Two-dimensional Finite Element Program Research Articles

Liquefaction analyses of sandy ground improved by sand compaction piles

The two-dimensional finite element program NUP2 of dynamic effective stress analysis is developed based on the two-phase mixture theory of Biot and the strain space plasticity theory of soil. The numerical analyses are performed to investigate the liquefaction behavior of sandy ground improved by the sand compaction piles. The good performance of the numerical procedure used here is proved by the comparison of numerical and experimental results. It is also demonstrated that the numerical results provide substantial information which aid in the understanding of the liquefaction mechanisms of improved soil ground. The results of numerical and experimental investigation show that there may exist unstable zones in the compacted area near the unimproved area and an optimum compaction width to resist liquefaction of the ground for design purposes.

Finite-element simulation of powder-metal forming

A two-dimensional finite-element computer program, bulk2pm, has been developed to perform the simulation of sinter-forming processes. The code allows the analysis of the forming of complex parts and gives the distribution of the principal field-variables, including the density. The paper describes the finite-element flow formulation for powder-metal forming. The constitutive equations of porous materials are presented and the formulation is shown to be equivalent to the penalty approach used in the modeling of dense-material forming. Contact problems that emerge from the high deformations suffered by the workpiece and the complexity that tools can present are considered also. A simple but efficient re-meshing scheme is included also for the simulation of large plastic-deformation processes. A numerical example concerning the axisymmetric closed-die forging of a porous material is presented, in order to show the application of the finite-element code.

Finite-element analysis of ring gear/casing spline contact

The speed reduction from turbine to propeller is achieved in the Pratt and Whitney PT6 turbo propeller engines through a two-stage epicyclic gear train. In this arrangement, the ring gear is locked to the casing through external splines. The orbitting of the planet gears generate cyclic stresses in the teeth fillets of the ring gear and the casing. The sliding contact between the steel ring gear and the casing splines generates wear. A two-dimensional finite-element computer program was extended to iteratively solve the problem of load-dependent contact between the splines. Using this program, the nonuniform distribution of the reactive load and the relative sliding on the loaded splines are calculated for any planet gear load position. The analysis predicts that the relative sliding reduces through a change in the spline pressure angle from 20-30 deg. Spline wear is practically eliminated in field engine gearboxes through this design change. The cyclic variation of the fillet stresses are also determined due to the orbitting planet load using a detailed network and by imposing boundary displacements. Qualitative comparison of the stress prediction is made using instrumented test results. The paper demonstrates the analysis procedure using a typical ring gear and casing combination.

A study of bi-metal coins by the finite element method

A two-dimensional finite-element program, based on a rigid-plastic formulation has been used to simulate the joint of a bi-metal coin. Several geometric joint profiles have been analyzed and theoretical predictions of the joining load, the deformed grid patterns, the velocity field and the strain field are presented. The strength of the joint has been checked experimentally by measuring the separating load. Experiments have been performed on prototypes with different joint profiles in order to obtain the load necessary to separate the center of the coin from the outer ring. The results obtained have been compared with those found for two bi-metal coins currently produced, and show that the joint profiles proposed presently are suitable for industrial purposes.

Adaptive grids for coupled viscous flow and transport

An adaptive grid refinement and coarsening scheme in two dimensions for biquadratic elements is developed. This has been incorporated in a two-dimensional finite element program for steady and transient generalized Newtonian flow problems. Numerical results are given for Navier-Stokes and power law non-Newtonian flow calculations as well as coupled fluid flow and transport problems including free surfaces, thermocapillary flows, die swell and electro-rheological flows.

A monotone streamline upwind finite element method for convection-dominated flows

A new streamline upwind approximation for treating advection-dominatcd transport is presented. The proposed method is quite simple to implement with existing finite element methods. For this work, the method is used in a two-dimensional finite element computer program. The new method is applied to several test cases that have been presented in previous articles to evaluate the stability and accuracy of proposed methods for treating advection-dominatcd flows. The results demonstrate that the new method is able to predict the test cases with a significant increase in accuracy compared to previous techniques. In addition, these results demonstrate conclusively that the method does not exhibit the non-physical spatial oscillations that have plagued previous methods.

Comparison of two viscoplastic flow laws as applied to a problem of crack growth

The finite element method is incorporated in the study of the mechanical response of an advanced nickel-based superalloy IN-100 with inelastic time-dependent material behavior at 1350°F (732°C). The material's time-dependent plastic deformation (viscoplasticity) is analytically modeled by both the Bodner-Partom equations and the Malvern overstress flow law. The Bodner-Partom constitutive equations involve the use of nine material parameters which are determined from a complex procedure. Various forms of the Malvern overstress flow law are studied since this flow law uses only a few material parameters which are easily determined from uniaxial experimental data. Both the Malvern and Bodner-Partom constitutive equations are formulated in multiaxial from in a two-dimensional finite element program incorporating the constant strain triangle. The program is applied to the analysis of a center crack plate of IN-100 under a monotonic tension load. The residual force method is utilized to handle variations in material stiffness due to time-dependent plastic deformation. A Hybrid Experimental Numerical (HEN) procedure is used in order to track crack opening displacement near the crack tip. This HEN procedure controls the crack growth rate in the finite element model by following the experimental displacement rates accurately. Thus, crack growth predictions become a byproduct of both the rate sensitive model and the near field experimental displacement rates. The predictions of the two constitutive models are compared with respect to total plastic work and effective stress profiles in addition to crack growth rate.

Self-consistent vector calculation of magnetic recording using the finite element method

A two-dimensional finite element program has been developed for application to magnetic recording. It solves, as a boundary value problem, the system of a magnetic recording head with appropriate geometry, driven by a current carrying coil and interacting with a recording media whose properties are obtained from a new vector hysteresis model. Details of the program and the hysteresis model will be discussed.

A finite-element program for modeling transient phenomena in GaAs MESFET's

A two-dimensional finite-element program has been developed for analyzing transient and steady-state characteristics of GaAs devices with arbitrary geometric boundary shapes. The program code consists of two separate programs, GRID and FET, which are discussed in some detail. GRID serves to generate a nonuniform mesh, while FET computes a self-consistent solution of Poisson's and the current continuity equations. A GaAs FET with a trapezoidal recessed gate structure has been studied to demonstrate the capabilities of the program to analyze odd shapes. Current-voltage characteristics were computed for the recessed gate and a planar device. The results from both FET structures are compared and analyzed. In particular the effect of the recessed gate on the field distribution in the device is discussed. Large signal transient behaviors of both devices were examined, and it was found that both device structures produce similar results in steady-state and transient conditions.

An experimental and finite element investigation of fracture in aluminium thin plates

Detailed strain and crack-opening measurements have been made on centre crack and double edge crack specimens of aluminium alloys L70 and L71 in plates 1.6 mm thick, using the Moire technique to measure strains in front of the instantaneous crack tip during stable crack growth. The specimen load-displacement curves were also monitored during stable crack growth, using a displacement-controlled loading machine, and fracture resistance (R-) curves calculated. A two-dimensional elastic-plastic finite element program was used in a numerical model of the experiments, with stable crack growth being simulated by relaxation of the nodal reactions ahead of the initial crack tip. The numerical models were used to calculate the energy changes occurring during crack growth and also the Rice J-integral. These parameters were then examined as possible fracture criteria, and a simple energy balance proved adequate in explaining the main features of stable and unstable crack growth. This result was confirmed by modelling fracture data on L70 obtained by other investigators.

Elastic Stresses in Layered Snow Packs

AbstractA two-dimensional finite element computer program has been used to compute the elastic stress distribution in realistic multi-layered snow packs. Computations have been done on three-layered and five-layered snow packs intended to simulate conditions on the Lift Gully at Berthoud Pass, Colorado. Calculations have been performed to determine the effect of a layer of new snow and the effect of a weak sub-layer. Stress levels were obtained which are reasonable compared with available snow strength data.

Elastic Stresses in Layered Snow Packs

Abstract A two-dimensional finite element computer program has been used to compute the elastic stress distribution in realistic multi-layered snow packs. Computations have been done on three-layered and five-layered snow packs intended to simulate conditions on the Lift Gully at Berthoud Pass, Colorado. Calculations have been performed to determine the effect of a layer of new snow and the effect of a weak sub-layer. Stress levels were obtained which are reasonable compared with available snow strength data.