Shape Optimization Of Composites Based On
Minimum Potential Energy
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.
Related Book
Other papers in this volume
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