An adaptive finite element method for solving incompressible steady-state free surfaces flow problems, driven by surface tension, is presented. Eulerian free surface capturing, the pseudo-concentration technique, is used to locate interfaces. This approach adds a transport equation to the Navier-Stokes equations. This system of equations is solved in a coupled manner using stabilized finite ele...

We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiti...

This paper presents how to determine the thickness of hysteresis ring of hysteresis motor using the finite element method combined with a vector hysteresis model. From the magnitude and direction of the magnetic field intensity, the magnetization of each ring element is calculated by the vector hysteresis model and the torque can be obtained from the vector sum of each torque of each element or...

We consider the 9-node shell element referred to as the MITC9 shell element in plate bending solutions and present a simplified mathematical analysis. The element uses bi-quadratic interpolations of the rotations and transverse displacement, and the “rotated Raviart-Thomas” interpolations for the transverse shear stresses. A rigorous mathematical analysis of the element is still lacking, even f...

It is well known that the conventional edge element method in solving vector Maxwell’s eigenvalue problem will lead to the presence of nonphysical zero eigenvalues. This paper uses the mixed finite element method to suppress the presence of these nonphysical zero eigenvalues for 2D vector Maxwell’s eigenvalue problem in anisotropic media. We introduce a Lagrangian multiplier to deal with the co...

the incremental sheet metal forming (ismf) process is a new and flexible method that is well suited for small batch production or prototyping. this paper studies the use of the finite element method in the incremental forming process of aa1050 sheets to investigate the influence of tool diameter, vertical step size, and friction coefficient on forming force, spring-back, and thickness distribut...

The displacements of three-dimensional linearly elastic plate domains can be expanded as a compound power-series asymptotics, when the thickness parameter tends to zero. The leading term u in this expansion is the well-known Kirchho?–Love displacement Aeld, which is the solution to the limit case when → 0. Herein, we focus our discussion on plate domains with either clamped or free lateral boun...

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...