A nonlinear composite shell element with continuous interlaminar shear stresses

A numerical model for layered composite structures based on a geometrical nonlinear shell theory is presented. The kinematic is based on a multi-director theory, thus the in-plane displacements of each layer are described by independent director vectors. Using the isoparametric apporach a finite element formulation for quadrilaterals is developed. Continuity of the interlaminar shear stresses is obtained within the nonlinear solution process. Several examples are presented to illustrate the performance of the developed numerical model.List of symbols reference surface - convected coordinates of the shell middle surface - ⁱ coordinate in thickness direction - ⁱh thickness of layer i - X_o position vector of the reference surface - ⁱX_o position vector of midsurface of layer i - t_k orthonormal basis system in the reference configuration - ⁱa_k orthonormal basis system of layer i - ⁱW axial vector - R_o orthonormal tensor in the reference configuration - ⁱR orthonormal tensor of layer i - ⁱ Cauchy stress tensor - ⁱP First Piola-Kirchhoff stress tensor - ⁱq vector of interlaminar stresses - ⁱn,ⁱm vector of stress resultants and stress couple resultants - v_x components of the normal vector of boundary - ⁱN, ⁱQ, ⁱM stress resultants and stress couple resultants of First Piola-Kirchhoff tensor - stress resultants and stress couple resultants of Second Piola-Kirchhoff tensor - ⁱ, ⁱ, ⁱ strains of layer i - _K transformation matrix - u_o displacement vector of layer 1 - ⁱ local rotational degrees of freedom of layer i