Hencky-Prandtl Nets and Constrained Michell Trusses,
MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF MATHEMATICS
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The geometry of slip lines is a beautiful part of the theory of plasticity. Parallel to it, and equally remarkable, is the Michell-Prager theory of optimal design. In plane strain both problems lead to Hencky-Prandtl nets, which define orthogonal curvilinear coordinates with a special property. One goal fo this note is to suggest a problem in which we anticipate that Hencky-Prandtl nets of both kinds will appear in the solution. Part of the region should be covered by a Michell truss, and part by slip lines -- if this conjecture is correct. Since it is a problem of shape optimization, a third part of the original cross-section may carry no stress in the optimal design and be completely removed. This note outlines the proposed design problem and describes both its mathematical framework and a possible approach to the computations.