Boundary element methods for boundary condition inverse problems in elasticity using PCGM and CGM regularization

Zhou, Huanlin; Wei, Jiang; Hu, Hao; Niu, Zhongrong

doi:10.1016/j.enganabound.2013.08.004

Cited by 11 publications

(5 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Based on inverse problem, Zhou et al proposed a boundary element method to solve the boundary condition in lasticity using PCGM and CGM regularization. The numerical results confirm that this method produced convergent and stable numerical solutions [15]. Bustillo et al presented a method for ultrasonic characterization of porous silicon in which a genetic algorithm-based optimization is used to solve the inverse problem [16].…”

Section: Introductionmentioning

confidence: 59%

See 1 more Smart Citation

Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

Xue

Yang

et al. 2014

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In the process of curves and surfaces fairing with multiresolution analysis, fairing accuracy will be determined by final fairing scale. On the basis of Dyadic wavelet fairing algorithm (DWFA), arbitrary resolution wavelet fairing algorithm (ARWFA), and corresponding software, accuracy control of multiresolution fairing was studied for the uncertainty of fairing scale. Firstly, using the idea of inverse problem for reference, linear hypothesis was adopted to predict the corresponding wavelet scale for any given fairing error. Although linear hypothesis has error, it can be eliminated by multiple iterations. So faired curves can be determined by a minimum number of control vertexes and have the best faring effect under the requirement of accuracy. Secondly, in consideration of efficiency loss caused by iterative algorithm, inverse calculation of fairing scale was presented based on the least squares fitting. With the increase of order of curves, inverse calculation accuracy becomes higher and higher. Verification results show that inverse calculation scale can meet the accuracy requirement when fitting curve is sextic. In the whole fairing process, because there is no approximation algorithm such as interpolation and approximation, faired curves can be reconstructed again exactly. This algorithm meets the idea and essence of wavelet analysis well.

show abstract

Section: Introductionmentioning

confidence: 59%

“…The given fairing accuracy of this curve is = 0.02 mm. The primitive curve is a space curve determined by formula (15) and is shown in…”

Section: Accuracy Analysis Of Multiresolutionmentioning

confidence: 99%

Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

Xue

Yang

et al. 2014

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…The PCGM is an iterative regularization method to solve the linear algebraic equation, and it is one of the most effective methods [23,24]. For the ill-posed linear algebraic equation Ax b  , we have the computation procedure as follows .…”

Section: The Preconditioned Conjugate Gradient Methods (Pcgm)mentioning

confidence: 99%

The PCGM for Cauchy inverse problems in 3D potential

Zhou¹,

Bian²,

Cheng³

et al. 2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

Self Cite

View full text Add to dashboard Cite

The preconditioned conjugate gradient method (PCGM) in combination with the boundary element method (BEM) is developed for reconstructing the boundary conditions in 3-D potential. Morozov's discrepancy principle is employed to select the iteration step. The semi-analytical integral algorithm is proposed to treat the nearly singular integrals when the interior points are very close to the boundary. The numerical results confirm that the PCGM produces convergent and stable numerical solutions with respect to decreasing the amount of noise added into the input data. The numerical solutions are sensitive to the locations of the interior points when these points are distributed near the boundary without boundary conditions. The results are more accurate when these points are closer to the boundary.

show abstract

“…This inverse method selected the strains at the internal points as the additional information and was believed to be applicable for the reconstruction of the residual stress and contact stress. Based on the BEM, Zhou et al utilized the preconditioned conjugate gradient method (PCGM) to determine the unknown boundary conditions by the displacements of the internal points [19]. The numerical results indicated that the PCGM was able to acquire reliable solutions.…”

Section: Introductionmentioning

confidence: 99%

Inverse method for the reconstruction of contact stress in point contact with surface profile measurement

Lin¹,

Sun²,

Chen³

2022

Meas. Sci. Technol.

View full text Add to dashboard Cite

Based on the boundary element method and surface profile measurement, a method is developed to solve the inverse problems with point contact. The missing contact stress is modeled by six contact parameters. Using the boundary element method, the contact parameters are related to the surface profiles after deformation. The contact parameters is optimized with a global optimization algorithm by minimizing the difference between the modeled and measured surface profiles. A numerical example is adopted to evaluate the accuracy of the proposed method as well as its robustness against the noises introduced to the surface profiles. Subsequently, the inverse method is used for the reconstruction of the contact stress in the point contact. The agreement between the reconstructed results and the applied load validates the effectiveness of the inverse method in engineering practice.

show abstract

Boundary element methods for boundary condition inverse problems in elasticity using PCGM and CGM regularization

Cited by 11 publications

References 38 publications

Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

The PCGM for Cauchy inverse problems in 3D potential

Inverse method for the reconstruction of contact stress in point contact with surface profile measurement

Contact Info

Product

Resources

About