Finite Element Description Research Articles

Micromagnetics calculation for two-dimensional thin-film geometries using a finite-element formulation

Micromagnetics problems in two dimensions are formulated in terms of a finite-element description. The free energy, including exchange, anisotropy, external field, and demagnetization contributions, is approximated by means of integrals over linear triangular finite elements and minimized with respect to the nodal variables. By enforcing the constraint that the magnetization vectors at the nodes have constant magnitude, the resulting minimization equations are nonlinear. They are solved using Gauss-Seidel iteration. The finite-element description allows calculations to be performed for arbitrary two-dimensional geometries. In the examples presented, the magnetization distributions obtained were in agreement with expectations based on domain theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Inter-ply rotational compatibility for composite plates

Through-the-thickness shear effects have been considered within a new finite element incorporating two methods of handling interply compatibility as well as large displacements. The first method is based upon a slope and displacement continuity while the second method is formulated with a curvature continuity. Both methods can be incorporated into a general finite element description. The results indicate some promise in describing the interlaminar characteristics of laminated plates. Large displacement solutions are carried out considering transverse loading in addition to collapse in-plane loading for rectangular plates.

Elastic Radiation From Explosively-Loaded Axisymmetric Cavities

Our earlier calculations of the radiation spectra from explosively-driven ellipsoidal cavities in an unbounded medium have been extended to axisymmetric cavities of a more general shape. These calculations are based on a finite element description of conditions on the cavity surface, together with a numerical implementation of the elastodynamic integral representation theorem to determine the far field. In addition, a simple, analytical model was developed which provides very good agreement with the numerical results. Elongated cavities are found to be effective low-pass filters for seismic radiation in the direction parallel to the long axis. For the cylinder, the ‘corner’ frequency varies inversely with length or, relative to a sphere with the same volume, with the 2/3-power of the aspect ratio. Ellipsoidal cavities behave similarly. Separated spheres, cylinders connected to spheres and annular configurations were also investigated. Most of the calculations were for an unbounded medium, but free surface effects were studied as well for ellipsoidal cavities. The significance of the results is discussed in connection with the potential use of large cavities for decoupling underground nuclear explosions.

Rayleigh‐Ritz analysis and finite element descriptions derived from variational principles of diffraction by a circular disk

The Kirchhoff‐Helmholtz integral equation yields a variational principle for the pressure on the surface of a vibrating body [A. D. Pierce and X.‐F. Wu, J. Acoust. Soc. Am. Suppl. 1 74, S107 (1983)]. A comparable principle is derived here for wave diffraction by a rigid body. Both versions offer the prospect of a more efficient treatment of diffraction effects than other methods, such as T matrices and the doubly asymptotic approximation. As a first application, algorithms for the evaluation of the pressure on the surface of a vibrating disk are derived and developed for constant frequency excitation and an axisymmetric surface pressure. For radiation, this situation arises when the vibrational pattern is axisymmetric. Axisymmetry for the reflection problem is obtained for low values of ka at arbitrary incidence, or else for normal incidence at arbitrary ka. The variational principles are used to derive system equations associated with (1) assumed mode functions and (2) finite elements. In the former, a sequence of admissible functions are selected to represent the surface pressure, and the variational principle provides the best combination of (complex) amplitudes describing the overall contribution of each mode. The finite element version yields simultaneous equations for the pressures at the nodes of the finite element mesh. In both techniques the system equations are simultaneous linear algebraic equations. The only difference in the treatment of the radiation and reflection problems is the inhomogeneous terms in the equations. [Work supported by ONR.]

A probabilistic study relating to tolerancing and path generation error

The effect of manufacturing tolerances on the performance of constrained kinematic chains is analyzed using probability theory. In particular, the method is applied to examples of path generating mechanisms to determine the mean and standard deviation of the vector position of a coupler point. The mean and standard deviation of errors in linkage lengths is thus accumulated to produce the mean coupler curve and the deviated curves. Theory is compared with experimental results for a specific coupler curve obtained from microadjustment of the links on a planar coupler path plotter. The probabilistic analysis utilizes a finite-element description of the kinematic chain and partial derivatives of the output variable with each length variable result from easy manipulation of the system coordinate transformation.

Finite Element Elastic Beam‐Column

An accurate and unified finite element description is presented, in both stiffness and flexibility formats, of the response of planar elastic beams subject to terminal loads. The stability and bowing functions are inter‐related, their descriptions accounting for the effects of axial deformability and a measure of the shear deformation effects. A perturbation technique is used to solve the non‐linear governing equations. The solutions so derived are cast in four distinct forms: (1) Deformation; (2) incremental; (3) perturbation; and (4) asymptotic forms of structural analysis. A brief comparison between related formulations presented in the literature is included.

FLUX: A general interactive finite elements package for 2D electromagnetic fields

Achievement of finite element methods leads nowadays to the development of general purpose packages. FLUX, developed by the Laboratoire d'Electrotechnique de l'Institut National Polytechnique de Grenoble is an interactive system in which graphic facilities are combined with a convenient command language to allow a high level of conversationnal use. FLUX is made of three independant programs : a pre-precessor : ENTREE for geometrical, physical and finite element descriptions of the model, the computation processor RESOL in which equations occuring from finite elements are solved, and, finally EXPLOI, the post-processor for flux plots, field visualisation, forces and torques. FLUX is implemented under the conversationnal system MULTICS on the HB68 computer of the Centre Inter-universitaire de Calcul de Grenoble. It is available in France through TRANSRAC, the french computer network, and in all western EUROPE through EURONET.

Coordinate transformation and truncation for rotating spacecraft with flexible appendages

The analytical structures of alternative coordinate transformations for the variables that characterize the deformations of finite element models of flexible appendages on rotating spacecraft are examined. Particular emphasis is given to the truncation operations that are essential for efficient numerical simulations of flexible spacecraft, due to the necessarily large number of coordinates employed in a finite element description. A theorem is developed which establishes necessary conditions for the commutativity of the required truncation and inversion operations. The recommended alternative for the rotating elastic appendage is a complex transformation with previously published orthogonality properties, which permit the derivation in this paper of a relatively simple explicit set of transformed and truncated equations of modal vibration in real variables.