On Traces ofd-stresses in the Skeletons of Lower Dimensions of Piecewise-lineard-manifolds
✍ Scribed by R.M. Erdahl; K.A. Rybnikov; S.S. Ryshkov
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 228 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
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✦ Synopsis
We show how a d-stress on a piecewise-linear realization of an oriented (non-simplicial, in general) d-manifold in R d naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of self-stresses in spatial frameworks. The mappings we construct are not linear, but polynomial. In the 1860-70s J. C. Maxwell described an interesting relationship between self-stresses in planar frameworks and vertical projections of polyhedral 2-surfaces. We offer a spatial analog of Maxwell's correspondence based on our polynomial mappings. By applying our main result we derive a class of three-dimensional spider webs similar to the two-dimensional spider webs described by Maxwell. We also conjecture an important property of our mappings that is based on the lower bound theorem (g 2 (d +1) = dim Str ess 2 ≥ 0) for d-pseudomanifolds generically realized in R d+1 [10].