Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions...

The experimental method of caustics was used for the evaluation of the stress-singularities created by concentrated oblique load applied at the apex of a wedge or on the horizontal straight boundary of a half-plane. The wedge was considered to be elastic, isotropic and under generalized plane stress conditions. According to the method of caustics, the light rays impinging normally at the thin p...

In the 1960s, geology was transformed by the paradigm of plate tectonics. The 1965 paper of Bullard, Everett and Smith was a linking transition between the theories of continental drift and plate tectonics. They showed, conclusively, that the continents around the Atlantic were once contiguous and that the Atlantic Ocean had grown at rates of a few centimetres per year since the Early Jurassic,...

Simplified theories governing behavior of beams and plates keeping the fundamental characteristics of the being modeled objects are proposed and discussed. By simplification, we mean decrease of order of partial differential equations (PDEs) with respect to spatial coordinates. Our approach is used for both discrete and continuous models. An advantage of Padé approximation is addressed. First p...

Via structures in multi-layer printed circuit boards (PCBs) and packages are studied using an equivalent transmission line model. Thus, transmission line theories, such as characteristic impedance and propagation constant, can be used to characterize the performance of via structures in a signal path. The closed-form expressions of R, L, G, C parameters of the equivalent transmission line model...

We use the global collocation method, the first and the third-order shear deformation plate theories, the Mori–Tanaka technique to homogenize material properties, and approximate the trial solution with multiquadric radial basis functions to analyze free vibrations of functionally graded plates. Frequencies computed by the present method are found to agree well with those from the analytical so...

Flexural wave motion in an infinite transversely isotropic, thermoelastic plate in the context of conventional coupled thermoelasticity (CT), Lord-Shulman (LS) and Green-Lindsay (GL) theories of generalized thermoelasticity has been studied by asymptotic method. The asymptotic operator plate model for flexural motion in a transversely isotropic thermoelastic plate leads to fifth degree polynomi...

Blocks of acid sulfate altered rock ejected from Halema`uma`u crater in the March 2008 eruption provide evidence of deeper processes that are driving the shallow hydrothermal alteration in this area. Previous work shows that the surficial alteration is dominated by remnant opal (SiO2) and anatase (TiO2), which are compositionally similar to materials found at Home Plate on Mars. The opal deposi...

A mathematical framework is proposed to predict the features of the (5 5 7) lath transformation in low-carbon steels based on energy minimisation. This theory generates a one-parameter family of possible habit plane normals and a selection mechanism then identifies the (5 5 7) normals as those arising from a deformation with small atomic movement and maximal compatibility. While the calculation...

In this paper, we discuss and critique existing hypotheses about the geology of Middle-earth in light of current geological theories of planetary formation, mountain building (orogeny) and plate tectonics. We dispute the prevailing tectonic explanation for the major geological features of Middle-earth and Arda on the basis of evidence as yet not fully considered about the formation of the plane...