Abstract
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.
Highlights
Laminates and sandwiches are used as primary structural components in aerospace and other branches of engineering, owing to their excellent properties
The numerical results show that the optimization procedure effectively recovers the stress concentrations while simultaneously improving the dynamic response of laminates and sandwiches
The tailoring optimization technique based on variable-stiffness concepts (OPTI), developed and progressively refined by the authors in references [17,18] overcomes this problem since it determines the optimal fibre angle variation over the faces, solving in exact or numerical form the Euler–Lagrange equations following from the extremization of the strain energy under spatial variation of the stiffness properties
Summary
Laminates and sandwiches are used as primary structural components in aerospace and other branches of engineering, owing to their excellent properties (e.g., high specific stiffness and strength, favourable thermo-mechanical properties). The tailoring optimization technique based on variable-stiffness concepts (OPTI), developed and progressively refined by the authors in references [17,18] overcomes this problem since it determines the optimal fibre angle variation over the faces, solving in exact or numerical form the Euler–Lagrange equations following from the extremization of the strain energy under spatial variation of the stiffness properties The purpose of this technique is to obtain a closed form solution that defines in a specific ply the solution that minimizes the transverse shear stresses at the critical interfaces and the bending deformation. The through-the-thickness variation of the transverse displacement and of the transverse normal stress, which can have a significant bearing for keeping equilibrium in many practical cases (e.g., thermo-elasticity, cut-outs, free edges, crushing behaviour of sandwiches), are accurately described This enables the model to very accurately represent the strain energy stored in the structure, making it suitable for the optimization technique adopted here. It will be shown that the application of different distributions computed by OPTI in different zones of the same ply will lead to a reduction in both the shear stress at the critical interfaces of sandwiches and the transverse displacement
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