A modified trust region algorithm for hierarchical NLP

Nelson, Sigurd A.; Papalambros, Panos Y.

doi:10.1007/bf01213996

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Consider the case where the modi ed design is a scaled design ¹K ¤ , as given by Eq. (16). Then, from Eq.…”

Section: Scaling Of the Initial Stiffness Matrixmentioning

confidence: 99%

“…where 1X L and 1X U are predetermined lower and upper limits, respectively, on the design variable changes. An alternative approach, used in trust region algorithms, 16 is to restrict the solutions to some region around X ¤ by constraints of the form approximations (such as the Taylor series), where small changes in the design variables are assumed. They are not effective for the CA method applied to nd accurate solutions for large changes in the design.…”

Section: Nearly Scaled Designsmentioning

confidence: 99%

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Exact and Accurate Solutions in the Approximate Reanalysis of Structures

Kirsch

Papalambros

2001

AIAA Journal

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Combined approximations (CA) is an ef cient method for reanalysis of structures where binomial series terms are used as basis vectors in reduced basis approximations. In previous studies high-quality approximations have been achieved for large changes in the design, but the reasons for the high accuracy were not fully understood. In this work some typical cases, where exact and accurate solutions are achieved by the method, are presented and discussed. Exact solutions are obtained when a basis vector is a linear combination of the previous vectors. Such solutions are obtained also for low-rank modi cations to structures or scaling of the initial stiffness matrix. In general the CA method provides approximate solutions, but the results presented explain the high accuracy achieved with only a small number of basis vectors. Accurate solutions are achieved in many cases where the basis vectors come close to being linearly dependent. Such solutions are achieved also for changes in a small number of elements or when the angle between the two vectors representing the initial design and modi ed design is small. Numerical examples of various changes in cross sections of elements and in the layout of the structure show that accurate results are achieved even in cases where the series of basis vectors diverges.

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“…Consider the case where the modi ed design is a scaled design ¹K ¤ , as given by Eq. (16). Then, from Eq.…”

Section: Scaling Of the Initial Stiffness Matrixmentioning

confidence: 99%

Section: Nearly Scaled Designsmentioning

confidence: 99%