Optimization of Variable Stiffness Laminates and Sandwiches Undergoing Impulsive Dynamic Loading

This paper, which deals with variable stiffness composites, is aimed at showing the effects of optimization on the response characteristics and stress fields of these materials. A new optimization technique that has recently been developed is used to find spatially variable distributions of stiffness properties at any point, which minimize the interlaminar stresses without significant stiffness loss. After solving the Euler–Lagrange equations obtained by the strain energy extremization with varying the stiffness properties, curvilinear paths of fibres are found in closed form that modify natural frequencies, improve dynamic response and aid in recovery of critical interlaminar stresses. In the current version of the optimization technique, a more realistic description of the optimized shear coefficients is provided in order to accurately describe local effects. As a structural model, a zig-zag model with variable through-the-thickness kinematics is adopted, which is able to adapt itself to variations in solutions, thus providing accurate results from constitutive equations. This model is adopted because an accurate description of strain energy is mandatory for an effective application of the optimization procedure proposed. The numerical results show that the optimization procedure effectively recovers the stress concentrations while simultaneously improving the dynamic response of laminates and sandwiches.