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.
