Matrix free meshless method for transient heat conduction problems

In the paper, the element free Galerkin method (EFGM) is applied to calculate two-dimensional unsteady state heat conduction problems. As is well known, most of the meshless methods have higher computational cost than that of finite element method (FEM). In order to overcome this shortcoming especially for transient heat conduction problems, mass lumping procedure is adopted in EFGM, which can decrease the computational cost evidently. Moreover, this technique which can simplify the solution procedure makes the essential boundary conditions enforced directly. The results obtained by EFGM combining mass lumping technique are compared with those obtained by finite element method as well as analytical solutions, which shows that the solutions of the present method are in good agreement with FEM’s and analytical solutions.     

Meshless element free Galerkin method for unsteady nonlinear heat transfer problems

In this paper, meshless element free Galerkin (EFG) method has been extended to obtain the numerical solution of nonlinear, unsteady heat transfer problems with temperature dependent material properties. The thermal conductivity, specific heat and density of the material are assumed to vary linearly with the temperature. Quasi-linearization scheme has been used to obtain the nonlinear solution whereas backward difference method is used for the time integration. The essential boundary conditions have been enforced by Lagrange multiplier technique. The meshless formulation has been presented for a nonlinear 3-D heat transfer problem. In 1-D, the results obtained by EFG method are compared with those obtained by finite element and analytical methods whereas in 2-D and 3-D, the results are compared with those obtained by finite element method.     

The meshless analog equation method for solving heat transfer to molten polymer flow in tubes

In this paper, we proposed a meshless analog equation method (MAEM) to solve a heat transfer problem of molten polymer flow, which is considered to be a generalized Newtonian viscous flow. The MAEM, free from mesh generation and numerical integration, is a powerful meshless method. The numerical solutions are expressed by a linear combination of the derived radial basis functions (RBFs). This paper considers two different viscosity models for the molten polymer; one is temperature-independent power-law model and the other is temperature-dependent power-law model. The viscous dissipation term is included in the energy equation to capture the relevant physical phenomena. From the comparisons of numerical simulation, the meshless solutions are in good agreement with some analytical solutions and other finite element solutions. Moreover, the MAEM uses much less CPU-time and computer memory to simulate molten polymer flows. Therefore, it is believed that the RBF-based meshless method of the MAEM is a promising and flexible numerical scheme for molten polymer flow simulation.     

A Novel Variational Formulation of Inverse Problem of Heat Conduction with Free Boundary on an Image

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A coupled meshless-finite element method for fracture analysis of cracks

This paper presents a coupling technique for integrating the element-free Galerkin method (EFGM) with the traditional finite element method (FEM) for analyzing linear-elastic cracked structures subject to mode-I and mixed-mode loading conditions. The EFGM was used to model material behavior close to cracks and the FEM in areas away from cracks. In the interface region, the resulting shape function, which comprises both EFGM and FEM shape functions, satisfies the consistency condition thus ensuring convergence of the method. The proposed method was applied to calculate mode-I and mode-II stress–intensity factors (SIFs) in a number of two-dimensional cracked structures. The SIFs predicted by this method compare very well with the existing solutions obtained by all-FEM or all-EFGM analyses. A significant saving of computational effort can be achieved due to coupling in the proposed method when compared with the existing meshless methods. Furthermore, the coupled EFGM–FEM method was applied to model crack propagation under mixed-mode loading condition. Since the method is partly meshless, a structured mesh is not required in the vicinity of the cracks. Only a scattered set of nodal points is required in the domain of interest. A growing crack can be modeled by simply extending the free surfaces, which correspond to a crack. By sidestepping remeshing requirements, crack-propagation analysis can be dramatically simplified. A number of mixed-mode problems were studied to simulate crack propagation. The agreement between the predicted crack trajectories with those obtained from existing numerical simulation and experiments are excellent.     

Meshless analysis of the substrate temperature in plasma spraying process

The substrate temperature plays a very important role in coating formation and its quality during the thermal spraying. Heating effect of the plasma and particle flux on the substrate is explored in detail in terms of different spraying distances using the meshless local Petrov–Galerkin method (MLPG). Based on this approach, a 3D transient heat transfer model is derived rigorously, in which the moving least-squares (MLS) method is introduced to construct the shape functions. A quartic spline function is selected as the weight function of the MLS scheme and also the test function for the discretized weak form, in which the penalty technique is used to treat the essential boundary conditions. For comparison, the finite element method (FEM) is also adopted to solve the same problem. It is found that the computed temperature is in very good agreement with the empirical data and better than that obtained using FEM, which validates the meshless formulation. Both numerical and experimental results indicate that the spraying distance has a crucial influence on heating effect of the plasma jet and particle flux onto the substrate.     

基于有限元等效应力法的重力坝安全性分析

为消除重力坝角缘部位有限元应力失真的影响,采用数值方法对重力坝建基面的有限元应力进行积分,求得建基面上的轴力和弯矩,利用偏心受压公式计算出截面上的有限元等效应力分布。结果表明,有限元等效应力法可消除角缘部位的有限元应力失真现象,且不受网格尺寸的影响,计算结果和材料力学法具有相同的计算精度,得出的坝踵、坝趾应力结果可按《混凝土重力坝设计规范》规定的应力标准评价重力坝坝体安全度。     

ADINA软件在土石坝渗流场计算中的应用

根据基本方程及定解条件的比较分析,将AD INA软件的温度场模块分析功能应用于渗流场的分析,并采用死活单元技术,通过迭代算法计算自由水面位置(浸润线),解决了实际工程观音岩心墙土石坝渗流稳定问题的求解。该方法可以解决复杂边界、多种介质的渗流问题,为实际工程设计应用提供强有力的途径。     

Singular boundary method for steady-state heat conduction in three dimensional general anisotropic media

The singular boundary method (SBM) is a recent strong-form meshless boundary collocation method. Like the method of fundamental solutions (MFS), the SBM uses the fundamental solution of the governing differential equation of interest as the basis function and is mathematically simple, truly meshless, accurate, and easy-to-program. Unlike the MFS, the SBM, however, uses the concept of the origin intensity factor to isolate the singularity of the fundamental solutions and overcomes the fictitious boundary issue which has long perplexed the MFS. This study makes the first attempt to apply the SBM to steady-state heat conduction in three-dimensional (3D) anisotropic materials. Five benchmark numerical examples demonstrate that the SBM is accurate, convergent, stable, and computationally efficient in solving this kind of problems.     

Error and variance of solution to the stochastic heat conduction problem by multiquadric collocation method

Error and variance of the solution to the heat conduction problem having stochastic initial and boundary conditions are determined by a formulation based on a meshless method known as the multiquadric collocation method. This formulation expresses the solution in terms of initial and boundary conditions. Inspection of solutions to two test problems reveals that a large value of the shape parameter, which is the free parameter of multiquadrics, should not be used for a stochastic problem because it may lead to a solution that is too sensitive to uncertainties in boundary and initial conditions.     

渗流自由面计算的边界元法

用边界元法求解渗流自由面需预先设定自由面的初始位置.先对自由面初始位置进行优化,以便得到合理的计算网格,再按常规方法迭代求解.计算结果表明,与有限元法相比计算精度较高,具有更好的收敛性与更高的计算效率.     

坝基渗流分析的边界点法

采用边界点法分析坝基渗流问题,编制了计算程序并与有限单元法和裂隙网络法的计算结果比较.结果表明,采用边界点法处理坝基渗流问题计算程序简单、速度快、精度高.     

等效应力法在天花板双曲拱坝应力分析中的应用

针对天花板碾压混凝土拱坝应力集中问题,基于拱坝设计规范,对计算结果进行等效应力处理,研究了拱坝等效应力计算方法、编制了相关计算程序,根据天花板双曲拱坝的构造和受力特点构建了三维有限元数值仿真模型,并采用ADINA软件进行应力计算。结果表明,较好解决了天花板拱坝局部应力集中问题,为工程设计提供了参考依据。     

基于多边形比例边界有限元的重力坝地震断裂模拟

针对地震条件下重力坝中裂纹的稳定性,基于多边形比例边界有限元法(Polygon SBFEM)提出了一种重力坝地震开裂过程模拟的数值模型。该模型中SBFEM兼具边界元和有限元两种方法的优点,而多边形比例边界单元和局部网格重剖分技术的引入使得对裂纹扩展过程的模拟更加灵活、便捷。对Koyna大坝的地震断裂过程模拟结果与试验及文献的分析结果一致,说明该方法为混凝土坝地震断裂数值分析提供了新途径。     

Ram bending of a cylindrical pipe in the elastic range

The problem of ram bending of a straight cylindrical pipe is considered. Separate shell theory and finite element method (FEM) solutions are presented. The loading is idealized as a set of pads of uniform radial pressure, and results are given for the elastic range. Particular attention is paid to the FEM solution characteristics and the pipe springback behavior. The present study is a necessary preliminary step to the full elastic-plastic solution of the problem.     

A Novel Boundary-Integral Based Finite Element Method for 2D and 3D Thermo-Elasticity Problems

In this article a new hybrid boundary integral-based (HBI) finite element method (FEM) is presented for analyzing two-dimensional (2D) and three-dimensional (3D) thermoelastic problems with arbitrary distribution of body force and temperature changes. The method of particular solution is used to decompose the displacement field into homogeneous part and particular part. The homogeneous solution is obtained by using the HBI-FEM with fundamental solutions, yet the particular solution related to the body force and temperature change is approximated by radial basis function (RBF). The detailed formulation for both 2D and 3D HBI-FEM for thermoelastic problems are given, and two different approaches for treating the inhomogenous terms are presented and compared. Five numerical examples are presented to demonstrate the accuracy and performance of the proposed method. When compared with the existing analytical solutions or ABAQUS results, it is found that the proposed method works well for thermoelastic problems and also when using a very coarse mesh, results with satisfactory accuracy can be obtained.     

Shape identification for inverse geometry heat conduction problems by FEM without iteration

The boundary geometry shape is identified by the finite element method (FEM) without iteration and mesh reconstruction for two-dimensional (2-D) and three-dimensional (3-D) inverse heat conduction problems. First, the direct heat conduction problem with the exact domain is solved by the FEM and the temperatures of measurement points are obtained. Then, by introducing a virtual boundary, a virtual domain is formed. By minimizing the difference between the temperatures of measurement points in the exact domain and those in the virtual domain, the temperatures of the points on the virtual boundary are calculated based on the least square error method and the Tikhonov regularization. Finally, the objective geometry shape can be estimated by the method of searching the isothermal curve or isothermal surface for 2-D or 3-D problems, respectively. In the process, no iterative calculation is needed. The proposed method has a tremendous advantage in reducing the computational time for the inverse geometry problems. Numerical examples are presented to test the validity of the proposed approach. Meanwhile, the influences of measurement noise, virtual boundary, measurement point number, and measurement point position on the boundary geometry prediction are also investigated in the examples. The solutions show that the method is accurate and efficient to identify the unknown boundary geometry configurations for 2-D and 3-D heat conduction problems.     

Meshless method based on the local weak-forms for steady-state heat conduction problems

In this article, the meshless local Petrov–Galerkin (MLPG) method is applied to compute two steady-state heat conduction problems of irregular complex domain in 2D space. The essential boundary condition is enforced by the transformation method, and the MLS method is used for interpolation schemes. A numerical example that has analytical solution shows the present method can obtain desired accuracy and efficiency. Two cases in engineering with irregular boundary are computed to validate the approach by comparing the present method with the finite volume method (FVM) solutions obtained from a commercial CFD package FLUENT 6.3. The results show that the present method is in good agreement with FVM. It is expected that MLPG method (which is a truly meshless) is very promising in solving engineering heat conduction problems within irregular domains.     

BEM/FDM conjugate heat transfer analysis of a two-dimensional air-cooled turbine blade boundary layer

A coupled boundary element method （BEM） and finite difference method （FDM） are applied to solve conjugate heat transfer problem of a two-dimensional air-cooled turbine blade boundary layer. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. The Navier-Stokes equations are solved by HIT-NS code. In this code, the FDM is adopted and is used to resolve the convective heat transfer in the fluid region. The BEM code is used to resolve the conduction heat transfer in the solid region. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The numerical results from the BEM adopted in this paper are in good agreement with the results of analytical solution and the results of commercial code, such as Fluent 6.2. The BEM avoids the complicated mesh needed in other computation method and saves the computation time. The results prove that the BEM adopted in this paper can give the same precision in numerical results with less boundary points. Comparing the conjugate results with the numerical results of an adiabatic wall flow solution, it reveals a significant difference in the distribution of metal temperatures. The results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines.     

挤压边墙对面板堆石坝结构性态的影响分析

为深入了解挤压边墙施工对面板及堆石体应力和变形的影响,以柬埔寨某混凝土面板堆石坝为例,采用三维非线性有限元法建立了坝体三维有限元模型,对比分析了采用传统施工法与挤压边墙施工法时大坝应力和变形的变化规律,研究了挤压边墙对堆石体和面板应力和变形的影响。结果表明,正常蓄水位工况下采用挤压边墙施工对堆石体的应力和变形影响不明显;混凝土面板的顺坡向压应力减少约400kPa,拉应力区明显减小,拉应力值减少约800kPa,面板挠度减少约20mm,可见面板的受力状态和挠度有较大改善。