Optimal Shape Of Fibers In Composite Structure
Using Inverse Variational Principles
Author(s)
P. Procházka
Abstract
Inverse variational principles proved their importance in shape optimization of
structures. In this paper they are applied to searching for the optimal shape of
fibers in a composite structure. As the boundary element method seems to be
more promising than other modern numerical methods applied to the search for
optimal shape, in the submitting paper the boundary element method is redefined
to enable one to use such an approach, which leads to possibility for the optimal
interfacial energies and, hence, to the optimal bearing capacity of the composite
structure. Necessary discretization of the domain, which occurs in the finite
elements, is suppressed in our case. Standard procedure in the finite elements
leads to dependence of the stiffness matrix on the shape of the fibers. In this
case, following a basic idea for homogenization and localization, concentration
factors have to be calculated in terms of the boundary element method instead.
These terms are dependent on the shape of the fibers. It appears that the
procedure is still not convergent (we solve a strongly nonlinear problem) and
additional constraint has to be involved in the formulation. In order to formulate
and solve this problem, the idea of Inverse variational principles is applied here
for expressing necessary quantities. The paper concentrates on the calculation of
quantities, which are necessary to formulate the optimization problem. The main
attention is focused on calculation of concentration factors, which play the most
important role in the approach proposed.
Keywords: discrete element method, boundary element method, dynamical
equilibrium.
Keywords
discrete element method, boundary element method, dynamical
equilibrium.
Related Book
Other papers in this volume
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