A Subgradient Method for Contact Structural Optimization
 
Michael Patriksson
Department of Mathematics
Division of Optimization
Linköping Institute of Technology
S-581 83 Linköping
Sweden

and

Joakim Petersson
Department of Mechanical Engineering
Division of Mechanics
Linköping Institute of Technology
S-581 83 Linköping
Sweden

ABSTRACT:

We consider the problem of maximizing the stiffness of a structure in
unilateral contact by using a subgradient optimization algorithm.
The problem is in general a nonlinear programming problem subject to
equilibrium constraints, but can in certain cases be given a 
convex--concave saddle point formulation.
The structure is assumed to have a linear potential energy--design
dependence, an assumption which is fulfilled by discretized variable
thickness sheets and trusses.

The subgradient optimization scheme is applied to the primal 
(displacement-only) reformulation of the saddle problem;
convergence is guaranteed when design variables are allowed to take
zero values, and hence topology optimization is included.
The algorithm is augmented with a simple averaging scheme for generating
an optimal design as well.
Numerical examples illustrate the characteristics of the algorithm, and
demonstrate its viability for solving large-scale engineering problems.

KEY WORDS: Structural Optimization, Unilateral Contact, 
Nondifferentiable Convex Programming, Subgradient Method