Author(s)

P. Procházka

Abstract

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. Keynotes: optimization, Inverse variational principles, classical composites. 1 Introduction Conventionally, the optimal shape design problem consists of minimizing an appropriate cost functional with certain constraints, such as equilibrium and compatibility conditions and design requirements. The formulation of the cost function depends on the concrete intention of a designer. One of a reasonable and practical form of the cost function concerns the minimization of the strain energy of the body subjected to a specific load. Such a problem can easily be formulated in terms of inverse variational principles, which assure that the surface energy attains its minimum. The inverse variational principles are naturally connected with the finite element method, which starts with energetical formulation. But, the FEM is less

Keywords

optimization, Inverse variational principles, classical composites.