Moving boundary of fibers in FRC

摘要

The optimal shape design of structures is currently of great importance to a wide range of engineers and researchers. The particular problems associated with this lead to very complicated nonlinear systems and new solutions of optimization are investigated. It can be easily shown that some types of problems are more easily solved using the boundary element method than finite elements. The formulation is more complicated in BEM, but the consecutive numerical process is much easier. In composite-based materials the bearing capacity plays a very important role, as does the durability. In order to optimize this situation, the moving of the fiber boundary obeys certain additional conditions leading to keeping a volume fraction of the fibers (or matrix) equal to constant. In other words, maximum fiber stiffness is desired and an additional constraint is required: a constant volume fraction of the fiber. It will be shown that the external boundary conditions of representative volume element are not important. The example problem is solved on a unit cell, which is considered to be symmetric, for simplicity, and a necessary homogenization of the composite structure is carried out. The design parameters are then lengths of rays starting at the center of fibers and end at moving points on the fiber boundaries. The applications of the method proposed are concentrated on fiber reinforced concrete with particular emphasis on shotcrete linings of tunnels in geotechnics. The procedure described in what follows can also be applied to quite different topics such as composite implants of di-aphysal bones in human skeleton. The relation of the particular phases is even similar in both "structures".