Application of the Meshless Element-Free Galerkin Method to Freckle Formation in Directional Solidification

2009 ◽  
Author(s):  
Udaya K. Sajja ◽  
Sergio D. Felicelli
Keyword(s):  
Finite Element ◽  
Directional Solidification ◽  
Turbine Blades ◽  
Solidification Process ◽  
Solute Concentration ◽  
Momentum Equation ◽  
Thermosolutal Convection ◽  
Element Free Galerkin ◽  
Solidification Processes ◽  
Element Free

Freckles or channel segregates are the most severe form of the macrosegregation that can occur in unidirectionally solidified superalloy castings used in the manufacturing of gas turbine blades. These defects are formed due to thermosolutal convection during solidification. Mathematical modeling of the solidification process involves the simultaneous solution of the conservation equations of momentum, energy and solute concentration in all regions (liquid, mush and solid). Most numerical simulations of dendritic solidification processes have been performed using finite element or the finite volume techniques. The dependence of these methods on the mesh is not always advantageous for problems in which discontinuities or regions of sharp gradients do not coincide with the original mesh lines. In the present work, the meshless element free Galerkin (EFG) method has been investigated to simulate directional solidification processes in which sharp gradients in the field variables can occur as a result of the formation of channels. Simulations of a multicomponent Ni-Al-Ta-W alloy have been performed in a two dimensional domain. The calculations are started with the alloy in all-liquid state and the growth of the mushy zone is followed in time. A projection method is used to solve the momentum equation which makes the computation more efficient than the previously used penalty method. The accuracy of the EFG results is compared with that of the finite element calculations and the potential advantages of the meshless methods for this type of problems are discussed.

Simulations of the Effects of Mold Properties on Directional Solidification

2013 ◽  
Author(s):  
Mark A. Lauer ◽  
David R. Poirier ◽  
Robert G. Erdmann ◽  
Luke Johnson ◽  
Surendra N. Tewari
Keyword(s):  
Finite Element ◽  
Thermal Properties ◽  
Mushy Zone ◽  
Phase Change ◽  
Directional Solidification ◽  
Cross Section ◽  
Cross Sections ◽  
Mold Wall ◽  
Solidification Process ◽  
Thermosolutal Convection

The mold geometry and its thermal properties greatly influence the solidification process. Finite element simulations of directional solidification in various molds are presented. These simulations were performed using volume averaged properties in the mushy zone in order to model the convection, transport of solute and energy, and phase change occurring during solidification. These simulations show the interactions of the mold and alloy with the resultant solidification phenomena, including steepling. Mold geometries can cause macrosegregation because of shrinkage flows, by interrupting the development of the mushy zone, and by causing or influencing thermosolutal convection. Mold materials with different thermal properties result in different macrosegregation patterns even for the same geometries. Changes in cross section and the thermal properties of the mold also affect the gradients and solidification rates obtained in the alloy, as opposed to those measured on the mold wall. Simulations are compared qualitatively to a verification experiment of directionally solidifying a hypoeutectic Al-7wt%Si alloy in a mold with changing cross sections.

Coupled EFGM and F2LFEM for Fracture Analysis of Cracks

2009 ◽  
Author(s):  
K. N. Rajesh ◽  
B. N. Rao
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Consistency Condition ◽  
Shape Functions ◽  
Interface Elements ◽  
Element Free Galerkin ◽  
T Stress ◽  
Cracked Structures ◽  
As Stress ◽  
Element Free

This paper presents a coupling technique for integrating the element–free Galerkin method (EFGM) with fractal two-level finite element method (F2LFEM) for analyzing homogeneous, isotropic, and two dimensional linear–elastic cracked structures subjected to mixed–mode (modes I and II) loading conditions. F2LFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprises both the element–free Galerkin and the finite element shape functions, satisfies the consistency condition thus ensuring convergence of the proposed method. The proposed method combines the best features of EFGM and F2LFEM, in the sense that no structured mesh or special enriched basis functions are necessary and no post–processing (employing any path independent integrals) is needed to determine fracture parameters such as stress–intensity factors (SIFs) and T–stress. The numerical results show that SIFs and T–stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in this study. Also a parametric study is carried out to examine the effects of the similarity ratio, and the number of transformation terms on the quality of the numerical solutions.

The Studies on Numerical Simulation of Unidirectional Solidification Process in 23t Steel Ingot

2012 ◽  
Vol 502 ◽  
pp. 46-50
Author(s):  
Guang Wu Ao ◽  
Ming Gang Shen ◽  
Zhen Shan Zhang ◽  
Li Li Hong
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Temperature Distribution ◽  
Steel Ingot ◽  
Side Wall ◽  
Solidification Process ◽  
Unidirectional Solidification ◽  
Finite Element Software ◽  
Solidification Processes

In this paper, by using the commercial finite-element software of ProCAST, unidirectional solidification processes in 23t steel ingot were simulated. Emphasis is placed on analysis of required time for complete solidification of steel ingot and temperature distribution about ingot and side wall during the solidification process. By comparing simulation values and measured values of side wall during the solidification process, the simulated results conclusively demonstrate that our developed model is feasible and valuable.

A Coupled Finite Element-Element Free Galerkin Method for Liquefiable Soil-Structure Interaction Analysis Under Earthquake Loading

2009 ◽  
Author(s):  
Xiaowei Tang ◽  
Ying Jie ◽  
Maotian Luan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Soil Structure ◽  
Soil Structure Interaction ◽  
Element Free Galerkin Method ◽  
Structure Interaction ◽  
Element Free Galerkin ◽  
Liquefiable Soil ◽  
Element Free

This study presents a numerical method for the seismic behavior assessment of liquefiable soil-structure interaction. In the method, the element-free Galerkin method (EFGM) is applied to simulate the behavior of the liquefiable sandy soil which will take place large permanent deformation under earthquake loading. The finite element method (FEM) is used to describe the behavior of the structure. Then, the EFGM and FEM are related by contact elements. The cyclic elasto-plastic constitutive model and updated Lagrangian large-deformation formulation are jointly adopted to establish the governing equations in order to take account for both physical and geometrical nonlinearities. The shape function is established by moving least squares method while hexahedral background cells are used. The essential boundary conditions are treated with the help of the penalty method. The coupled method can avoid the volumetric locking in the numerical computations using finite element method when non-uniform deformations happen. In order to assess the effectiveness and accuracy of the current procedure, numerical simulation of caisson-type quay wall subjected to earthquake motion is conducted.

An Element-Free Galerkin-Finite Element Coupling Method for Elasto-Plastic Contact Problems

2005 ◽  
Vol 128 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Tianxiang Liu ◽  
Geng Liu ◽  
Q. Jane Wang
Keyword(s):  
Finite Element ◽  
Contact Problems ◽  
Elastic Cylinder ◽  
Coupling Method ◽  
Fe Method ◽  
Programming Technique ◽  
Galerkin Finite Element ◽  
Element Free Galerkin ◽  
Elasto Plasticity ◽  
Element Free

The element-free Galerkin-finite element (EFG-FE) coupling method, combined with the linear mathematical programming technique, is utilized to solve two-dimensional elasto-plastic contact problems. Two discretized models for an elastic cylinder contacting with a rigid plane are used to investigate the boundary effects in a contact problem when using the EFG-FE coupling method under symmetric conditions. The influences of the number of Gauss integration points and the size supporting the weight function in the meshless region on the contact pressure and stress distributions are studied and discussed by comparing the numerical results with the theoretical ones. Furthermore, the elasto-plastic contact problems of a smooth cylinder with a plane and a rough surface with a plane are analyzed by means of the EFG-FE method and different elasto-plasticity models.

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