The simple boundary element method for transient heat conduction in functionally graded materials

Alok Sutradhar; Glaucio H. Paulino

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The simple boundary element method for transient heat conduction in functionally graded materials

机译：功能梯度材料中瞬态热传导的简单边界元方法

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This paper presents a "simple" boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the standard homogeneous diffusion problem. A three-dimensional boundary element implementation, using the Laplace transform approach and the Galerkin approximation, is presented. The time dependence is restored by numerically inverting the Laplace transform by means of the Stehfest algorithm. A number of numerical examples demonstrate the efficiency of the method. The results of the test examples are in excellent agreement with analytical solutions and finite element simulation results.

机译：本文提出了一种用于功能梯度材料中瞬态热传导的“简单”边界元方法，该方法导致了仅边界的公式化而没有任何域离散。对于导热系数和比热的功能材料变化（二次方，指数方和三角方）的变化范围很广，可以将非均匀问题转化为标准的均匀扩散问题。提出了使用拉普拉斯变换方法和Galerkin逼近的三维边界元实现。通过使用Stehfest算法对Laplace变换进行数字反转，可以恢复时间依赖性。大量数值示例证明了该方法的有效性。测试例的结果与解析解和有限元模拟结果非常吻合。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2004年第44期|p.4511-4539|共29页
作者
Alok Sutradhar; Glaucio H. Paulino;
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作者单位

Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 2209 Newmark Laboratory, 205 North Mathews Avenue, Urbana, IL 61801-2352, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类自动化基础理论;工程基础科学;
关键词
transient heat conduction; boundary element method; galerkin; functionally graded materials; non-homogeneous materials; green's function; three-dimensional analysis;

机译：瞬态热传导;边界元法;壁橱;功能梯度材料;非均匀材料;格林函数;三维分析;

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3. A high-order control volume finite element method for 3-D transient heat conduction analysis of multilayer functionally graded materials [J] . Liu Qi, Ming Pingjian Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology . 2018,第1a6期

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4. Multiple reciprocity boundary face method for transient heat conduction in functionally graded materials [C] . Shuaiping Guo, Guangyao Li, Jianming Zhang International Conference on Boundary Elements and Other Mesh Reduction Methods . 2014

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5. A coupled finite element-boundary element method for two dimensional transient heat conduction and thermoelastic analyses. [D] . Guven, Ibrahim. 2000

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6. Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution [O] . Zhihe Jin 2011

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7. A Boundary Element Method for Transient Heat Conduction Problem of Nonhomogeneous Anisotropic Materials [O] . Azis Moh. Ivan 2014

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8. Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction [R] . Kontinos, Dean A. 1997

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The simple boundary element method for transient heat conduction in functionally graded materials

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