Singularity Sets of Constant Principal Strain Deformations

Singularity and fuzziness of fuzzy sets

Contours of constant principal angle and constant principal azimuth in the complex Îμ plane

Finite Plane Strain Deformations of Rubberlike Materials

A finite element program capable of analysing finite plane strain deformations of incompressible rubberlike (Mooney-Rivlin) materials has been develop~d. Two problems, namely a long wall loaded uniformly in two directions and a thick-wall cylindrical pressure vessel loaded internally, have been solved. The computed values of displacements, strains, stresses and hydrostatic pressure agree very c...

Boundary Values and the Transformation Problem for Constant Principal Strain Mappings

We initiate a study of homeomorphisms f with constant principal strains (cps) between smoothly bounded planar domains D, D′. An initial result shows that in order for there to be such a mapping of a given Jordan domainD ontoD′, a certain condition of an isoperimetric nature must be satisfied by the latter. Thereafter, we establish the fundamental fact that principal strain lines (characteristic...

Convex sets of constant width

A bounded convex set has constant width d iff any two parallel (and nonidentical) tangent planes to it have identical distance d from each other. Clearly balls have this property, but there are also other sets of constant width. This lecture was originally designed for a general audience as part of a series of lectures during the German “Year of Mathematics” 2008. It starts by presenting eviden...