‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.

Thermo-elastic damping is a significant dissipation mechanism in high quality factor microstructures. In this paper, thermo-elastic damping of the in-plane vibration of fully clamped rectangular micro-plates has been studied. The governing equation of the micro-plate motion and heat conduction equation were derived. Then, The Galerkin method has been used to solve the coupled heat-displacement ...

A solution is given for the elastic stress field in a half plane containing a plane crack parallel to the surface and subjected to a uniform normal pressure and a concentrated normal load. Frictional slip according to Coulomb's law is permitted between the crack faces. As the load is increased, a slip zone originates and grows either from a crack tip or from an intermediate point. Various arran...

Anisotropy of sand is mainly due to the geometrical arrangement of particles that depends on the orientation of applied load respect to the bedding plane. It is geologically due to micro-fabric created by the arrangement of the particles configured during deposition. Most of the models develop using stress/strain invariants are not capable of identifying this kind of anisotropy. This is mainly ...