Least-weight design of perforated elastic plates. I
The paper investigates implications of some recent mathematical developments in the fields of shape optimization and relaxation of variational problems. Considering the least-weight design of perforated elastic plates in either flexure or plane stress for a prescribed compliance, it is shown that at low rib densities microstructures consisting of a combination of first- and second-order infinitesimal ribs is superior to those consisting of purely first-order infinitesimal ribs. Moreover, it is indicated that thin ribs of infinite length/thickness ratio do not contribute significantly to the stiffness in a direction normal to their plane. On the basis of this conclusion, a simple specific cost function is derived and then it is used in the design of circular, uniformly loaded perforated plates with zero value of Poisson's ratio.
circular, uniformly loaded perforated plates
scientific article; zbMATH DE number 3980684