Finite Element Method Mesh Research Articles

Application of impedance boundary conditions in finite element analysis of linear motors

Results of performance analysis of a low-speed linear induction motor with a solid steel secondary are presented. The finite element method (FEM) combined with impedance boundary conditions at the surface of secondary steel has been used as a numerical tool. Numerical values of thrust and normal forces compare favorably with experimental data. Linearization of the ferromagnetic material by comparing the surface impedance for linear and nonlinear half-spaces yields good accuracy and reduces cpu time considerably. Application of the impedance boundary condition reduces the FEM mesh size, which substantially reduces the required volume of storage and computing time. The use of the impedance boundary condition is therefore recommended for other electromagnetic problems which involve the penetration of a time-varying field in a conductive nonlinear ferromagnetic medium and in which the skin depth is small compared with the geometry of the problem. >

Compatible description of tool surfaces and FEM meshes for analysing sheet forming operations

AbstractImplementation of the 3‐D finite element method (FEM) of sheet forming operations has proceeded slowly. In particular, describing the arbitrary tool surfaces in an accurate and smooth manner, with well behaved first and second derivatives, has been a major obstacle. A new geometric method, suitable for representing any rigid tool surface, has been developed and shown to be superior to the usual schemes. The new method relies on the described tool surface for position data only. The spatial derivatives are obtained by considering only the sheet mesh nodal positions. This new scheme has been implemented with a rigid‐viscoplastic FEM program using general surface descriptions based on B‐splines and linear inter‐polation. Analytic representations of a hemispherical and rounded square punch were also compared. the comparisons show that the proposed method offers several advantages over other general formulations.1. The new representation is the proper one for formulating the equilibrium condition. Alternate forms can produce spurious results.2. The proposed method introduces inherently smooth surface derivatives that improve numerical stability, even with crude surface resolution. Suitable test problems show covergence with the new method far past the divergence points of the simulations using the standard general surface description.3. The method is reasonably efficient, with a time penalty of approximately 30–50 per cent (unoptimized) with respect to analytic surface descriptions.

A finite element analysis for the temperature field produced by a moving heat source

Using moving mesh finite element method we discuss the temperature field produced by a moving heat source with the variable thermal conductivity and with the radioative and convective boundary conditions in a wide range of the velocity. The temperature-time relationships at various velocities in the static and moving coordinate systems are studied. The steady-state temperature distributions at various velocities in the moving coordinate systems are given. The temperature field produced by the plastic deformation at the process region (a region very near the crack tip) is also studied, and the results show that the highest temperature at the process region is lower than 1000°C or 1832°F.

MODELING THE SOLIDIFICATION OF FOUNDRY CASTINGS

Abstract A comprehensive technique is described for performing the simulation of the solidification of foundry castings. A finite element method (FEM) mesh is produced for the pattern of the part, using geometric modeling techniques. Results are presented to demonstrate selection rules for the mesh size. The size of the heat transfer problem is reduced by replacing the FEM mesh in the mold material by appropriate boundary conditions on the surface of the casting. The boundary conditions are found automatically by a program which relates local surface curvature on the part to a pre-calculated library of solutions. Methods for ensuring that all of the latent heat of fusion is included are presented, and comparisons are made between different solution methods.

Fixed mesh finite element approximations to a free boundary problem for an elliptic equation with an oblique derivative boundary condition

A method for approximating the solution of an elliptic equation with an oblique derivative on a curved boundary using an unfitted finite element mesh is presented and analysed. It is shown that the method retains the order of accuracy of the fitted mesh finite element method. A similar result is obtained for a variational inequality. The usefulness of this approach is then demonstrated by using it to approximate the solution of a free boundary problem on a fixed mesh.

Boundary integral equation solution of moving boundary phase change problems

AbstractBoundary integral equation methods are presented for the solution of some two‐dimensional phase change problems. Convection may enter through boundary conditions, but cannot be considered within phase boundaries. A general formulation based on space‐time Green's functions is developed using the complete heat equation, followed by a simpler formulation using the Laplace equation. The latter is pursued and applied in detail. An elementary, noniterative system is constructed, featuring linear interpolation over elements on a polygonal boundary. Nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution. The system performs well against basic analytical solutions, using these values in the interphase jump condition, with the simplest formulation of the surface normal at boundary vertices. Because the discretized surface changes automatically to fit the scale of the problem, the method appears to offer many of the advantages of moving mesh finite element methods. However, it only requires the manipulation of a surface mesh and solution for surface variables. In some applications, coarse meshes and very large time steps may be used, relative to those which would be required by fixed grid domain methods. Computations are also compared to original lab data, describing two‐dimensional soil freezing with a time‐dependent boundary condition. Agreement between simulated and measured histories is good.

Design calculations for annular induction electromagnetic pumps based on the finite element method

The paper presents an application of the Galerkin triangular mesh finite element method using linear approximation, in axisymmetrical and plane geometry, to the design of liquid metal annular induction pumps. The code was tested by comparison with: - analytical calculations in simple geometry cases (15 × 15 square mesh) - test results on pumps constructed. Each calculation is also checked by internal balance of powers. The finite element method is particularly suitable for this application where a practical analytical method is not sufficiently accurate.