Energy effect removal technique to model circular/elliptical holes in relatively thick composite plates under in-plane compressive load

Abstract

A new technique is introduced in this study to model laminates with circular and elliptical holes. Post-buckling and nonlinear behaviors of these perforated plates are examined when they are under uniaxial in-plane compressive load. Since the perforated plates are moderately thick, the plate theory used to embody the shear effects in the thickness direction is the first order shear deformation plate theory and Von Karman’s assumptions are also used to incorporate the geometric nonlinearity. The formulations are founded upon the principle of minimum potential energy and the approximation of displacement fields are based on Ritz method and obtained by Chebyshev polynomials. Convergence tests have been performed to determine the total number of terms to be used in the assumed displacement functions. The total potential energy of the perforated plate results from removing the energy contribution of the holes from the total potential energy of the perfect plate. All potential energy integrations are obtained numerically by applying the Guess quadrature rule, however, in the case of circular or elliptical cutouts, the required nodes of the Gauss-Chebyshev quadrature are arranged in two different ways; Cartesian and polar arrangements. The effects of cutout shape, size and location for perforated composite laminates with different boundary conditions are extensively investigated to show the capability of the proposed technique. The accuracy of the present work is investigated by comparing the results obtained from finite element method.