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**A new local meshless method for steady-state heat conduction in heterogeneous materials.**
*(English)*
Zbl 1244.80018

Summary: In this paper a truly meshless method based on the integral form of energy equation is presented to study the steady-state heat conduction in the anisotropic and heterogeneous materials. The presented meshless method is based on the satisfaction of the integral form of energy balance equation for each sub-particle (sub-domain) inside the material. Moving least square (MLS) approximation is used for approximation of the field variable over the randomly located nodes inside the domain. In the absence of heat generation, the domain integration is eliminated from the formulation of presented method and the computational efforts are reduced substantially with respect to the conventional MLPG method. A direct method is presented for treatment of material discontinuity at the heterogeneous material in the presented meshless method. As a practical problem the heat conduction in fibrous composite material is studied and the steady-state heat conduction in unidirectional fiber-matrix composites is investigated. The solution domain includes a small area of the composite system called representative volume element (RVE). Comparison of numerical results shows that the presented meshless method is simple, effective, accurate and less costly method for micromechanical analysis of heat conduction in heterogeneous materials.

### MSC:

80M25 | Other numerical methods (thermodynamics) (MSC2010) |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

### Keywords:

truly meshless method; heat conduction problem; heterogeneous material; micromechanical analysis; fiber reinforced composite
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\textit{I. Ahmadi} et al., Eng. Anal. Bound. Elem. 34, No. 12, 1105--1112 (2010; Zbl 1244.80018)

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