Maximum Buckling Load Design of General Cross-section Cylinders Using Lamination Parameters

For a non-circular cylinder the radius of curvature changes around the circumference. Therefore for constant stiffness non-circular cylinders, some specific locations in the circumference are more prone to buckle. The same problem exists for circular cylinders with non-uniform loading in the cross-section like a cylinder under bending. This explanation brings to the mind the idea of tailoring the material such that the material potential is used more efficiently and if possible all parts of the cylinder contribute in the buckling phenomenon. Since the changes in the radius of curvature and/or loading happens in the circumferential direction, tailoring the material properties in the circumferential direction is a logical pattern. By assigning a certain number of half-waves in the longitudinal direction, the buckling eigen-value problem is solved to find the buckling load and circumferential mode shapes. The inverse of buckling load is approximated using a homogeneous, conservative formulation to increase the computational efficiency during optimisation. This is a hybrid approximation expanded in terms of stiffness linearly and reciprocally. Multi-modal optimisation problem is formulated to minimise inverse of critical buckling factor. Variable stiffness design is compared with the quasi-isotropic design