First-order system least squares (FOSLS) was developed in [SIAM J. Numer. Anal., 34 (1997), pp. 1727–1741; SIAM J. Numer. Anal., 35 (1998), pp. 320–335] for Stokes and elasticity equations. Several new results for these methods are obtained here. First, the inverse-norm FOSLS scheme that was introduced but not analyzed in [SIAM J. Numer. Anal., 34 (1997), pp. 1727–1741] is shown to be continuou...

Homogenization method is applied to topology optimization of a weakly coupled two physics problem, where structures are made periodically perforated material. The microscopic periodic cell macroscopically modulated, the design characterized by material density and its homogenized Hooke’s law at each point domain. coupling weak because involved solved consecutively: first, fluid determined using...

in this paper, free vibration of functionally graded rectangular simply supported thick plates based on two variable refined plate theory is presented. according to a power-law distribution, the mass density and elasticity modulus of the plate are considered to vary while poisson’s ratio is constant. in order to extract the five constitutive equations of motion, hamilton principle is employed. ...

due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. in this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on gurtin-murdoch continuum model to consider surface stre...

In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are and have zero angular component. The weak formulation of reduces to a two on meridian involving weighted integrals. is formulated mixed method framework both stress displacement treated as unknowns. symmetry condition for tensor weakly imposed. Well posedness continuous its...

In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cros...

Introduction: Magnetic resonance elastography (MRE) is a non invasive method that combines externally applied vibrations with the motion sensitivity of MRI to measure the shear elasticity soft tissues [1]. In MRE this is traditionally achieved by solving an inverse problem with MRE shear wave images as input data [2]. A complementary approach, which does not require the solution of an inverse p...

The contact problem of elastic bodies, each consisting of a finite layer of uniform thickness rigidly adhering to a half-plane, is investigated on the basis of the two-dimensional theory of elasticity. The materials of the layer and the half-plane in the contact body are isotropic and homogeneous, yet each of them may have distinct elastic properties. The mixed boundary value problem is reduced...

Keeping the eigenfrequencies of a structure away from the external excitation frequencies is one of the main goals in the design of vibrating structures in order to avoid risk of resonance. This paper is devoted to the topological design of freely vibrating continuum structures with the aim of maximizing the fundamental eigenfrequency. Since in the process of topology optimization some areas of...