Nite Element Formulation Research Articles

Simulation and Modelling of Smart Beams with Robust Control Subjected to Wind Induced Vibration

This paper presents some recent developments in modelling and numerical analysis of piezoelectric systems and controlled smart structures based on a ?nite element formulation with embedded control. The control aims at vibration suppression of the structure subjected to external disturbances, like wind and noise, under the presence of model inaccuracies, using the available measurements and controls. A smart structure under dynamic loads is analysed and comparison between results for beam with and without control is made. The numerical results show that the control strategy is very effective and suppresses the vibrations of the structure.

Numerical Analysis of Double-Diffusive Convection/Solidification Under g-Jitter/Magnetic Fields

A e nite element model is presented for the g-jitter induced double-diffusive convection and solidie cation phenomena with and without the presence of magnetic e elds in an Sn-doped Bi crystal growth system planned for space experiments. The model is developed based on the deforming e nite element formulation with the penalty formulation forpressure approximation. An isothermalfront tracking algorithm is used to predict thesolid‐ liquid interface. Extensive numerical simulations are carried out and parameters studied include the solute concentration dependent melting temperature and magnetic e eld strength under both steady state and g-jitter conditions. Both synthesized g-jitter and real g-jitter data taken from space e ights are used. Computed results show that the concentration effects on interface morphology must be considered for an accurate prediction of solidie cation interface morphology, and g-jitter can induce signie cant convective e ows in the liquid pool, which, in turn, cause solute concentration nonuniformity during the space crystal growth. The use of an applied magnetic e eld can be effective in suppressing the deleterious g-jitter induced convection and solute nonuniformity and their effects on solidie cation.

Nonlinear Response of Composite Panels Under Combined Acoustic Excitation and Aerodynamic Pressure

A e nite element formulation is presented for the analysis of the large dee ection response of composite panels subjected to high acoustic excitation and aerodynamic pressure at supersonic e ow. The e rst-order shear defor- mation theory is considered for laminated composite plates, and the von Karm´ an nonlinear strain -displacement relations are employed for panel large dee ection response. The e rst-order piston theory aerodynamics and the simulated Gaussian white noise are employed for the aerodynamic and acoustic loads, respectively. The nonlinear equationsofmotion foranarbitrarily laminated compositepanelsubjectedto combined aerodynamicand acoustic pressures are formulated e rst in structure node degrees of freedom. The system equations are then transformed and reduced to a set of coupled nonlinear equations in modal coordinates. Modal participation is dee ned and the in vacuo modes to be retained in the analysis are based on the modal participation values. Numerical results include root mean square values of maximum dee ections, dee ection and strain response time histories, probability distributions, power spectrum densities, and skewness and kurtosis. Results showed that combined acoustic and aerodynamic loads have to be considered for panel analysis and design at high dynamic pressure values.

Finite element formulation of exact non-reflecting boundary conditions for the time-dependent wave equation

A modi ed version of an exact Non-re ecting Boundary Condition (NRBC) rst derived by Grote and Keller is implemented in a nite element formulation for the scalar wave equation. The NRBC annihilate the rst N wave harmonics on a spherical truncation boundary, and may be viewed as an extension of the secondorder local boundary condition derived by Bayliss and Turkel. Two alternative nite element formulations are given. In the rst, the boundary operator is implemented directly as a ‘natural’ boundary condition in the weak form of the initial–boundary value problem. In the second, the operator is implemented indirectly by introducing auxiliary variables on the truncation boundary. Several versions of implicit and explicit timeintegration schemes are presented for solution of the nite element semidiscrete equations concurrently with the rst-order di erential equations associated with the NRBC and an auxiliary variable. Numerical studies are performed to assess the accuracy and convergence properties of the NRBC when implemented in the nite element method. The results demonstrate that the nite element formulation of the (modi ed) NRBC is remarkably robust, and highly accurate. Copyright ? 1999 John Wiley & Sons, Ltd.

Modeling of Microcrack Damaged Composite Plates Undergoing Nonlinear Bimodular Flutter Oscillations

Numerical methods to investigate the e utter response and aeroelastic stability of plates made of composite materials, wherein microcracking occurs in the matrix material, are presented. The analytical modeling of the modulus reduction due to microcracks is based on a self-consistent method with a two-phase model and yields reduced moduli of the composites as functions of the crack density distribution. Both a e nite difference and a e nite element formulation are presented for two-dimensional laminated plates in supersonic e ow. From the numerical results, it is shown that the microcracking in composites results in a loss of aeroelastic stability through nonlinear bimodular oscillation as well as by a direct reduction in the bending stiffness. For three-dimensional e utter problems, however, reduction in thetorsionalrigidity and changes in elasticcouplings may furtherdecrease the stability.

Effects of yield surface shape on sheet metal forming simulations

Three phenomenological yield criteria are adopted to describe the plastic behaviour of sheet metals with normal plastic anisotropy. The sheet metals are assumed to be elastic-plastic, rate-sensitive and incompressible. A rate-sensitive thin shell nite element formulation based on the virtual work principle is derived for the three yield criteria. The eects of the yield surface shapes based on the three yield criteria with the same value of the plastic anisotropy parameter R on the strain distribution and localization are investigated under a hemispherical punch stretching operation and a plane strain drawing operation. The results of the simulations show that the yield surface shape, in addition to the plastic anisotropy parameter R, controls the punch force, strain distribution and strain localization for the punch stretching operation. However, the yield surface shape does not aect the punch force and the strain distribution signicantly for the plane strain drawing operation. ? 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng., 41, 559{584 (1998)

A THREE-DIMENSIONAL FINITE ELEMENT FORMULATION FOR THERMOVISCOELASTIC ORTHOTROPIC MEDIA

SUMMARY This paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the nite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the nite element solution. Use is made of a Dirichlet{Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method. ? 1997 by John Wiley & Sons, Ltd.