Computation Models and Numerical Solution Procedures for Nonlinear Analysis of Single Layer Lattice Shells

Abstract

Single-layer space frames consisting of reticulated surfaces with assumed pin or rigid jointed members are widely used in practice. This is accounted for by the fact that they meet the need to cover large spans without the use of intermediate supports, while at the same time, yielding a very small structural weight per unit of area covered. Because of the in-plane membrane action of shallow single-layer lattice shells associated with their initial curvature, such structures are able to carry considerable out-of-plane loads relative to the weight of the structure itself. However, in the case of shallow single-layer lattice shells with small rise-to-span ratios, the response is highly nonlinear even when the stresses in the members are small enough to ensure that the material properties fall within the elastic range. These structures become unstable at some critical value of the load and any design based on an elastic linearized analysis is potentially unsafe. Shallow single-layer lattice shells are characterized by a strong nonlinear behaviour with considerable softening, so they are extremely sensitive to out-of-plane instability and are affected by general and local instability. As far as the pre-buckling range is concerned, an extensive literature dealing with effective solver techniques exists for the numerical solutions of structural problems, but only a few algorithms have been put forth with a view to tracing the nonlinear response from the pre-limit range into the post-limit one. The main purpose of this paper is to review these methods and to discuss their performance. The author's ASEF-N computer program and selected numerical examples are presented.