Showing papers on "Bifurcation diagram published in 1970"

Bifurcation points of the elastic-plastic equilibrium in a simple frame model

Abstract: This is a study of the characteristics of equilibrium bifurcation in a geometrically symmetric simple frame model in which the beam is loaded symmetrically and gradually. The deformability of the model is concentrated in two “Shanley cells” for whose elements a nonholonomic bilinear force-lengthening (or force-contraction) relation is adopted.

Geometrical and topological optimization and their relation to the bifurcation laws in optimized arterial tree models

Abstract: In generating models of vascular trees, the method of Constrained Constructive Optimization (CCO) draws on the assumption that optimization criterions can be utilized to derive the geometrical and structural features of the tree models, without using informations from topographic anatomy. The boundary conditions imposed describe pressures and flows at the inlet and outlets of the binary branching model tree as well as the ratios of radii at a bifurcation ("power-law" for bifurcations). During phylogenesis of species, bifurcation laws, tree geometry and tree topology have most likely been simultaneously optimized. In contrast, a supposed optimum form of bifurcation law is prescribed in the CCO-simulation, and geometry together with structure are optimized "within" that frame. It is shown that CCO trees optimized under different bifurcation laws initially show slightly different geometries but identical topological structures. At a certain stage of development, however, accumulated geometric deviations lead to changes in topology as a result of optimization. From there on we observe different "evolutionary paths" of tree development.