Local stress‐constrained and slope‐constrained SAND topology optimisation

Munro, Dirk; Groenwold, Albert A.

doi:10.1002/nme.5360

Cited by 8 publications

(1 citation statement)

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“…These are typically negated with restriction methods and higher‐order elements . Popular approaches are based on the idea of a ‘density filter’ – for details, see the well‐known Matlab codes by Sigmund and co‐workers – and although Bourdin proved the method to be mathematically sound (i.e., not heuristic), it works by coupling large groups of density variables, which could be expensive in the SAND setting . A density filter is used in the SAND setting by, for example, Rojas‐Labanda and Stolpe .…”

Section: Topology Optimizationmentioning

confidence: 99%

On sequential approximate simultaneous analysis and design in classical topology optimization

Munro

Groenwold

2016

Numerical Meth Engineering

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Summary We study the simultaneous analysis and design (SAND) formulation of the ‘classical’ topology optimization problem subject to linear constraints on material density variables. Based on a dual method in theory, and a primal‐dual method in practice, we propose a separable and strictly convex quadratic Lagrange–Newton subproblem for use in sequential approximate optimization of the SAND‐formulated classical topology design problem. The SAND problem is characterized by a large number of nonlinear equality constraints (the equations of equilibrium) that are linearized in the approximate convex subproblems. The availability of cheap second‐order information is exploited in a Lagrange–Newton sequential quadratic programming‐like framework. In the spirit of efficient structural optimization methods, the quadratic terms are restricted to the diagonal of the Hessian matrix; the subproblems have minimal storage requirements, are easy to solve, and positive definiteness of the diagonal Hessian matrix is trivially enforced. Theoretical considerations reveal that the dual statement of the proposed subproblem for SAND minimum compliance design agrees with the ever‐popular optimality criterion method – which is a nested analysis and design formulation. This relates, in turn, to the known equivalence between rudimentary dual sequential approximate optimization algorithms based on reciprocal (and exponential) intervening variables and the optimality criterion method. Copyright © 2016 John Wiley & Sons, Ltd.

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