Topology Optimization of Continuum Structures with Local Stress Constraints

We introduce an extension of current technologies for topology optimization
of continuum structures which allows for treating local stress criteria. We
rst consider relevant stress criteria for porous composite materials, initially
by studying the stress states of the so-called rank 2 layered materials. Then,
on the basis of the theoretical study of the rank 2 microstructures, we propose
an empirical model which extends the power penalized sti ness model
(also called SIMP for Solid Isotropic Microstructure with Penalization for
intermediate densities). In a second part, solution aspects of topology problems
are considered. To deal with the so-called 'singularity' phenomenon of
stress constraints in topology design, an -constraint relaxation of the stress
constraints is used. We describe the mathematical programming approach
that is used to solve the numerical optimization problems, and show results
for a number of example applications.