of the results of the article of Lewiński et al. (Int J Mech Sci 36:375–398, 1994a) to the case of σ T ≠σ C . The present, first part of the work concerns the analytical formation of the Hencky nets or the lines of fibres filling up the interior of the optimal cantilevers corresponding to an arbitrary position of the point of application of the given concentrated force.
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Graczykowski, C., Lewiński, T. Michell cantilevers constructed within trapezoidal domains—Part I: geometry of Hencky nets. Struct Multidisc Optim 32, 347–368 (2006). https://doi.org/10.1007/s00158-005-0599-9
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DOI: https://doi.org/10.1007/s00158-005-0599-9