دانلود رایگان مقاله انگلیسی استفاده مناسب از روش سلول واحد در محاسبه حرارتی کامپوزیت ها - الزویر 2018

Abstract

The unit cell method is widely used in thermal calculations of composite. The formulation of a unit cell involves the construction of geometric configuration and the derivation of boundary conditions. The process is closely related to the structure symmetries of composites and the macro heat flux. In this work, two issues are studied to further appropriate utilization of such method. First, unit cells that formulated based on different paths of different structure symmetries could have the same configuration while different boundary conditions, and leads to some confusions; second, the uniform temperature boundary condition is frequently used without rigorous mathematical derivation and physical consideration, and leaves some uncertainty of its reliability. In this work, three typical composites, unidirectional fiber reinforced, plain woven and three-dimensional four-directional braided composites are studied. For each composite, one unit cell is formulated and two types of boundary conditions are derived. The influence of formulation path on unit cell formulation and the application scope of uniform temperature boundary conditions are then clarified based on corresponding calculations and analysis.

7 Conclusions

In this work, the utilization of unit cell method in thermal calculation of composites is studied and two issues, i.e., the confusion of one configuration with different boundary conditions and the application scope of uniform temperature boundary condition are clarified. Three types of composites, unidirectional fiber reinforced, plain woven and three-dimensional four-directional braided composites are studied. For each composite, one unit cell is formulated, and two types of boundary conditions are derived based on two different formulation paths: Path a of translational symmetries, and Path b of combinations of translational with reflectional or rotational symmetries. The numerical results show some conclusions:

1. A unit cell can be formulated by different paths and can have different boundary conditions, whereas the numerical results are unique. For such a unit cell, the specific formulation path is not concerned provided that the boundary condition is derived rigorously. Thus, one can choose a formulation path and derive corresponding boundary conditions that appropriate for his own work.

2. For unit cells and boundaries that can be formulated by reflectional symmetries, the widely used uniform temperature boundary condition (UBC) is correct, while for unit cells that can only be formulated by translational symmetries or 180° rotational ones, it is inappropriate. For UD composites, UBC is correct for thermal calculations in all directions; for plain woven composites, it is correct in x- and y-direction while inappropriate in z-direction; for three-dimensional four-directional braided composites, it is inappropriate for all directional thermal calculations.

3. The calculated temperature fields on boundary planes always indicate further structure symmetries that can be used to formulate unit cells with smaller size.