Shape optimization of interior cutouts in composite panels

This paper presents validated results of the optimization of cutouts in laminated carbon-fibre composite panels by adapting a recently developed optimization procedure known as Evolutionary Structural Optimization (ESO). An initial small cutout was introduced into each finite element model and elements were removed from around this cutout based on a predefined rejection criterion. In the examples presented, the limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure index. Plates with values below the product of the average Tsai-Hill number and a rejection ratio (RR) were subsequently removed. This process was iterated until a steady state was reached and the RR was then incremented by an evolutionary rate (ER). The above steps were repeated until a cutout of a desired area was achieved.Nomenclature ₁ stress in fibre direction - ₂ stress in transverse direction - ₁₂ shear stress - X tensile/compressive strength in fibre direction - Y tensile/compressive strength in transverse direction - S shear strength - e plate element number lying on edge of cutout - p plate element number - P total number of plates - TH Tsai-Hill number - TH(l) limiting Tsai-Hill number of platee - TH(p) limiting Tsai-Hill number of platep - RR rejection ratio - K] global stiffness matrix - {} displacement vector - {F} force vector - {} stress vector - l ply number - j number of plies per plate - FI failure index - T specified condition on which to terminate evolution (e.g. area of cutout) - _A stress at major vertex of ellipse - _B stress at minor vertex of ellipse - a ellipse major axis - b ellipse minor axis - i increment number - ER evolutionary rate