Structural reanalysis for general layout modifications

Kirsch, Uri; Liu, Shenghu

doi:10.2514/3.13514

Cited by 5 publications

(11 citation statements)

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“…Consequently, additional vectors can be considered without modifying the calculations that were carried out already. The accuracy of the results achieved by the CA method have been demonstrated in previous studies [11][12][13][14][15][16][17][18][19]. The approximations provide accurate solutions even in cases where the series of the original basis vectors (the binomial series) diverges.…”

Section: Approximate Reanalysismentioning

confidence: 57%

“…Topological changes are more complicated, particularly in cases where the number of degrees of freedom is changed. In previous studies, reanalysis procedures have been developed for topological optimisation [11,15,17]. Geometrical changes are conceptually similar to cross-section changes, in the sense that the number of degrees of freedom is unchanged.…”

Section: Introductionmentioning

confidence: 99%

“…The method has been used in previous studies for various problems and different types of design variables [11][12][13][14][15][16][17]. The solution procedure is based on the Combined Approximations (CA) approach, where the binomial series terms are used as basis vectors in reduced basis approximations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact and Accurate Reanalysis of Structures for Geometrical Changes

Kirsch

Papalambros

2001

Engineering with Computers

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A reanalysis approach for geometrical changes in structural systems is presented. The solution procedure is based on the combined approximations method, where the binomial series terms are used as basis vectors in reduced basis approximations. The calculations are based on results of a single exact analysis, calculation of derivatives is not required, and each reanalysis involves a small computational effort. The method is easy to implement, and can be used with general finite element programs. Exact solutions are obtained efficiently for low-rank modifications in the geometry. Accurate solutions are achieved in cases where the basis vectors come close to being linearly dependent. Such solutions are also achieved for nearly scaled geometries, when the angle between the two vectors representing the initial design and modified design is small. Numerical examples demonstrate the high accuracy achieved with a small number of basis vectors.

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Section: Approximate Reanalysismentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

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Exact and Accurate Reanalysis of Structures for Geometrical Changes

Kirsch

Papalambros

2001

Engineering with Computers

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“…The explicit relationships proposed herein could also be resorted to in the static analysis of interval structural problems [16][17][18][19][20][21][22], fuzzy problems [23], optimization and anti-optimization [24,25], stochastic finite elements methods [26][27][28][29][30], stability analysis of uncertain structures [31][32][33], re-analysis [34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Explicit solution for linear systems with parametric stiffness and application to uncertain structures

Settineri

Impollonia

2015

Meccanica

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The paper proposes a novel approximate explicit solution for the static response of structural systems discretized by finite elements with parametric stiffness. The solution exploits the following properties: (a) if the system comprises one parameter only, i.e. a single finite element has parametric stiffness, then the exact explicit solution can always be obtained; (b) if all element stiffnesses are considered as parameters and the exact solution is available at a given point of the parameter space (i.e. for a given realization of the parameters), then it is also known along the line passing through that point and the origin of the parameter space. The joint use of the two properties allows an accurate explicit relationship for nodal displacements which is suitable for treating different structural problems such as optimization, reanalysis, inverse analysis and reliability. The latter will be investigated in the numerical applications where Monte Carlo samples are produced by the explicit relationship rather than by the re-analysis of the structural problem with an evident reduction of computational burden.

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“…Instead of taking original unperturbed eigenvectors as the group of basis vectors, several methods are devoted to constructing new groups of basis vectors, such as Chen's mixed basis method, Pade's method, and Kirsch's combined approximate method. Pade's and Kirsch's methods are also reported to be available for relative large changes of matrix pencil. Later, Chen proposed an epsilon method with two variations: one of which mixed the epsilon algorithm with Kirsch's method and the other based on the standard perturbation method.…”

Section: Introductionmentioning

confidence: 99%

Modal re‐analysis of rotary wind turbine blades in refinement design

2012

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A modal re‐analysis approach is proposed for refinement designs of rotary wind turbine blades on the basis of matrix perturbation methods. The approach entails effects of stress stiffening, spin softening, uncertainty of material properties and structural modifications of blades. Three perturbation methods are used to conduct the re‐analysis approach, including the standard perturbation method and two improvements proposed by H. C. Hu and S. H. Chen, respectively. Numerical results of a typical wind turbine blade indicate that the two improved methods deliver better accuracy than the standard perturbation method in terms of eigenpairs. In application to blade designs, Chen's method is suitable for a multi‐step modal re‐analysis with explicit small parameters and cultivates the first‐order and second‐order perturbations of eigenpairs as well. In contrast, Hu's method is a better choice for a single‐step modal re‐analysis without determining any small parameter explicitly and directly offers approximate eigenpairs instead of somehow tedious perturbation processes. Copyright © 2012 John Wiley & Sons, Ltd.

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Structural reanalysis for general layout modifications

Cited by 5 publications

References 0 publications

Exact and Accurate Reanalysis of Structures for Geometrical Changes

Exact and Accurate Reanalysis of Structures for Geometrical Changes

Explicit solution for linear systems with parametric stiffness and application to uncertain structures

Modal re‐analysis of rotary wind turbine blades in refinement design

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