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The present paper is devoted to the solution of the steady laminar flow of an incompressible viscous electrically conducting fluid over a rotating disk in the presence of a uniform transverse magnetic field. Classical von Kármán problem of a rotating disk is extended to the case where the disk surface admits partial slip. Using von Kármán similarity transformation the nonlinear equations of motion...
The use of conventional continuum mechanics can provide solutions to a variety of problems involving the physics of granular solids. However, analysts have resorted to artificial constraints to obtain the counter‐intuitive experimental results where vertical stresses across the rigid base under a conical sand pile reach a local minimum, not a global maximum, beneath the apex. An explanation is provided...
In this paper we discuss the constitutive relations for micropolar plates recently obtained by Altenbach and Eremeyev. We pay particular attention to their relation for the resultant drilling stress couple and compare it with that used so far in the statically and kinematically exact nonlinear six‐parameter shell theory. Using the results of Altenbach and Eremeyev, we present bounds on values of the...
All piezoelectric actuators are of finite dimension. The effect of finite geometry on the electro‐elastic responses is of significance to the design of practical actuators. Electromechanical model is established for an interface electrode in a piezoelectric actuator with finite dimension. The methods of infinite series and Cauchy singular integral equation are employed to perform the electro‐elastic...
We investigated dynamic responses of a parametric pendulum obtained experimentally. Using the recurrence plot technique designed to analyze experimental time series we have distinguished different types of motion. This method, supplemented by recurrence quantification analysis (RQA), has been used to identify oscillations, rotations, and transient chaotic vibrations for relatively short time series...
Highly scalable parallel domain decomposition methods for elliptic partial differential equations are considered with a special emphasis on problems arising in elasticity. The focus of this survey article is on Finite Element Tearing and Interconnecting (FETI) methods, a family of nonoverlapping domain decomposition methods where the continuity between the subdomains, in principle, is enforced by...
We present here a Boundary Element Method (BEM) implementation for SH harmonic waves in a class of inhomogeneous anisotropic media. The inhomogeneity is assumed to be the same not only for the stiffnesses, but also for the density. The implementation is based on a closed form fundamental solution for SH waves derived by Daros [C. H. Daros, A fundamental solution for SH‐waves in class of inhomogeneous...
An exact closed form 2D Green's function for an inhomogeneous elastic solid is presented. Assuming a unidirectional exponential inhomogeneity, the Green's function is expressed in terms of the modified Bessel function of the second kind. It is pointed out that the decomposition of the Green's function into the grading and non‐grading terms is impossible in the sense of the closed form solution. An...
We consider the in‐plane motion of elastic strings on tree‐like network, observed from the ‘leaves’. We investigate the inverse problem of recovering not only the physical properties, i.e. the ‘optical lengths’ of each string, but also the topology of the tree which is represented by the edge degrees and the angles between branching edges. To this end we use the Boundary Control method for wave equations...
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