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Topology Optimization of Mechanical Structures: On Bars, Holes, and the Anglerfish

Professor Wolfgang Achtziger, University of Erlanger-Nüremberg Germany

Abstract:

While classical techniques of design optimization of engineering structures are based on the parameterization of boundaries or other geometrical properties of the structure, modem methodologies try to discover new initial designs by regarding structures as an optimal material distribution within the design space.

By this methodology, the principal shape of the structure i not pre-determined meaning that, e.g, the number of holes in a structure may ary during the design process. This realizes a so-called free design optimization, i.e, optimization of structural topology. The price of this freedom is hidden in the mathematical challenges to be covered by the mechanical and mathematical background as well as by the used optimization methods.

The talk will give an introduction into these problems and their difficulties from the viewpoint mathematical optimization.

A frequently considered experimental field in this area the design optimization of trusses. Some classical truss problem formulations allow the mathematical reformulation as convex optimization problems, and therefore globally optimal truss designs can be calculated. More realistic formulations, however, incorporating stress constraints or the consideration of pre-fabricated truss bars etc., are challenging, een for small academic instances. For discretized continuum structures, i.e., based on finite elements, the consideration of stress constraints seems to be a must for practicioners. The topology nature of the problem, i.e., the unknowm location of holes in the structure, leads to so-called vanishing constraints. The talk will also explain the relation of these constraints. The talk will also explain the relation of these constraints to the Anglerfish and will show ways how to catch it....

Refreshment will be served