Sensitivities and optimal design of hexagonal array fiber composites with respect to interphase properties

Abstract

The focus of this paper is the calculation of sensitivities of stresses at an interphase between a fiber and matrix, in a hexagonal cell of a fiber-reinforced composite, with respect to interphase stiffnesses and the use of these sensitivities to carry out optimal design of the interphase stiffnesses. The interphase is modeled here as a spring layer. Sensitivities are of interest in the design of composites since interphase properties can substantially affect the mechanical and thermal behavior of a composite. The sensitivity calculations are carried out here by using the direct differentiation approach (DDA) of the corresponding boundary element method (BEM) formulation of the problem. Optimization calculations are carried out by coupling the standard and sensitivity analyses to an optimizer. The optimizer chosen here uses sequential quadratic programming to obtain the desired optimal values of interphase stiffnesses that minimize the possibility of failure of a composite under prescribed loading. Numerical results for sensitivities and optimization, for some illustrative examples, are presented in this paper.