A Balancing Domain Decomposition Method by Constraints (BDDC) is constructed and analyzed for the Reissner-Mindlin plate bending problem discretized with MITC finite elements. This BDDC algorithm is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints. After the implicit elimination of the interior degrees of freedom...

This paper establishes a very general theory for a posteriori error analysis of finite element methods of the Reissner-Mindlin plate problem in the literature. The theory assures reliability of explicit residual error estimates. The conclusion of this theory is sparsity in the mathematical research of uniform a posteriori error control. Indeed, the a posteriori error estimate for various finite...

|For crystal resonators, it is always desirable to calculate the electric properties accurately for application purposes. As an extension of the Mindlin plate theory based nite element analysis of crystal resonators, a new theory for the electroded plates is derived and the piezoelectrically forced vibrations are formulated and implemented in this paper in a manner similar to our previous work....

In this paper, a fundamental solution for the Mindlin plate theory with damping is derived in the Laplace transform domain first time. The applications of this fundamental solution are demonstrated by the method of fundamental solution (MFS). All variables in the time domain can be obtained by the Durbin’s Laplace transform inversion method. Numerical examples demonstrate the accuracy of the me...

Free vibration of a magnetoelectroelastic plate resting on a Pasternak foundation is investigated based on Mindlin theory. The in-plane electric and magnetic fields can be ignored for plates. According to the Maxwell equation and magnetoelectric boundary condition, the variation of electric and magnetic potentials along the thickness direction of the plate is determined. Using Hamilton’s princi...

The high frequency vibrations of quartz crystal plates have been extensively studied for the design and optimization of resonators which work at the thickness-shear vibration mode with relatively high frequency in the RF range. Earlier research work started from the development of special plate equations required for the high frequency vibrations of quartz crystal plates by Mindlin, known as th...

This paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the Reissner-Mindlin theory for thick plates and using Hamilton's principle, the governing equa...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...