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Title: Incremental Volumetric Remapping Method: Analysis and Error Evaluation

Abstract

In this paper the error associated with the remapping problem is analyzed. A range of numerical results that assess the performance of three different remapping strategies, applied to FE meshes that typically are used in sheet metal forming simulation, are evaluated. One of the selected strategies is the previously presented Incremental Volumetric Remapping method (IVR), which was implemented in the in-house code DD3TRIM. The IVR method fundaments consists on the premise that state variables in all points associated to a Gauss volume of a given element are equal to the state variable quantities placed in the correspondent Gauss point. Hence, given a typical remapping procedure between a donor and a target mesh, the variables to be associated to a target Gauss volume (and point) are determined by a weighted average. The weight function is the Gauss volume percentage of each donor element that is located inside the target Gauss volume. The calculus of the intersecting volumes between the donor and target Gauss volumes is attained incrementally, for each target Gauss volume, by means of a discrete approach. The other two remapping strategies selected are based in the interpolation/extrapolation of variables by using the finite element shape functions or moving leastmore » square interpolants. The performance of the three different remapping strategies is address with two tests. The first remapping test was taken from a literature work. The test consists in remapping successively a rotating symmetrical mesh, throughout N increments, in an angular span of 90 deg. The second remapping error evaluation test consists of remapping an irregular element shape target mesh from a given regular element shape donor mesh and proceed with the inverse operation. In this second test the computation effort is also measured. The results showed that the error level associated to IVR can be very low and with a stable evolution along the number of remapping procedures when compared with the other two methods. Besides, the method proved to be very robust even in critical remapping situations such as poor geometrical definition of the mesh domain boundaries.« less

Authors:
; ; ;  [1];  [2]
  1. CEMUC, Department of Mechanical Engineering, University of Coimbra, Polo II, Rua Luis Reis Santos, Pinhal de Marrocos, 3030-788 Coimbra (Portugal)
  2. Department of Mechanical Engineering, University of Minho, Campus de Azurem, 4800-058 Guimaraes (Portugal)
Publication Date:
OSTI Identifier:
21061765
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 908; Journal Issue: 1; Conference: NUMIFORM 2007: 9. international conference on numerical methods in industrial forming processes, Porto (Portugal), 17-21 Jun 2007; Other Information: DOI: 10.1063/1.2740914; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALLOYS; COMPUTERIZED SIMULATION; D CODES; ERRORS; EVALUATION; EXTRAPOLATION; FINITE ELEMENT METHOD; INTERPOLATION; LEAST SQUARE FIT; MESH GENERATION; METALS; PERFORMANCE; SHEETS; WEIGHTING FUNCTIONS

Citation Formats

Baptista, A. J., Oliveira, M. C., Rodrigues, D. M., Menezes, L. F., and Alves, J. L. Incremental Volumetric Remapping Method: Analysis and Error Evaluation. United States: N. p., 2007. Web. doi:10.1063/1.2740914.
Baptista, A. J., Oliveira, M. C., Rodrigues, D. M., Menezes, L. F., & Alves, J. L. Incremental Volumetric Remapping Method: Analysis and Error Evaluation. United States. doi:10.1063/1.2740914.
Baptista, A. J., Oliveira, M. C., Rodrigues, D. M., Menezes, L. F., and Alves, J. L. Thu . "Incremental Volumetric Remapping Method: Analysis and Error Evaluation". United States. doi:10.1063/1.2740914.
@article{osti_21061765,
title = {Incremental Volumetric Remapping Method: Analysis and Error Evaluation},
author = {Baptista, A. J. and Oliveira, M. C. and Rodrigues, D. M. and Menezes, L. F. and Alves, J. L.},
abstractNote = {In this paper the error associated with the remapping problem is analyzed. A range of numerical results that assess the performance of three different remapping strategies, applied to FE meshes that typically are used in sheet metal forming simulation, are evaluated. One of the selected strategies is the previously presented Incremental Volumetric Remapping method (IVR), which was implemented in the in-house code DD3TRIM. The IVR method fundaments consists on the premise that state variables in all points associated to a Gauss volume of a given element are equal to the state variable quantities placed in the correspondent Gauss point. Hence, given a typical remapping procedure between a donor and a target mesh, the variables to be associated to a target Gauss volume (and point) are determined by a weighted average. The weight function is the Gauss volume percentage of each donor element that is located inside the target Gauss volume. The calculus of the intersecting volumes between the donor and target Gauss volumes is attained incrementally, for each target Gauss volume, by means of a discrete approach. The other two remapping strategies selected are based in the interpolation/extrapolation of variables by using the finite element shape functions or moving least square interpolants. The performance of the three different remapping strategies is address with two tests. The first remapping test was taken from a literature work. The test consists in remapping successively a rotating symmetrical mesh, throughout N increments, in an angular span of 90 deg. The second remapping error evaluation test consists of remapping an irregular element shape target mesh from a given regular element shape donor mesh and proceed with the inverse operation. In this second test the computation effort is also measured. The results showed that the error level associated to IVR can be very low and with a stable evolution along the number of remapping procedures when compared with the other two methods. Besides, the method proved to be very robust even in critical remapping situations such as poor geometrical definition of the mesh domain boundaries.},
doi = {10.1063/1.2740914},
journal = {AIP Conference Proceedings},
number = 1,
volume = 908,
place = {United States},
year = {Thu May 17 00:00:00 EDT 2007},
month = {Thu May 17 00:00:00 EDT 2007}
}
  • Since sheet metal forming has a high percentage contribution in the overall design costs of a new car, this engineering area assisted in the last decades to considerable development efforts. The present challenge is to simulate all the production stages, from the initial blank sheet to the final part ready to assembly. On this particular issue of multi-step deep-drawing simulation, this work presents a new remapping method called Incremental Volumetric Remapping (IVR) developed to minimize the error that occurs, when performing the variable transfer operation between two different meshes. The IVR method is based in a volumetric approach where themore » calculus of the remapped state variables is obtained by means of a weighted average of the intersection volume between the meshes. The method performance is tested and compared with a standard extrapolation-interpolation, by applying a numerical example of the Numisheet'005 Conference, 'The Channel Draw/Cylindrical Cup Benchmark'.« less
  • Asymmetric incremental sheet forming (AISF) is a relatively new manufacturing process for the production of low volumes of sheet metal parts. Forming is accomplished by the CNC controlled movements of a simple ball-headed tool that follows a 3D trajectory to gradually shape a sheet metal blank. The local plastic deformation under the tool leads to a number of challenges for the Finite Element Modeling. Previous work indicates that implicit finite element methods are at present not efficient enough to allow for the simulation of AISF for industrially relevant parts, mostly due to the fact that the moving contact requires amore » very small time step. Explicit Finite Element methods can be speeded up by means of mass or load scaling to enable the simulation of large scale sheet metal forming problems, even for AISF. However, it is well known that the methods used to speed up the FE calculations can entail poor results when dynamic effects start to dominate the solution. Typically, the ratio of kinetic to internal energy is used as an assessment of the influence of dynamical effects. It has already been shown in the past that this global criterion can easily be violated locally for a patch of elements of the finite element mesh. This is particularly important for AISF with its highly localised loading and complex tool kinematics. The present paper details an investigation of dynamical effects in explicit Finite Element analysis of AISF. The interplay of mass or time scaling scheme and the smoothness of the tool trajectory is analysed with respect to the resulting errors. Models for tool path generation will be presented allowing for a generation of tool trajectories with predefined maximum speed and acceleration. Based on this, a strategy for error control is proposed which helps reduce the time for setting up reliable explicit finite element models for AISF.« less
  • There are two fundamentally different strategies for solving the standard transport or continuity equation, corresponding to whether it is expressed as a partial differential equation or as an integral statement of conservation. The more common approach is to discretize the partial differential equation and to march the solution forward in time. The alternative method is to project cell volumes along Lagrangian trajectories as far forward or backward in time as desired, and then to remap the resulting density distribution onto some target mesh. This latter approach is known as remapping. Remapping has many advantages, not the least of which ismore » that the time step is limited only by accuracy considerations, but it tends to be expensive and complex. In this paper the authors show that if the time step is made sufficiently short such that trajectories are confined to the nearest neighbor cells, then the remapping may be written as a flux-form transport algorithm, and it becomes nearly as simple and efficient as standard transport schemes. The resulting method, called incremental remapping, retains most of the advantages of general remapping. These include: (a) geometric basis for transport, (b) compatibility of associated tracer transport with simple tracer advection, i.e. retention of tracer monotonicity properties, and (c) efficient handling of multiple tracers since each additional tracer adds only a relatively small incremental cost.« less
  • The precision and speed of Ashworth's rapid lifetime determination method (RLD) for a single exponential decay is evaluated. The RLD is compared to the weighted linear least-squares (WLLS) method. Results are presented as a function of integration range and signal noise level. For both the lifetime and the preexponential factor, optimum fitting regions exist, yet the errors increase rather slowly on either side of the optimum. The optimum conditions for determination of the preexponential factor and the lifetime are similar, so both can be determined with good precision even at low total counts (10/sup 4/). In the optimum region, themore » relative standard deviations for the RLD are only 30-40% worse than for WLLS, but the calculations are tens to hundreds of times faster, depending on how the data are taken. The speed and precision of the RLD coupled with the ease of data acquisition make it an attractive data reduction tool for real time analyses.« less
  • Of great interest in Performance-Based Earthquake Engineering (PBEE) is the accurate estimation of the seismic performance of structures. A performance prediction and evaluation procedure is based on nonlinear dynamics and reliability theory. In this method, a full integration over the three key stochastic models is as follow: ground motion hazard curve, nonlinear dynamic displacement demand, and displacement capacity. Further, both epistemic and aleatory uncertainties are evaluated and carried through the analysis.In this paper, jacket and soil-pile system have been modeled using Finite Element program (OpenSees) and the incremental dynamic analysis (IDA) are performed to investigate nonlinear behavior of offshore platforms.more » The system demand is determined by performing time history response analyses of the jacket under a suite of FEMA/SAC uniform hazard ground motions. The system capacity in terms of the drift ratio against incipient collapse is generally difficult to predict since the structural response goes into nonlinear range before collapse. All the analyses are performed in two directions and the results are compared with each others. The confidence level of a jacket in each direction for a given hazard level is calculated using the procedure described.« less