On the analysis and design of uniform truss structures.

摘要

This research answers some of the fundamental questions about the behavior and design of uniform truss structures, i.e., trusses which are generated by replication of a characteristic cell uniformly through space. Emphasis is placed on derivation of explicit equations and simple rules which provide significant physical insight and can be readily employed by designers and analysts. Numerous examples are presented to illustrate the application of newly derived equations to truss design. The issues considered herein are divided into two main topics: truss morphology and truss mechanics. Within the topic of morphology, it is concluded that the nature of the anisotropy exhibited by a truss is generally determined by the rotational symmetry present within the truss, regardless of the presence of reflective or inversive symmetry. Also, a necessary condition is derived for kinematic stability in uniform two-dimensional trusses, and this condition is verified through comparison with finite element analysis. Furthermore, it is impossible to simultaneously satisfy this condition and the familiar Maxwell's equation for static determinacy. Thus, uniform two-dimensional truss lattices must be indeterminate (redundant) if they are to be kinematically stable in the absence of boundary restraints. Within the topic of mechanics, procedures are developed for determining and tailoring the equivalent continuum stiffnesses and strengths of uniform trusses using an existing equivalent continuum theory and a new analytical strength tensor. It is also shown that the discrete arrangement of members within trusses dictates that their equivalent continuum stiffnesses must obey the six Cauchy relations. Thus, the continuum stiffness tensor, C