On the trajectories of the epsilon-relaxation approach for stress-constrained truss topology optimization

By Mathias Stolpe, Krister Svanberg. 2001

106 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ae0b3c9c82f642aa76e96a0d9fdaaa4036e7ba7f

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Damage approach: A new method for topology optimization with local stress constraints (2015, background): “However, Stolpe and Svanberg (2001) have shown that the trajectory of the global solution might be discontinuous.”
Topology optimization of continuum structures with local and global stress constraints (2009, background): “Thus, Stolpe and Svanberg explained that the trajectories to the optimum produced by the relaxed approach are not unique and they depend on the initial design [31].”
Optimum design of truss topology under buckling constraints (2005, background): “unsurprisingly, we cannot guarantee that the obtained results are all global optimal solutions, since the considered problem is non-convex in nature ( Stolpe and Svanberg 2001 ).”
Modelling topology optimization problems as linear mixed 0–1 programs (2003, background): “However, the non-linear programs that result from this modelling are in general nonconvex and the obtained solution need not even be a feasible solution to the original 0–1 problem, see e.g. Stolpe and Svanberg [20].”
Topology Optimization (2009, methodology): “It can thus be concluded that, in agreement with the results obtained in truss optimization [38, 40], the global trajectory may be discontinuous, i.”
On design-dependent constraints and singular topologies (2001, methodology): “It has been shown by Svanberg and Stolpe [2000, see also Stolpe and Svanberg (2001) ] that a smooth envelope function (SEF) method may not converge to the correct global optimal solution.”
Stress-constrained topology optimization with design-dependent loading (2012, unknown): “However, Stolpe and Svanberg (2001) showed that although the global optimum can be obtained, there is no guarantee that the solution will in general converge to the global optimum of the original problem.”
A sequential parametric convex approximation method with applications to nonconvex truss topology design problems (2010, methodology): “A relaxation method for the TTD problem with stress constraints has been presented in [7] and was further analyzed in [11].”
Topology optimization of trusses with stress and local constraints on nodal stability and member intersection (2005, background): “It is very difficult, however, to determine appropriate value of the parameter for relaxing the constraints, and to assign the initial solution to reach the globally optimal solution as noted by Stolpe and Svanberg (2001).”