Topological Solutions for Infinite Grids on Elastic Foundation

摘要

Grids of beams with 2D translational symmetry are standard solutions for bridging large spans, stiffening plates or protecting structures on which they rest. This paper is concerned with the study of such periodic grillages supported on elastic foundation. If the loading is localized and if the perturbation does not reach the boundaries of the design domain these structures can conveniently be assumed as infinite in the directions of the symmetry. In several respects the analysis of such structures bears resemblance with the dynamic response under harmonic excitation, as in , where infinite grillages with rectangular cells was investigated. Herein, static analysis under arbitrary loading is considered in the context of the Representative Cell Method. We investigate and compare several topologies of infinite elastically supported grillage. In particular we study the three typical patterns that divide the plane into regular polygones: equilateral triangles, squares and hexagones (Fig. 1). Two cases are considered: lattices elastically supported at junctions and lattices on elastic foundation. The primal objectives is to obtain minimum compliance or minimum stress levels per unit space for a load applied at a typical node. In the case of discrete elastic supports the measure of comparison between the different configurations is an equal number of supports per unit covered area under a constant volume constraint and by using identical beams. In the case of continuous elastic foundation the comparison is for an equal volume of material per unit covered surface. Next the reliablity of these type of grillages is compared for cases where one of their components is lost.