A Numerical Study on the Entry Problem of an Elastic Body Using Level Set Method and Combined Formulation

2011 ◽  
Author(s):  
Hyoung Gwon Choi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Elastic Body ◽  
Level Set Method ◽  
Level Set ◽  
Mixed Finite Element ◽  
Element Formulation ◽  
Surface Tracking ◽  
Element Method

A finite element method based on level set and combined formulation was studied for the analysis of entry problem of an elastic body. Both free surface tracking and the interaction of an entry body with the fluid flow need to be considered in the entry problem. Free surface tracking was achieved using a level set method in which advection and reinitialization equations for level set variable were discretized using a least square finite element method. The coupling of the motion of the elastic body with fluid flow was conducted using combined mixed finite element formulation. ALE (arbitrary Lagrangian Eulerian) method was adopted for the movement of a grid since the downward motion of the body is dominant in entry problem. Since a mixed finite element is adopted, a linear basis function that belongs to H1 space is used for velocity and level set variables on each sub-element (Th) while a linearly interpolated pressure variable that belongs to L2 space is adopted on each element (T2h). The level set method based on a least square finite element method was verified by solving some free surface tracking problems and then, the finite element formulation for entry problem was validated by comparing with an existing experimental results. Further, the comparison of the entry of an elastic body with that of a rigid body was investigated.

Fractional-Step Finite Element Method for Calculation of 3-D Free Surface Problem Using Level Set Method

2006 ◽  
Vol 18 (6) ◽  
pp. 742-747 ◽  
Author(s):  
Lan-hao Zhao ◽  
Tong-chun Li ◽  
Ling Wang ◽  
M. I. Herreros ◽  
M. Pastor
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Fractional Step ◽  
Element Method

scholarly journals An interface-enriched generalized finite element method for level set-based topology optimization

2020 ◽  
Vol 63 (1) ◽  
pp. 1-20
Author(s):  
S. J. van den Boom ◽  
J. Zhang ◽  
F. van Keulen ◽  
A. M. Aragón
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Level Set ◽  
Element Formulation ◽  
Generalized Finite Element Method ◽  
Level Set Function ◽  
Analytical Sensitivities ◽  
Generalized Finite Element ◽  
Element Method

AbstractDuring design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.

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 MIXED FINITE ELEMENT FORMULATION OF THE BIHARMONIC EQUATION

2005 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
A. D. GARNADI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimate ◽  
Biharmonic Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Formulation ◽  
Abstract Setting ◽  
First Time ◽  
Element Method

<p>We will provide an abstract setting for mixed finite element method for biharmonic equation. The abstract setting casts mixed finite element method for first biharmonic equation and sec- ond biharmonic equation into a single framework altogether. We provide error estimates for both type biharmonic equation, and for the first time an error estimate for the second biharmonic equation.</p>

A Stabilized Mixed Finite Element Method for Nearly Incompressible Elasticity

2005 ◽  
Vol 72 (5) ◽  
pp. 711-720 ◽  
Author(s):  
Arif Masud ◽  
Kaiming Xia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
A Priori ◽  
Mixed Finite Element Method ◽  
Element Formulation ◽  
Patch Tests ◽  
Stabilized Finite Element Method ◽  
Incompressible Elasticity ◽  
Element Method

We present a new multiscale/stabilized finite element method for compressible and incompressible elasticity. The multiscale method arises from a decomposition of the displacement field into coarse (resolved) and fine (unresolved) scales. The resulting stabilized-mixed form consistently represents the fine computational scales in the solution and thus possesses higher coarse mesh accuracy. The ensuing finite element formulation allows arbitrary combinations of interpolation functions for the displacement and stress fields. Specifically, equal order interpolations that are easy to implement but violate the celebrated Babushka-Brezzi inf-sup condition, become stable and convergent. Since the proposed framework is based on sound variational foundations, it provides a basis for a priori error analysis of the system. Numerical simulations pass various element patch tests and confirm optimal convergence in the norms considered.

Sign in / Sign up

Export Citation Format

Share Document