Exact and Accurate Reanalysis of Structures for Geometrical Changes

Kirsch, Uri; Papalambros, Panos Y.

doi:10.1007/s366-001-8302-9

Cited by 30 publications

(7 citation statements)

References 18 publications

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“…The CA method was originally developed for linear static problems [32], and then extended to multidisciplinary problems. Kirsch and Papalambros presented a reanalysis approach for geometric changes in structural systems based on the CA method [33]. Rong et al extended Kirsch's method to a new effective modal reanalysis method for topological modification [34].…”

Section: / 42mentioning

confidence: 99%

Closed loop geometry based optimization by integrating subdivision, reanalysis and metaheuristic searching techniques

Huang

Wang

et al. 2017

Computers & Structures

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A closed loop geometry based optimization method is developed in this work by integrating subdivision, reanalysis and metaheuristic searching techniques. For that purpose, subdivision surfaces using triangle meshes are simultaneously applied to CAD (computer aided design) modeling and CAE (computer aided engineering) analysis. In this framework, feature objects are defined by the subdivision model, so that the subdivision models can be controlled by geometric parameters. Global optimization with metaheuristic algorithms is then performed, and an independent coefficients (IC) reanalysis method is introduced to enhance the efficiency of optimization. In order to improve the accuracy of triangular meshes, the ES-FEM (edge-based smoothed finite element method) technique is employed for analysis work. The proposed approach is successfully tested in three real engineering geometry optimization problems.

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Section: / 42mentioning

confidence: 99%

Closed loop geometry based optimization by integrating subdivision, reanalysis and metaheuristic searching techniques

Huang

Wang

et al. 2017

Computers & Structures

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“…Equation (12) shows that, when the reduced basis expression with s terms [Eq. (11)] is equal to the exact solution, then the s C 1 basis vector is a linear combination of the previous s vectors. That is, the s C 1 basis vectors are linearly dependent.…”

Section: A Linearly Dependent Basis Vectorsmentioning

confidence: 99%

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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“…The combined approximation (CA) method has become one of the most popular approximate reanalysis methods in recent years. Kirsch has applied the CA method to linear static, geometric change and engineering problems . However, exact solutions usually cannot be achieved via approximate methods.…”

Section: Introductionmentioning

confidence: 99%

An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

Liu

et al. 2020

Numerical Meth Engineering

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Summary An efficient optimization framework is developed in this study by integrating auxiliary projection‐based multigrid isogeometric reanalysis (MG‐IGR) and metaheuristic searching techniques. It is well known that the inherent characteristics of isogeometric analysis (IGA) are superior in shape optimization problems. Inheriting the characteristics of IGA, an auxiliary projection‐based MG reanalysis (MGR) is proposed to construct mapping between the mesh before modification and after modification during the optimization process. Subsequently, MG‐IGR is utilized to reanalyze the modified design efficiently by reusing the initial evaluated results. Moreover, the proposed MG‐IGR also eliminates the restriction of mesh consistency. In this framework, the structure can be designed directly through parameterized control of the non‐uniform rational B‐spline (NURBS) model, and the MG‐IGR fast solver enables any metaheuristic algorithm to perform the optimization procedure. Moreover, the accuracy of the simulation can be guaranteed by the NURBS model and the convergence criterion of the MG. Finally, two geometric optimization examples are presented to validate the performance of the developed framework.

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Exact and Accurate Reanalysis of Structures for Geometrical Changes

Cited by 30 publications

References 18 publications

Closed loop geometry based optimization by integrating subdivision, reanalysis and metaheuristic searching techniques

Closed loop geometry based optimization by integrating subdivision, reanalysis and metaheuristic searching techniques

Exact and Accurate Solutions in the Approximate Reanalysis of Structures

An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

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