• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.175-190
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• 2010

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.819-828
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• 2004

A new process for estimating the natural frequency and the corresponding damping ratio in large structures is discussed. In a practical situation, it is very difficult to analyze large structures precisely because they are too complex to model using the finite element method and too heavy to excite using the exciting force method; in particular, the measured signals are seriously influenced by ambient noise. In order to identify the structural impulse response associated with the information of natural frequency and the corresponding damping ratio in large structures, the analysis process, a so-called "multiresolution blind system identification algorithm" which combines Mallat algorithm and the bicepstrum method. High time-frequency concentration is attained and the phase information is kept. The experimental result has demonstrated that the new analysis process exploiting the natural frequency and the corresponding damping ratio of structural response are useful tools in structural analysis application.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.16-23
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• 1997

The Reproducing Kernel Particle Method (RKPM), one of the popular meshless methods, is developed and applied to stress concentration problems. Since the meshless methods require only a set of particles (or nodes) and the description of boundaries in their formulation, the adaptivity can be implemented with much more ease than finite element method. In addition, due to its intrinsic property of multiresolution, the shape function of RKPM provides us a new criterion for adaptivity. Recently, this multiple scale Reproducing Kernel Particle Method and its adaptive procedure have been formulated for large deformation problems by the authors. They are also under development for damage materials and localization problems. In this paper the multiple scale RKPM for linear elasticity is presented and the adaptive procedure is applied to stress concentration problems. Therefore, this work may be regarded as the edition of linear elasticity in the complete framework of multiple scale RKPM and the associated adaptivity.