Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Based on the nonlocal theory and Mindlin plate theory,the governing equations(i.e.,a system of partial differential equations(PDEs)for bending problem)of magnetoelectroelastic(MEE)nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle.The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions(MPS)to solve the governing equations numerically.It is confirmed that for the present bending model,the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points.The effects of different boundary conditions,applied loads,and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method.Some important conclusions are drawn,which should be helpful for the design and applications of electromagnetic nanoplate structures.

HIGH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR 2-D RESONATOR PROBLEM

The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.

A radial basis function for reconstructing complex immersed boundaries in ghost cell method

It is important to track and reconstruct the complex immersed boundaries for simulating fluid structure interaction problems in an immersed boundary method（IBM）. In this paper, a polynomial radial basis function（PRBF） method is introduced to the ghost cell immersed boundary method for tracking and reconstructing the complex moving boundaries. The body surfaces are fitted with a finite set of sampling points by the PRBF, which is flexible and accurate. The complex or multiple boundaries could be easily represented. A simple treatment is used for identifying the position information about the interfaces on the background grid. Our solver and interface reconstruction method are validated by the case of a cylinder oscillating in the fluid. The accuracy of the present PRBF method is comparable to the analytic function method. In ta flow around an airfoil, the capacity of the proposed method for complex geometries is well demonstrated.

ON APPROXIMATION BY SPHERICAL REPRODUCING KERNEL HILBERT SPACES

The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given.

On Higher Order Pyramidal Finite Elements

In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions.Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one.It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials.The space of ansatz functions contains all quadratic functions on each of four subtetrahedra that form a given pyramidal element.