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Two-dimensional problems of anisotropic piezoelectric composite wedges and spaces are studied. The Stroh formalism is employed to obtain the basic real-form solution in terms of two arbitrary constant vectors for a particular wedge. Explicit real-form solutions are then obtained for (i) a composite wedge subjected to a line force and a line charge at the apex of the wedge and (ii) a composite space subjected to a line force, line charge, line dislocation, and an electric dipole at the center of the composite space. For the composite wedge the surface traction on any radial plane θ = constant and the electric displacement Dθ normal to the radial plane θ = constant vanish everywhere. For the composite space these quantities may not vanish but they are invariant with the choice of the radial plane.

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Surface tension measurement based on spontaneous capillary wave resonance in confined micrometer-sized liquid interfaces was demonstrated. A single-beam quasi-elastic laser scattering method was used to detect the resonance. Characteristic resonant modes were observed on a 44-μm-sized circular water surface. The frequencies of the peaks agreed well with those simulated by assuming planar resonance, and the relationship was further confirmed for triangular, square, and pentagonal water surfaces. Then, the applicability of the method was successfully demonstrated by surface tension measurements of aqueous solutions of sodium dodecyl sulfate. The sensitive detection of capillary resonance opens new possibilities for the chemical and biochemical analysis of liquid interfaces.

Summary Exact solutions of radially symmetric deformation of a spherically anisotropic and radially inhomogeneous linear elastic hollow sphere subjected to uniform radial tractions on the surfaces are derived. The power-law function is assumed to represent the radially inhomogeneity. Stress amplification/shielding phenomena are fully investigated and the benefits of using functionally graded materials are indicated. For a solid sphere under external uniform loadings, the conditions in which infinite stresses occur at the centre of the sphere regardless of applied traction magnitudes are specified. Also, circumferential stresses might have opposite sign of the applied loadings. Cavitation and blackhole phenomena at the centre of the sphere are also discussed.

Explicit results for a piezoelectric half-space x 2 ≥ 0 subject to linearly-varying surface loadings along x 3 axis are derived. The extended Stroh formalism is employed to provide three-dimensional solutions with the generalized displacement vector u expressed as a function of (z, x 2 , x 3 ). A general polynomial solution for u with order of m in x 3 is suggested and it provides a particularly efficient solution for half-space problem with loadings on the surface. A simple uniform surface loading is considered first to clarify the derivations. Then explicit solution in case of a linearly-varying surface loading along x 3 -direction is obtained. In addition, the Green's function for a piezoelectric half-space with a linearly-varying surface line loading along x 3 -axis is constructed.