A new local meshless method for steady-state heat conduction in heterogeneous materials

Ahmadi, Isa; Sheikhy, Nasrin; Aghdam, M.M.; Nourazar, S. Salman

doi:10.1016/j.enganabound.2010.06.012

Cited by 13 publications

(5 citation statements)

References 23 publications

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“…Currently, lots of meshless methods have been applied for researching heat conduction in anisotropic materials, such as local meshless method [1], regularized meshless method [2], radial basis integral equation method [3], meshless singular boundary method [4], radial basis function method [5], and so on. Compared with the traditional finite element method, a meshless method [6][7][8][9] needs only the distribution of discrete nodes, which can avoid the meshing-related drawbacks.…”

Section: Introductionmentioning

confidence: 99%

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

Cheng¹,

Xing²,

Peng³

2022

Computer Modeling in Engineering &Amp; Sciences

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In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steadystate heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form. The influences of node distribution, weight functions, scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively, and these numerical solutions show that less computational resources are spent when using the IEFG method.

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Section: Introductionmentioning

confidence: 99%

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

Cheng¹,

Xing²,

Peng³

2022

Computer Modeling in Engineering &Amp; Sciences

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“…Phan and Mukherjee (2009) presented a multi-domain boundary contour method for interfaces and different materials that offers additional dimensionality reduction. Ahmadi et al (2010) presented a method for studying steady state heat conduction in anisotropic and heterogeneous materials that does not use a local mesh. Soghrati (2014), Soghrati and Ahmadian (2015), Soghrati and Barrera (2016) and Aragón et al (2020) proposed a hierarchical interface-enriched finite element method (HIFEM) for simulating various interfaces of materials in proximity or contact while capturing the gradient discontinuity.…”

Section: Introductionmentioning

confidence: 99%

A generalized finite element interface method for mesh reduction of composite materials simulations

Alves

Evangelista

Paiva

2022

Lat. Am. j. solids struct.

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This paper proposes interface and polynomial enrichments using the generalized finite element method (IGFEM) for the material interface in composite materials without matching the finite element mesh to the boundaries of different materials. Applications in structural members such as laminated beams and heterogeneous composites (matrix and inclusions) employing coarse and fine meshes are employed. The results were compared with conventional GFEM and analytical solutions. Verification and simulations proved the efficiency of the suggested framework for solving problems with discontinuous gradients resulting from a material interface. The proposed method allows flexibility in mesh generation for composite materials by letting the interface be embedded in an element without the need to match the mesh to the material interface. This improves the computational efficiency over conventional methods.

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“…Lagrange multipliers are used to enforce the continuity of the displacements on the interface boundary. This simple model is used frequently in other methods …”

Section: Introductionmentioning

confidence: 99%

“…This simple model is used frequently in other methods. [29][30][31][32] The mixed approach 16 is attractive for its efficiency and ease of implementation, and it has been applied to solve many engineering problems, [32][33][34][35][36] even the material discontinuity. 32 In the work of Jalušić et al, 32 for boundary nodes, only boundary conditions are assembled into the system equations.…”

Section: Introductionmentioning

confidence: 99%

A mixed DOF collocation method for elastic problems in heterogeneous structure

Mao

2019

Numerical Meth Engineering

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Summary In this paper, a collocation method with mixed degrees of freedom (DOFs) is proposed for heterogeneous structures. Local tractions of the outer and interface boundaries are introduced as DOFs in the mixed collocation scheme. Then, the equilibrium equations of all the nodes and the outer boundary conditions are discretized and assembled into the global stiffness matrix. A local force equilibrium equation for modeling the stress discontinuity through the interface is developed and added into the global stiffness matrix as well. With those contributions, a statically determined stiffness matrix is obtained. Numerical examples show that the present method is superior to the classical mixed collocation method in the heterogeneous structure because it improves the accuracy and the convergence and remains the efficiency. Besides, almost constant convergence rates of displacements and stresses are found in all the examples, even for three‐dimensional problems.

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A new local meshless method for steady-state heat conduction in heterogeneous materials

Cited by 13 publications

References 23 publications

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

A generalized finite element interface method for mesh reduction of composite materials simulations

A mixed DOF collocation method for elastic problems in heterogeneous structure

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