Simulation of bridge die extrusion using the finite element method

This communication reviews previous work on the extrusion of hollow shapes and uses a three-dimensional (FEM) solution to predict load-required, temperature of the extrudate and material flow during the process. A comparison with experiments is made to assess the relative importance of some extrusion parameters in the extrusion process and to ensure that the numerical discretisation yields a realistic simulation of the process. The usefulness and limitations of FEM when modelling complex shapes is also discussed. Methods to assess the difficulty of extrusion of hollow extrusions in general are presented. The paper also illustrates the essentials of numerical analysis to assist the reader in the comprehension of the thermomechanical events occurring during extrusion through bridge dies. Results are presented for velocity distribution in the extrusion chamber, iso-temperature contours and pressure/ displacement traces. These are compared with experiments conducted using a 5 MN press. It is shown that the finite element program predicts the pressure requirement: the pressure/displacement trace showing a double peak which is discussed in some detail. The finite element program appears to predict all the major characteristics of the flow observed macroscopically

Adaptive Finite Element Method for Simulation of Optical Nano Structures

We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components into the unbounded and possibly heterogeneous exterior. We apply the finite element method to the optimization of the design of a hollow core photonic crystal fiber. Thereby we look at the convergence of the method and discuss automatic and adaptive grid refinement and the performance of higher order elements

Evaluation of coupled finite element/meshfree method for a robust full-scale crashworthiness simulation of railway vehicles

The crashworthiness of a railway vehicle relates to its passive safety performance. Due to mesh distortion and difficulty in controlling the hourglass energy, conventional finite element methods face great challenges in crashworthiness simulation of large-scale complex railway vehicle models. Meshfree methods such as element-free Galerkin method offer an alternative approach to overcome those limitations but have proved time-consuming. In this article, a coupled finite element/meshfree method is proposed to study the crashworthiness of railway vehicles. A representative scenario, in which the leading vehicle of a high-speed train impacts to a rigid wall, is simulated with the coupled finite element/element-free Galerkin method in LS-DYNA. We have compared the conventional finite element method and the coupled finite element/element-free Galerkin method with the simulation results of different levels of discretization. Our work showed that coupled finite element/element-free Galerkin method is a suitable alternative of finite element method to handle the nonlinear deformation in full-size railway vehicle crashworthiness simulation. The coupled method can reduce the hourglass energy in finite element simulation, to produce robust simulation

Efficient periodic band diagram computation using a finite element method, Arnoldi eigensolver and sparse linear system solver

We present here a Finite Element Method devoted to the simulation of 3D periodic structures of arbitrary geometry. The numerical method based on ARPACK and PARDISO libraries, is discussed with the aim of extracting the eigenmodes of periodical structures and thus establishing their frequency band gaps. Simulation parameters and the computational optimization are the focus. Resolution will be used to characterize EBG (Electromagnetic Band Gap) structures, such as plasma rods and metallic cubes

Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws

A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In the proposed hybrid approach, the finite volume (FV) element, consisting of structured FV subcells, is embedded in the base hexahedral element containing discontinuity, and an FV based high-order shock-capturing scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is captured at the resolution of FV subcells within an embedded FV element. In the smooth flow region, the SD element is used in the base hexahedral element. Then, the governing equations are solved by the SD method. The SD method is chosen for its low numerical dissipation and computational efficiency preserving high-order accurate solutions. The coupling between the SD element and the FV element is achieved by the globally conserved mortar method. In this paper, the 5th-order WENO scheme with the characteristic decomposition is employed as the shock-capturing scheme in the embedded FV element, and the 5th-order SD method is used in the smooth flow field. The order of accuracy study and various 1D and 2D test cases are carried out, which involve the discontinuities and vortex flows. Overall, it is shown that the proposed hybrid method results in comparable or better simulation results compared with the standalone WENO scheme when the same number of solution DOF is considered in both SD and FV elements.Comment: 27 pages, 17 figures, 2 tables, Accepted for publication in the Journal of Computational Physics, April 201

A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation

Large-eddy simulations of incompressible Newtonian fluid flows with approximate deconvolution models based on the van Cittert method are reported. The Legendre spectral element method is used for the spatial discretization to solve the filtered Navier--Stokes equations. A novel variant of approximate deconvolution models blended with a mixed scale model using a dynamic evaluation of the subgrid-viscosity constant is proposed. This model is validated by comparing the large-eddy simulation with the direct numerical simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds number of 12'000. Subgrid modeling in the case of a flow with coexisting laminar, transitional and turbulent zones such as the lid-driven cubical cavity flow represents a challenging problem. Moreover, the coupling with the spectral element method having very low numerical dissipation and dispersion builds a well suited framework to analyze the efficiency of a subgrid model. First- and second-order statistics obtained using this new model are showing very good agreement with the direct numerical simulation. Filtering operations rely on an invertible filter applied in a modal basis and preserving the C0-continuity across elements. No clipping on dynamic parameters was needed to preserve numerical stability

A well-posed optimal spectral element approximation for the Stokes problem

A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem