The construction of finite element multiwavelets for adaptive structural analysis

Wang, Youming; Chen, Xuefeng; He, Yinnian; He, Zhengjia

doi:10.1002/cnm.1320

Cited by 14 publications

(5 citation statements)

References 28 publications

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“…Various wavelets, including spline wavelet [23], Daubechies wavelet [24], Hermite wavelet [25], Lagrange wavelet [26], and trigonometric wavelet [27], have been employed in numeral computation. In this study, the second-generation Lagrange wavelet [26] with convenient computational characteristics is adopted to fulfill the adaptive dynamic force reconstruction.…”

Section: The Refinement Of Lagrange Wavelet Functionmentioning

confidence: 99%

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Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Yang

Zhu

2018

Shock and Vibration

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The shape function-based method is one of the very promising time-domain methods for dynamic force reconstruction, because it can significantly reduce the number of unknowns and shorten the reconstruction time. However, it is challenging to determine the optimum time unit length that can balance the tradeoff between reconstruction accuracy and efficiency in advance. To address this challenge, this paper develops an adaptive dynamic force reconstruction method based on multiscale wavelet shape functions and time-domain deconvolution. A concentrated dynamic force is discretized into units in time domain and the local force in each unit is approximated by wavelet scale functions at an initial scale. Subsequently, the whole response matrix is formulated by assembling the responses induced by the wavelet shape function forces of all time units which are calculated by the structural finite element model (FEM). Then, the wavelet shape function-based force-response equation is established for force reconstruction. Finally, the scale of the force-response equation is lifted by refining the wavelet shape function with high-scale wavelets and dynamic responses with more point data to improve the reconstruction accuracy gradually. Numerical examples of different structural types are analyzed to verify the feasibility and effectiveness of the proposed method.

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Section: The Refinement Of Lagrange Wavelet Functionmentioning

confidence: 99%

“…In this study, the second-generation Lagrange wavelet [26] with convenient computational characteristics is adopted to fulfill the adaptive dynamic force reconstruction. When defined within the interval [0, 1], the scaling functions (Scale 0) of Lagrange wavelets are…”

Section: The Refinement Of Lagrange Wavelet Functionmentioning

confidence: 99%

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Yang

Zhu

2018

Shock and Vibration

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“…However, during the past few years, the implementation of the multiresolution approach in computational methods for mechanics has been reported. Wang et al have constructed finite element multiwavelets using linear Lagrange and cubic Hermite scaling functions that showed very good results in static analyses of rods and beams [9]. Liu et al have proposed a multiresolution wavelet Galerkin method using Daubechies wavelets for the static solution of 2D problems [10].…”

Section: Introductionmentioning

confidence: 99%

Enhanced Simulation of Guided Waves and Damage Localization in Composite Strips Using the Multiresolution Finite Wavelet Domain Method

Dimitriou

Nastos

Saravanos

2022

Lecture Notes in Civil Engineering

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A multiresolution finite wavelet domain method, that utilizes Daubechies wavelet and scaling functions for the hierarchical approximation of state variables, is presented. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, while additional equations of finer components are subsequently added. A coarse solution is first calculated, and finer solutions can be sequentially superimposed on the coarse solution until convergence to the final solution is achieved. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing a unique capability to separate coexisting wave modes and detect converted and reflected waves in the presence of damage. Two wavelet-based beam elements are explored, the first encompasses the Timoshenko shear beam theory and the second a high-order layerwise laminate theory for the accurate prediction of both symmetric and antisymmetric guided waves. Numerical results illustrate the inherent property of the method to a priori localize and isolate coexisting guided wave modes and their conversions, induced by different material regions and weak or debonded layer interfaces, thus demonstrating the method's intrinsic capabilities towards the design of wave-based SHM systems.

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“…Jang et al 22 have exploited hat interpolation wavelets for the development of an adaptive multiresolution wavelet‐based method, capable of handling Dirichlet and Neumann boundary conditions along curved boundaries. Wang et al 23 have constructed finite element multiwavelets using linear Lagrange and cubic Hermite scaling functions and the lifting scheme in order to achieve scale decoupling in the static analyses of rod and beam elements. Liu et al 24 have developed explicitly a stable wavelet interpolant which they have applied to a proposed wavelet multiresolution interpolation Galerkin method for targeted local enrichment in solving 2D static problems with complex load cases and boundaries.…”

Section: Introductionmentioning

confidence: 99%

Multiresolution Daubechies finite wavelet domain method for transient dynamic wave analysis in elastic solids

Nastos

Saravanos

2021

Numerical Meth Engineering

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The multiresolution capability provided by the family of Daubechies wavelets is exploited to develop a new computational approach, termed as multiresolution finite wavelet domain method for the fast and hierarchical prediction of transient dynamic problems with focus on wave propagation in one-and two-dimensional structural configurations. In the developed method, both scaling and wavelet functions are employed as basis functions for the approximation of displacements in the governing dynamic equations. Because of the orthogonal and the multiresolution properties of Daubechies wavelets, a two-scale system of mass uncoupled dynamic equations, representing the coarse and the fine spatial wave component solutions is derived. Numerical results concerning wave propagation in one-and two-dimensional elastic structures demonstrate substantial computational gains of the method in comparison with other well-established numerical methods. Moreover, additional benefits of the involved coarse and fine solutions enabling the analysis and characterization of the resultant wave response are revealed and discussed.

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The construction of finite element multiwavelets for adaptive structural analysis

Cited by 14 publications

References 28 publications

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Enhanced Simulation of Guided Waves and Damage Localization in Composite Strips Using the Multiresolution Finite Wavelet Domain Method

Multiresolution Daubechies finite wavelet domain method for transient dynamic wave analysis in elastic solids

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