
Accession Number : ADP000046
Title : HenckyPrandtl Nets and Constrained Michell Trusses,
Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF MATHEMATICS
Personal Author(s) : Strang,Gilbert ; Kohn,Robert V.
Report Date : 1981
Pagination or Media Count : 6
Abstract : The geometry of slip lines is a beautiful part of the theory of plasticity. Parallel to it, and equally remarkable, is the MichellPrager theory of optimal design. In plane strain both problems lead to HenckyPrandtl 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 HenckyPrandtl 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 crosssection 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.
Descriptors : *Structural engineering, *Structural mechanics, *Plastic properties, *Theorems, *Optimization, Structural analysis, Structural response, Nets, Trusses, Lines(Geometry), Strain(Mechanics), Coordinates, Curves(Geometry), Linearity, Orthogonality, Mathematical analysis
Distribution Statement : APPROVED FOR PUBLIC RELEASE