scholarly journals Numerical simulation of acoustic waves in air and porelastic media using the partition of unity finite element method

2013 ◽  
Author(s):  
Jean-Daniel Chazot ◽  
Benoit Nennig ◽  
Emmanuel Perrey-Debain
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Acoustic Waves ◽  
Partition Of Unity ◽  
Element Method

scholarly journals Partition of Unity Finite Element Method applied to exterior problems with Perfectly Matched Layers

Acta Acustica ◽  
2020 ◽  
Vol 4 (4) ◽  
pp. 16
Author(s):  
Christophe Langlois ◽  
Jean-Daniel Chazot ◽  
Emmanuel Perrey-Debain ◽  
Benoit Nennig
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Acoustic Waves ◽  
Degrees Of Freedom ◽  
Partition Of Unity ◽  
Local Approximation ◽  
Computational Domain ◽  
Perfectly Matched Layers ◽  
Exterior Problems ◽  
Element Method

The Partition of Unity Finite Element Method (PUFEM) is now a well established and efficient method used in computational acoustics to tackle short-wave problems. This method is an extension of the classical finite element method whereby enrichment functions are used in the approximation basis in order to enhance the convergence of the method whilst maintaining a relatively low number of degrees of freedom. For exterior problems, the computational domain must be artificially truncated and special treatments must be followed in order to avoid or reduce spurious reflections. In recent papers, different Non-Reflecting Boundary Conditions (NRBCs) have been used in conjunction with the PUFEM. An alternative is to use the Perfectly Match Layer (PML) concept which consists in adding a computational sponge layer which prevents reflections from the boundary. In contrast with other NRBCs, the PML is not case specific and can be applied to a variety of configurations. The aim of this work is to show the applicability of PML combined with PUFEM for solving the propagation of acoustic waves in unbounded media. Performances of the PUFEM-PML are shown for different configurations ranging from guided waves in ducts, radiation in free space and half-space problems. In all cases, the method is shown to provide acceptable results for most applications, similar to that of local approximation of NRBCs.

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

Multi-Step Forward Finite Element Method for the Numerical Simulation of Sheet Metal Forming

2011 ◽  
Vol 474-476 ◽  
pp. 251-254
Author(s):  
Jian Jun Wu ◽  
Wei Liu ◽  
Yu Jing Zhao
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Deep Drawing ◽  
Metal Forming ◽  
Mapping Method ◽  
Constitutive Relationship ◽  
Element Method

The multi-step forward finite element method is presented for the numerical simulation of multi-step sheet metal forming. The traditional constitutive relationship is modified according to the multi-step forming processes, and double spreading plane based mapping method is used to obtain the initial solutions of the intermediate configurations. To verify the multi-step forward FEM, the two-step simulation of a stepped box deep-drawing part is carried out as it is in the experiment. The comparison with the results of the incremental FEM and test shows that the multi-step forward FEM is efficient for the numerical simulation of multi-step sheet metal forming processes.

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