hp-Finite Element Methods for Composites

The efficient numerical modelling of laminated composites has received increasing attention in recent years - examples are sandwich plates and shells, fiber-reinforced composites and the like.

While the global response to external loadings can be reliably assessed on the basis of averaged, or homogenized, models, interlamina stresses which are critical for specimen failure can only be obtained by resolution of the small scales of the problem.

This requirement of SCALE RESOLUTION and the low solution regularity at the matrix-composite interface seems to conflict with the use of high order FE approaches which is commonly based on large elements with polynomial shape functions of high order.

We present a new approach which is able to exploit the microstructure of the material. We prove that this approach realizes exponential convergence independently of ε. The approach generalizes the classical asymptotic approach and is based on a spectral homogenization technique. Numerical results confirm the theoretical analysis.

The work is joint with A.M. Matache and I. Babuska.