T. J. Urbanik A theory of thin plates which is physically as well as kinematically nonlinear is Research Engineer, developed and used to characterize elastic material behavior for arbitrary stretching Forest Products Laboratory, and bending deformations. It is developed from a few clearly defined assumptions Forest Service, and uses a unique treatment of strain energy. An effective strain conce...

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces’ areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature.We dis...

In this paper we define and study for a finite partially ordered set P class of simplicial complexes on the $$P_r$$ r-element multichains P. The depend strictly monotone function from [r] to [2r]. We show that there are exactly $$2^r$$ such functions which yield subdivisions order complex P, $$2^{r-1}$$ pairwise different. Within are, example, intervals in zig-zag poset $$r{\hbox {th}}$$ edgewi...