Higher-order modeling of continua by finite-element, boundary-element, meshless, and wavelet methods

Basu, Prodyot K.; Jorge, Ariosto Bretanha; Badri, Seyed Amin; Lin, Ji

doi:10.1016/s0898-1221(03)90078-2

Cited by 24 publications

(11 citation statements)

References 9 publications

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“…Additionally, a study using B-spline wavelet as the shape functions was conducted [4]. Basu et al did a study comparing the FEM, BEM, Meshless Method, and Wavelet Methods [5,6]. Meanwhile, thin plate problems were analyzed with Daubechies wavelets [7].…”

Section: Introductionmentioning

confidence: 99%

1st‐Order Shear Deformable Beam Formulation Based on Meshless Wavelet Galerkin Method

Lee

2017

Mathematical Problems in Engineering

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This paper examined and discussed a Meshless Wavelet Galerkin Method (MWGM) formulation for a first-order shear deformable beam, the properties of the MWGM, the differences between the MWGM and EFG, and programming methods for the MWGM. The first-order shear deformable beam (FSDB) consists of a pair of second-order elliptic differential equations. The weak forms of two differential equations are deduced using Hat wavelet series. The exact integration and reduced integration were used to analyze the problems. Some indeterminate beam problems are considered. Condition numbers of the stiffness matrix were analyzed with exact integration and reduced integration for two cases of these problems. Consequently, the results were converged on the analytic solutions. The shear-locking phenomenon also occurred in the MWGM as it occurs in the conventional FEM. The stiffness matrix calculated from the reduced integration causes a similar numerical error to the stiffness matrix calculated from the exact integration in the MWGM. The MWGM showed desirable results in the examples.

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Section: Introductionmentioning

confidence: 99%

1st‐Order Shear Deformable Beam Formulation Based on Meshless Wavelet Galerkin Method

Lee

2017

Mathematical Problems in Engineering

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“…So it is the best one among all existing wavelets in approximation of numerical calculation [32]. Based on the good characteristics of BSWI, several investigators have tried to combine it with FEM to solve practical problems [33][34][35][36][37]. However, the above-mentioned methods, which are all constructed in a determined wavelet space, can hardly make a satisfying approximation for the influence caused by structural uncertainties.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis

Zhang

Chen

Yang

et al. 2014

Shock and Vibration

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A stochastic finite element method based on B-spline wavelet on the interval (BSWI-SFEM) is presented for static analysis of 1D and 2D structures in this paper. Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. By means of virtual work principle and BSWI, the wavelet finite elements of beam, plate, and plane rigid frame are obtained. Combining the Monte Carlo method and the constructed BSWI elements together, the BSWI-SFEM is formulated. The constructed BSWI-SFEM can deal with the problems of structural response uncertainty caused by the variability of the material properties, static load amplitudes, and so on. Taking the widely used Timoshenko beam, the Mindlin plate, and the plane rigid frame as examples, numerical results have demonstrated that the proposed method can give a higher accuracy and a better constringency than the conventional stochastic finite element methods.

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“…Unlike traditional finite element method, the desirable advantages of wavelet-based elements are multi-resolution properties and various basis functions for structural analysis [12][13][14]. Recently, continuous wavelets transform maybe a good choice to solve partial differential equations (PDEs).…”

Section: Introductionmentioning

confidence: 99%

A novel wavelet-based finite element method for the analysis of rotor-bearing systems

Xiang

Chen

et al. 2009

Finite Elements in Analysis and Design

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Higher-order modeling of continua by finite-element, boundary-element, meshless, and wavelet methods

Cited by 24 publications

References 9 publications

1st‐Order Shear Deformable Beam Formulation Based on Meshless Wavelet Galerkin Method

1st‐Order Shear Deformable Beam Formulation Based on Meshless Wavelet Galerkin Method

A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis

A novel wavelet-based finite element method for the analysis of rotor-bearing systems

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