Design sensitivity analysis technique for composites undergoing finite elastoplastic deformation

The paper develops the theory of nonlinear structural design sensitivity analysis for composites undergoing finite elastoplastic deformation. The rate (time-independent) constitutive model, which is objective, is employed to account for the plastic material behavior undergoing finite deformations. The reference volume concept is used to unify the shape and nonshape design problems. A higher order approximation procedure of the integration of the rate constitutive equations is used for the response analysis. The direct differentiation approach is adopted to obtain the design sensitivity equations. A method of partial differentiation of the rate constitutive equations, which yields a set of linear differential equations in the partial derivatives of stresses and internal variables with respect to the design variable, is used. The presentation of the general theory is followed by a numerical example. A composite laminated beam is used as an example and results obtained using the theory developed are compared with those from finite difference.