Improvement of Axial Buckling Capacity of Elliptical Lattice Cylinders

Abstract

A formulation to improve the axial buckling capacity of elliptical lattice cylinders by varying the lattice rib angle as a function of circumferential location is discussed. The isogrid lattice is a classic case, and a circular cylinder with an isogrid construction is considered here as the baseline. By assigning an eccentricity to the circular isogrid cylinder, an elliptical isogrid cylinder of the same circumference, and therefore the same weight, results, but the axial buckling capacity is considerably reduced relative to the circular case. This is due to the fact that for a noncircular cross section the circumferential location with the largest radius of curvature attains its axial buckling capacity at a load lower than any other circumferential location. To mitigate the reduction in axial buckling capacity, the lattice rib angle is varied with circumferential location so that each circumferential location attains its buckling capacity at the same level of compressive strain. The analysis developed to proscribe the rib angle variation with circumferential location is based on representing the lattice cylinders as equivalent orthotropic cylinders, with the homogenized orthotropic material properties depending upon rib angle, rib modulus, and rib cross-sectional dimensions. By combining the known variation of the radius of curvature with circumferential location around the elliptical cylinders with a one-dimensional equation for the buckling stress of an orthotropic circular cylinder, variable rib angle elliptical lattice cylinders are designed. Though the variable rib angle elliptical lattice cylinder does not fully recover the buckling capacity of the baseline isogrid circular cylinder, it does outperform the elliptical isogrid cylinder. Results from a finite element analysis compare well with the predictions of the developed analysis. Three levels of eccentricity and two overall cylinder sizes are considered to illustrate the generality of the findings. It is fully expected that the approach developed is applicable to other noncircular cross-sectional geometries.