A semi-analytical iterative approach for enhancing the existing two-dimensional quasi-continuous axisymmetric stress field for a brittle matrix micro-composite (e.g., a single fiber surrounded by a concentric matrix cylinder), is presented. The existing solution due to Pagano employs Reissner’s variational theorem in conjunction with an equilibrium stress field in which the radial (r-) dependence is assumed a priori.
In the present approach, the stress distribution in the radial direction obtained from the afore-cited variational model is improved a posteriori through an iterative approach that involves successive substitution of the previously computed strains (or stresses) into the equations of compatibility and equilibrium. The equations of compatibility are selected such that they form Euler equations corresponding to an appropriate variational principle, such as the principle of minimum complementary potential energy, etc.
The boundary/interface conditions at r = constant and z = constant surfaces/interfaces are satisfied in the pointwise sense. The expressions for the improved axisymmetric displacement and stress fields are derived using the symbolic language, MAPLE. An illustrative thermal stress problem is currently being solved, and will be used to compare with the existing variational solution.