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An asymptotically correct analysis of passive anisotropic thin-walled open cross-section beam-like structures using the variational asymptotic method (VAM) is extended to include embedded macro fiber composites. Application of the VAM to beam-like structures splits the problem into non-linear 1D theory along the selected beam reference line and linear 2D generalized 5 Â 5 Vlasov theory augmented by a 5 Â 1 actuation vector over the cross-section. The linear 2D cross-sectional theory is validated against the University of Michigan/variational beam sectional analysis 2D finite element software. The validation examples selected were based on practical cross-sectional geometry and material anisotropy under DC actuation voltage. Actuation-induced deformations predicted at the beam reference line are obtained using an intrinsic geometrically exact beam theory for open cross-sections. The predicted generalized deformations are compared with those obtained using the 3D finite element analysis software ANSYS Multiphysics, which further validates the extended theory. The analytical theory is shown to be straightforward to implement and efficient, yet sufficiently reliable to perform interdisciplinary studies and optimization of various engineering applications of such structures.

Numerical methods for stress analysis are increasingly being employed in the micromechanics of solids. In this paper, the boundary integral equation (BIE) method for two-dimensional general anisotropic elasticity, based on the quadratic isoparametric element formulation, is extended to treating some inclusion problems. All the cases analysed involved an elliptical zirconia inclusion in an alumina matrix, noting that ZrO2–Al2O3 is an advanced ceramic increasingly used in structural applications. The BIE results are compared with those calculated using Eshelby's equivalent inclusion approach where possible, and excellent agreements between them are obtained. The present work demonstrates the suitability of using this numerical technique for analysing such problems and, in particular, the ease with which it may be used even in the case of general anisotropy.