scholarly journals Research on 3D Improved Extended Finite Element Method for Electric Field of Liquid Nitrogen with Bubbles

2021 ◽  
Vol 11 (11) ◽  
pp. 4839
Author(s):  
Nana Duan ◽  
Xinyu Ma ◽  
Shaocong Lu ◽  
Weijie Xu ◽  
Shuhong Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electric Field ◽  
Liquid Nitrogen ◽  
Level Set ◽  
Extended Finite Element Method ◽  
Interpolation Function ◽  
Extended Finite Element ◽  
Level Set Function ◽  
Set Function

In this paper, the improved extended finite element method (XFEM) for analyzing the three-dimensional (3D) electric field is presented. The interface between two media is described by using a four-dimensional (4D) level set function. For elements with multiple interfaces, the local level set method is used to improve the accuracy. By using weak discontinuous enrichment function and moving level set function, the interpolation function is modified. The new interpolation function makes it unnecessary to repeat the mesh generation when a moving interface occurs. The cost of calculation is greatly reduced. The reliability of 3D improved XFEM in the electric field is verified through numerical calculation examples of single bubble, multi-bubbles, and moving deformed bubble in liquid nitrogen.

scholarly journals Extended finite -element method for modeling the mechanical behavior of functionally graded material plates with multiple random inclusions

2017 ◽  
Vol 20 (K3) ◽  
pp. 119-125
Author(s):  
Bang Kim Tran ◽  
Huy The Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Functionally Graded Material ◽  
Extended Finite Element Method ◽  
Functionally Graded ◽  
Extended Finite Element ◽  
Graded Material ◽  
Element Method

Functionally graded material is of great importance in many engineering problems. Here the effect of multiple random inclusions in functionally graded material (FGM) is investigated in this paper. Since the geometry of entire model becomes complicated when many inclusions with different sizes appearing in the body, a methodology to model those inclusions without meshing the internal boundaries is proposed. The numerical method couples the level set method to the extended finite-element method (X-FEM). In the X-FEM, the finite-element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of random inclusions. Numerical examples are presented to demonstrate the accuracy and potential of this technique. The obtained results are compared with available refered results and COMSOL, the finite element method software.

scholarly journals A novel hybrid approach for level set characterization and tracking of non-planar 3D cracks in the extended finite element method

2016 ◽  
Vol 160 ◽  
pp. 1-14 ◽  
Author(s):  
Alireza Sadeghirad ◽  
David L. Chopp ◽  
Xiang Ren ◽  
Eugene Fang ◽  
Jim Lua
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Level Set ◽  
Extended Finite Element Method ◽  
Hybrid Approach ◽  
Extended Finite Element ◽  
Element Method

scholarly journals Revised Level Set-Based Method for Topology Optimization and Its Applications in Bridge Construction

2017 ◽  
Vol 11 (1) ◽  
pp. 153-166
Author(s):  
Jing Wu ◽  
Li Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Level Set ◽  
The Finite Element Method ◽  
Bridge Design ◽  
Bridge Construction ◽  
Level Set Function ◽  
Set Function ◽  
Element Method

To cure imperfections such as low accuracy and the lack of ability to nucleate hole in the conventional level set-based topology optimization method, a novel method using a trapezoidal method with discrete design variables is proposed. The proposed method can simultaneously accomplish topology and shape optimization. The finite element method is employed to obtain element properties and provide data for calculating design and topological sensitivities. With the aim of performing the finite element method on a non-conforming mesh, a relation between the level set function and the element densities field has to be clearly defined. The element densities field is obtained by averaging the Heaviside function values. The Lagrange multiplier method is exploited to fulfill the volume constraint. Based on topological and design sensitivity and the trapezoidal method, the Hamilton-Jacobi partial differential equation is updated recursively to find the optimal layout. In order to stabilize the iterations and improve the efficiency of the algorithm, re-initiation of the level set function is necessary. Then, the detailed process of a cantilever design is illustrated. To demonstrate the applications of the proposed method in bridge construction, two numerical examples of a pylon bridge design are introduced. It is shown that the results match practical designs very well, and the proposed method is a helpful tool in bridge design.

scholarly journals XFEM/Level-set for modelling of coated inclusion composites

2017 ◽  
Vol 39 (1) ◽  
pp. 69-78
Author(s):  
Tran Anh Binh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Level Set ◽  
Extended Finite Element Method ◽  
Finite Thickness ◽  
Extended Finite Element ◽  
Integration Rule ◽  
Numerical Examples ◽  
Coated Inclusion ◽  
Simple Integration

In this paper, Extended Finite Element method (XFEM) is used to model the embedded coated inclusion composite. The coated inclusion with finite thickness is associated with two level-set functions, which describe its inside and outside interfaces.  A simple integration rule is employed for numerical quadrature in elements cut by two interfaces. Accuracy and efficiency of the proposed approach are demonstrated through 3D numerical examples and applied to homogenization of such materials.

An Extended Finite Element Method Based Approach for Modeling Crevice and Pitting Corrosion

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Ravindra Duddu ◽  
Nithyanand Kota ◽  
Siddiq M. Qidwai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Electrical Potential ◽  
Chloride Concentration ◽  
Two Dimensions ◽  
Extended Finite Element ◽  
Level Set Function ◽  
Current Densities ◽  
Element Method

A sharp-interface numerical approach is developed for modeling the electrochemical environment in crevices and pits due to galvanic corrosion in aqueous media. The concentration of chemical species and the electrical potential in the crevice or pit solution environment is established using the steady state Nernst–Planck equations along with the assumption of local electroneutrality (LEN). The metal-electrolyte interface fluxes are defined in terms of the cathodic and anodic current densities using Butler–Volmer kinetics. The extended finite element method (XFEM) is employed to discretize the nondimensionalized governing equations of the model and a level set function is used to describe the interface morphology independent of the underlying finite element mesh. Benchmark numerical studies simulating intergranular crevice corrosion in idealized aluminum–magnesium (Al–Mg) alloy microstructures in two dimensions are presented. Simulation results indicate that corrosive dissolution of magnesium is accompanied by an increase in the pH and chloride concentration of the crevice solution environment, which is qualitatively consistent with experimental observations. Even for low current densities the model predicted pH is high enough to cause passivation, which may not be physically accurate; however, this model limitation could be overcome by including the hydrolysis reactions that potentially decrease the pH of the crevice solution environment. Finally, a mesh convergence study is performed to establish the accuracy of the XFEM and a sensitivity study examining the relationship between crevice geometry and species concentrations is presented to demonstrate the robustness of the XFEM formulation in handling complex corrosion interface morphologies.

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