Optimization of variable stiffness composite plates with cut-outs subjected to compression, tension and shear using an adjoint formulation

van Tooren, M.J.L., Jahangir, Ifat and Elham, A. (2016) Optimization of variable stiffness composite plates with cut-outs subjected to compression, tension and shear using an adjoint formulation. In 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics.. (doi:10.2514/6.2016-1970).

Abstract

This paper presents an improved and extended version of a framework for the design of variable stiffness fiber composite panels developed by the authors. The framework supports the design of panels subjected to multiple load cases, each case a combination of compression or tension and shear. The framework consists of a finite element (FE) solver, an optimizer, a novel approach to relate design variables to the stiffness matrix in the FE module, constraint evaluation modules for manufacturing and buckling constraints and a postprocessor that translates the theoretical optimal result from the optimizer into discrete tow paths for each ply including a cut and restart function. The formulation of the design variables using a manufacturing mesh separate from the FE mesh limits the number of design variables while preserving smoothness of the solution and allows easy specification of manufacturing constraints enforced by the envisioned fiber steering process, for example the minimum course radius to prevent tow buckling. The framework is intended for inclusion in an MDO based aircraft wing weight estimation tool in which it is combined with aerodynamic analysis and optimization. Results obtained with the framework show the structural benefit of using variable stiffness also in case of multiple load cases. The design variable formulation and the adjoint based sensitivity analysis lead to acceptable calculation time while preserving accuracy and smoothness of the solution. Separation of optimizer and tow path planner allows multiple practical interpretations of the theoretical optimization result. This preserves the influence of the manufacturing engineer on the practical panel lay-up and enables the user to control overlaps and gaps using cut-and-restart functionality.

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