2005 Fiscal Year Final Research Report Summary
Development of Characteristic Galerkin Finite Element Method using Marker Particle for Large Deformation Analysis of Solid
| Project/Area Number |
16560049
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | Yokohama National University |
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Principal Investigator |
YAMADA Takahiro Yokohama National University, Graduate School of Environment and Information Sciences, Associate Professor, 大学院・環境情報研究院, 助教授 (40240022)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Eulerian mesh / marker particle / finite element / Characteristic Galerkin Method / large deformation / elasto-plasticity / heat conduction / manufacturing process |
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| Research Abstract |
A novel approach of the Eulerian finite element method for large deformation problems of solid has been developed in this project. The proposed method uses Lagrangian marker particles to evaluate the motion of materials including the free surfaces and advection of internal variables. The equation of motion is approximated by the characteristic Galerkin finite element method with a fixed spatial mesh. In this approximation, the material derivatives are evaluated by the special numerical integration along the characteristics in which the locations of the integration points are set at those of the marker particle. The internal variables at the marker are updated from the spatial derivatives of velocity field calculated on the fixed finite element mesh. It is remarked that no advection equation appears in the proposed method and the proposed method exhibits less diffusive properties than the conventional Eulerian method. These features make the present approach effective when the complicated constitutive models with many internal variables are employed in the simulation of machining process.
The actual algorithm is split into two calculation phases. One is the mesh phase in which the momentum equation is evaluated by the finite element approximation of velocity field. Another is the marker phase in which the location of marker particles and Lagrangian variables are updated. Thus the solution variables are defined on either marker particle or mesh.
In manufacturing processes, heat conduction plays an important role and should be considered in precise simulations of practical problems. In this project, a numerical procedure for advection-diffusion equations that is consistent with the proposed method for large deformation problems has been developed to deal with the heat conduction.
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