Dynamic sensitivity analysis of frictional contact impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric non-linearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using the Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting non-linear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking) and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.