A semi-analytical approach for linear and non-linear analysis of unstiffened laminated composite cylinders and cones under axial, torsion and pressure loads

• A semi-analytical model for linear and non-linear buckling analysis is proposed.
• Axial compression, torsion, pressure and any additional forces can be applied to the shell surface.
• The elephant’s foot effect, a common failure mode for cylinders and cones, is taken into account.
• Important implementation aspects are covered in the manuscript and the code is available on-line.
• The equations are presented in matrix form and therefore can be easily applicable to other problems.

A semi-analytical model for the non-linear analysis of simply supported, unstiffened laminated composite cylinders and cones using the Ritz method and the Classical Laminated Plate Theory is proposed. A matrix notation is used to formulate the problem using Donnell׳s and Sanders׳ non-linear equations. The approximation functions proposed are capable to simulate the elephant׳s foot effect, a common phenomenon and a common failure mode for cylindrical and conical structures under axial compression. Axial, torsion and pressure loads can be applied individually or combined, and solutions for linear static, linear buckling and non-linear buckling analyses are presented and verified using a commercial finite element software. The presented non-linear buckling analyses used perturbation loads to create the initial geometric imperfections, showing the capability of the method for arbitrary imperfection patterns. The linear stiffness matrices are integrated analytically and for the conical structures an approximation is proposed to overcome the non-integrable expressions.