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A new shear lag (SL) type model for stress transfer in a composite with cylindrical fibres is derived. It accounts for fibre end stresses in an approximate yet realistic manner, and leads to a new formula for predicting the Young's modulus of the composites. The predictions of this model were found to agree well with data for metal matrix composites (MMCs) with fibres of various aspect ratios. The accuracy and relative simplicity of the new model have been exploited in the development of an approximate analytical model for the stress transfer and macroscopic yield stress of a composite that contains a weak layer in the matrix adjacent to the reinforcement. With the aid of the latter model, the proof stress of MMCs which contain a precipitate free zone (PFZ) around the reinforcement, can be studied; experimental data obtained for aged 8090 MMCs is consistent with the model predictions.

Two-dimensional equations of motion of successively higher-order approximations for piezoelectric crystal plates with triclinic symmetry are deduced from the three-dimensional equations of linear piezoelectricity by expansion in series of trigonometric functions of the thickness coordinate of the plate. These equations, complemented by two additional relations: one, the usual relation of face tractions to the mass of electrodes, and the other relating face charges to face potentials and face displacements, can accommodate either the traction and charge boundary conditions at the faces of the plate without electrodes or the traction and potential boundary conditions at the faces of the plate with electrodes. Dispersion curves are obtained from the first- to fourth-order approximate plate equations for a rotated 45° Y-cut lithium tantalate plate without electrodes, and these curves are compared with those from the frequency equation of the three-dimensional equations with close agreement. Solutions of forced vibrations of an AT-cut quartz plate with electrodes are obtained from the first-order plate equations complemented by the two additional relations. It is shown that cutoff frequencies of the fundamental thickness-shear vibrations from the approximate equations are identical to the ‘‘exact’’ ones obtained from the three-dimensional equations.

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