Infinite Finite Elements Research Articles

Energy finite element formulation for unbound acoustic domains

The Energy Finite Element Analysis (EFEA) method has been developed for conducting structural-acoustics simulations for complex vehicles at mid-to-high frequencies where conventional finite element methods are no longer computationally efficient. In applications where exterior heavy fluid loading effects must be included in the model, these effects are currently accounted in the EFEA formulation through an added mass and a radiation damping approach. This is suitable when there is an interest in computing the vibration of the structure and the total radiated power emitted in the exterior fluid. A new formulation for modeling the exterior fluid explicitly with energy finite elements is presented. There are three main components in the new development: deriving the differential equation; solving it numerically using a finite element approach; and introducing infinite finite elements in order to represent the non-reflective conditions at the outer domain of a finite element model. In this presentation, the technical aspects associated with the main elements of the new EFEA formulation for exterior non-reverberant acoustic domains will be discussed. Comparisons with analytical closed form solutions for validating the new developments and their numerical implementation will be presented.

Three-dimensional finite element analysis of interfacial delamination in traveling wave ultrasonic motors

Ultrasonic motors (USMs) are novel electric motors used for positioning controls. Due to the drive characteristic of USMs, wear and fatigue of friction material at the contact friction interface are inevitable. Contact deformation can cause local damage of USMs. Therefore, obtaining the details of the stress distribution due to the inelastic deformation is important. In this paper, a contact model of traveling wave ultrasonic motor (TWUSM) is proposed. A three-dimensional finite element model with cohesive zone elements embedded between friction layer and rotor is then developed. Infinite finite elements are included in this modeling as the boundary condition. The evolution of deformation in friction layer and rotor due to the mechanical surface loading is presented. The possible interfacial delamination process between friction material and rotor is also numerically investigated.

NONLINEAR ANALYSIS OF ONE AND TWO DIMENSIONAL CONSOLIDATION PROBLEMS FOR UNBOUNDED SATURATED SOIL MEDIA

Soil in general is not a linear material, in which the relation between stress and strain is more complicated than the simple, linearly elastic relation. To make accurate deformation analysis of clay deposits, the incremental Biot's theory of consolidation is used together with elasto-viscoplastic constitutive relations based on the critical state concept using the modified Cam-clay model. One and two dimensional consolidation problems were analyzed numerically by the infinite-finite elements. Results show that the proposed method can describe the effect of sample thickness on consolidation phenomena. Also the two dimensional behavior of a clay foundation during the construction of embankment was analyzed.

An energy finite element formulation for high-frequency vibration analysis of externally fluid-loaded cylindrical shells with periodic circumferential stiffeners subjected to axi-symmetric excitation

A hybrid method is developed for predicting the high-frequency vibration response of fluid-loaded cylindrical shells with periodic circumferential stiffeners. In this method, the cylindrical shell is modeled using the Energy Finite Element Analysis (EFEA) method which includes added mass and radiation effects due to the surrounding exterior fluid medium. The joint matrices of the EFEA formulation at the location of the periodic stiffeners are computed based on Periodic Structure (PS) theory. Thus, the periodicity effects such as pass/stop characteristics are captured in the EFEA solution. The hybrid EFEA-PS method is used to analyze the vibration of a fluid-loaded axisymmetric cylindrical shell with periodic circumferential stiffeners. The flexural energy stored in each periodic section is computed. The results are compared with the solution produced by a very dense axisymmetric Finite Element (FE) model with infinite finite elements for the fluid domain. The good correlation indicates that the new hybrid method captures properly both the heavy fluid effects of the exterior fluid medium and the periodicity characteristics due to periodic stiffeners.

Flow noise predictions of a submerged cylinder under turbulent boundary layer excitations

The unsteady fluctuated pressure underneath turbulent boundary layers (TBL) is one of major noise sources in moving vehicles. Recently, discretized TBL forcing functions have been applied to planar structures in air [Y. F. Hwang and S. A. Hambric, Noise-Con, 2000; M. Allen and N. Vlahopoulos, Computers and Structures, 2000; M. Allen and N. Vlahopoulos, Finite Elements in Analysis and Design, 2001; M. Allen, R. Sbragio, and N. Vlahopoulos, AIAA J. 2001]. This paper discusses prediction of the flow-induced radiated noise and surface responses of a submerged hemisphere-capped cylindrical shell (L/D=11). The FEM/IFEM (infinite finite element method) approach is used to calculate structural acoustic transfer functions and to accurately account for the fluid loading effects. The effect on TBL due to the curvature of a cylinder is captured by utilizing the potential flow—boundary layer theory to determine key boundary layer parameters. Predictions of the surface intensity and far field responses are developed through stochastic analysis due to the natural of the TBL excitations. A MATLAB script is generated to determine the power spectral density of the responses. [Work supported by ONR Code 334.]

MODIFIED CONDUCTION SHAPE FACTORS FOR ISOTHERMAL BODIES EMBEDDED IN A SEMI-INFINITE MEDIUM

Numerical finite-element method calculations were performed for isothermal surfaces embedded in a semi-infinite medium with convection boundary conditions. A modified shape factor was defined that combines the conduction heat transfer in the medium and the convection to the environment, with the geometrical characteristics of the problem. Infinite finite elements are used; these form the last layer of elements in the infinite directions. The modified shape factors for a sphere and for a long horizontal cylinder are presented in graphs and correlations, both using nondimensional parameters. The heat flux distribution on the surface of the body and the temperature and heat transfer on the surface of the medium are also presented.