Structural design sensitivity analysis for composites undergoing elastoplastic deformation

Nonlinear structural design sensitivity analysis for structures undergoing elastoplastic deformation is developed in this paper. The reference volume concept is used to unify the shape and nonshape design problems. The rate (time-independent) constitutive model is employed to account for the plastic material behavior. In the response analysis, a higher order approximation procedure of the integration of the rate constitutive equations is proposed. The direct differentiation approach (DDA) is adopted to obtain the design sensitivity equation for the response variables. 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 included in the DDA procedure. In Part I of this paper, the general theory is described. In Part II, the theory is applied to a composite laminated beam problem.