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A two-noded, 10 degree of freedom per node, laminated composite thin-walled beam finite element was developed for vibration analysis. The thin-walled element presented here is suitable for either open-section or closed-section beams of any shape, stacking sequence, and boundary conditions. Natural frequencies of several thin-walled composite structures were calculated and compared with full-scale shell finite element results.

When a heterogeneous elastic material is represented by an effective homogeneous elastic solid, average stress and strain fields are used. The meaning of the J-integral in the effective homogeneous solid is investigated. A periodically layered medium is considered. The relation between the J-integrals in the original layered medium and the effective medium is derived.