1992
DOI: 10.1007/bf01742747
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Optimality criteria methods usingK-S functions

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Cited by 11 publications
(6 citation statements)
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“…The original SIMP method (Algorithm 1) does not directly considers this kind of constraints as it is based on a volume constraint. Reference 61 presents a TO algorithm where the volume constraint of the SIMP method is substituted by a maximum stress‐measure constraint, such as the KS functions 62 . As the effect of the FE discretization will be present regardless of the method considered to impose the satisfaction of the stress constraints, for the sake of simplicity, we implement a very basic, not necessarily efficient, modification of the SIMP method to impose this kind of constraints, whose behavior has been checked for the examples presented in this article.…”
Section: Topology Optimization In Cgfemmentioning
confidence: 99%
“…The original SIMP method (Algorithm 1) does not directly considers this kind of constraints as it is based on a volume constraint. Reference 61 presents a TO algorithm where the volume constraint of the SIMP method is substituted by a maximum stress‐measure constraint, such as the KS functions 62 . As the effect of the FE discretization will be present regardless of the method considered to impose the satisfaction of the stress constraints, for the sake of simplicity, we implement a very basic, not necessarily efficient, modification of the SIMP method to impose this kind of constraints, whose behavior has been checked for the examples presented in this article.…”
Section: Topology Optimization In Cgfemmentioning
confidence: 99%
“…According to the statistical theorem that the Chi-squared distribution is a special case of the Gamma distribution, the Chi-squared function (3) is converted to the Gamma (1.5,2) function to match the actual distribution, and the interval values searching strategy is used to determinate both parameters of the Gamma function. The search problem is mathematically equivalent to parameter estimation, and the Kolmogorov-Smirnoff (K-S) distance [22] is used to test its estimation effect. The cumulative distribution function of the generalized Gamma distribution is listed, and parameter estimation is carried out according to the relationship between the sample points and their corresponding probability.…”
Section: Fig 6 Probability Distribution Of Code Stream For Vector Stmentioning
confidence: 99%
“…10with ∂ i /∂x as given by Eq. (3) still holds even in the presence of repeated eigenvalues, as long as a M-orthonormal set of eigenvectors is taken. This is ensured by the following result: Proof From Eq.…”
Section: P-norm Smooth Approximation For Smallest Magnitude Eigenvaluementioning
confidence: 99%
“…We highlight that the use of smooth approximations for maximum/minimum operators is not new [4,11]. In fact, several works already employed p-norm approximations to solve differentiability issues in the context of structural optimization (see the works by [3,12,13,25], to name a few). However, for some reason, this approach was not extensively applied to structural optimization considering least magnitude eigenvalues.…”
Section: Introductionmentioning
confidence: 99%