Shape optimization of composites based on minimum potential energy

摘要

Shape optimization of fibers based on the highest bearing capacity of composite aggregate on a unit cell is studied using Inverse variational principles. They have been applied mostly in connection with finite elements. It appears now that boundary elements are much more efficient. On the other hand, it is necessary to find an appropriate function, which describes boundary density of potential energy and at the same time variational bounds or homogenization of the composite have to be carried out. If one starts with homogenization, a mathematical formulation has to prove that a solution exists and is unique. The latter problem seems not to be as simple as it first seems. Additional constraints must be introduced to ensure the uniqueness of the solution. If bounds are sought, we start with extended Hashin-Shtrikman principles. A study is carried out for different relations of fibers and matrices.