scholarly journals Analysis of 2D heat conduction in nonlinear functionally graded materials using a local semi-analytical meshless method

2021 ◽  
Vol 6 (11) ◽  
pp. 12599-12618
Author(s):  
Chao Wang ◽  
◽  
Fajie Wang ◽  
Yanpeng Gong ◽  
◽  
...  
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Meshless Method ◽  
Large Scale ◽  
Heat Conduction Problem ◽  
Functionally Graded ◽  
Graded Materials ◽  
Kirchhoff Transformation ◽  
Graded Material ◽  
Equation Of Heat Conduction

<abstract> <p>This paper proposes a local semi-analytical meshless method for simulating heat conduction in nonlinear functionally graded materials. The governing equation of heat conduction problem in nonlinear functionally graded material is first transformed to an anisotropic modified Helmholtz equation by using the Kirchhoff transformation. Then, the local knot method (LKM) is employed to approximate the solution of the transformed equation. After that, the solution of the original nonlinear equation can be obtained by the inverse Kirchhoff transformation. The LKM is a recently proposed meshless approach. As a local semi-analytical meshless approach, it uses the non-singular general solution as the basis function and has the merits of simplicity, high accuracy, and easy-to-program. Compared with the traditional boundary knot method, the present scheme avoids an ill-conditioned system of equations, and is more suitable for large-scale simulations associated with complicated structures. Three benchmark numerical examples are provided to confirm the accuracy and validity of the proposed approach.</p> </abstract>

Transient Heat Conduction in Functionally Graded Materials by LT-MFS

2011 ◽  
Vol 189-193 ◽  
pp. 1664-1669 ◽  
Author(s):  
Ning Zhao ◽  
Lei Lei Cao ◽  
Hui Guo
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Fundamental Solutions ◽  
Functionally Graded ◽  
Time Variable ◽  
Graded Materials ◽  
Time Space ◽  
Transient Heat Conduction Problem

: The LT-MFS approach is proposed to solve two-dimensional transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to move the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, the solution in Laplace space is approximated by the linear combination of fundamental solutions. Further, Stefest’s algorithm is employed to convert the results in Laplace space back into the time–space domain. Finally, the method is tested on several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

scholarly journals Finite cell method for functionally graded materials based on V-models and homogenized microstructures

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Benjamin Wassermann ◽  
Nina Korshunova ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
Gershon Elber
Keyword(s):  
Functionally Graded Materials ◽  
Large Scale ◽  
Functionally Graded ◽  
Material Behavior ◽  
Modeling Framework ◽  
Finite Cell Method ◽  
Geometric Framework ◽  
Graded Materials ◽  
Cell Method ◽  
Finite Cell

AbstractThis paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM—which is heterogeneously micro-structured—characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach.

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

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