Domain Decomposition Methods In Structural Optimization.

Abstract

Application of domain decomposition techniques for structural analysis and design
are outlined in this paper. This technique divides the whole finite element problem into subdomains
in order to solve for each subdomain a smaller problem, and interface unknowns should
be explicitly treated. Procedures for structural analysis are described either in the so called
primal or dual solution of the interface problem.
Structural size optimization problems are also addressed. Element size (i.e. plate thickness)
are design variables of the optimization problem, and the structure volume the objective function.
The nodal displacements may be introduced as optimization variables in the so called
Structural ANalysis and Design (SAND) problems. The number of variables in this case is increased,
but there is no need to solve the equilibrium equations, and sensibility matrices are
explicit. Interior point algorithms are used to solve the minimization problem.