


Abstract
Andreas Wiegmann, Thu, 17.5018.20

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Fast Structural Topology Design
Andreas Wiegmann (ITWM Kaiserslautern)
We describe an algorithmic approach for the topology design of elastic
structures. At the core, our approach relies on three distinct
ideas. Given a design, we apply the Explicit Jump Immersed Interface
(finite difference) Method for rapidly computing the stresses for a
given design shape by embedding this design in a rectangle. The
equations are extended to the full rectangle, and the second order
accurate solution to the Lamé equations is found via BiCGStab in a
somewhat similar fashion to earlier capacitance matric methods. This
means that the Schur complement for the jumps in the solution and it's
derivatives on the domain boundary is solved, effectively reducing the
dimension of the problem by one. The needed inversion of the Lamé
equations on the rectangle is done with a new FFTbased direct
elastostatic solver. We then use a narrow band level set method to
perturb this shape with velocities based on the stresses and progress
towards an improved design. Criteria are provided for advancing the
shape in an appropriate direction, and to correct the evolving shape
when given constraints are violated.




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