Gradient-based determination of principal design influences on composite structures

Optimization of fiber-reinforced composite structures with nonlinear load-bearing behavior is a complex task that is becoming increasingly relevant in practice. Therefore, it is desirable to automatically determine essential influences on the structural behavior of fiber composite shells and stability-relevant objective functions and constraints in the context of structural optimization. This work deals with a variational approach for the derivation and computation of design sensitivities of elastic solid shell structures, as described in [1], and the extension to anisotropic layered composite structures. Design sensitivities concerning fiber angles and layer thicknesses are derived and quantitatively determined in the context of the finite ele-ment method (FEM). The anisotropic analysis model is founded on [2], in which a sophisti-cated solid-shell formulation based on reduced integration, as described in [3], is extended to discretize the composite with only one element over the whole thickness by means of mul-tiple integration points. This can be understood as a special case of equivalent-single-layer theories (ESLT). Examination of global stiffness and sensitivity matrices using methods from principal component analysis (PCA), such as singular value decomposition (SVD), are used to identify crucial design changes corresponding to major changes in the structural behavior of the composite. Results are discussed by referecne to a chosen numerical example.