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An analytical study was performed to study the effects of various conditions on low-velocity impact damage in quasi-isotropic nonlinear composite laminates and provide a quick tool for evaluating the significance of low-velocity impact damage. Damaged laminates are modeled as quasi-isotropic nonlinear axisymmetric plates with multiple, equal-diameter, equally spaced, and circular delaminations. Its boundary is supported by distributed linear springs with arbitrary spring constants for rotational and in-plane movements to consider the effect of the arbitrary boundary constraints. Closed-form expressions of nonlinear simultaneous equations are derived for the responses of the damaged plates to a transverse concentrated load based on the Rayleigh–Ritz method. The resulting energy release rate is given in a closed-form in terms of the applied load and the generalized coordinates. The nonlinear response considering damage growth is solved to quantitatively show the effects of various design factors such as boundary conditions, dimensions of the plate, number of multiple delaminations, and interlaminar fracture toughness. The present solutions agree well with finite element solutions.

Analytical approach for evaluation of impact damage in nonlinear quasi-isotropic plates of arbitrary boundary conditions