A meshless local Kriging method for large deformation analyses

Article

Gu, Y. T., Wang, Q. X. and Lam, K. Y.. 2007. "A meshless local Kriging method for large deformation analyses." Computer Methods in Applied Mechanics and Engineering. 196 (9-12), pp. 1673-1684. https://doi.org/10.1016/j.cma.2006.09.017
Article Title

A meshless local Kriging method for large deformation analyses

ERA Journal ID4173
Article CategoryArticle
AuthorsGu, Y. T. (Author), Wang, Q. X. (Author) and Lam, K. Y. (Author)
Journal TitleComputer Methods in Applied Mechanics and Engineering
Journal Citation196 (9-12), pp. 1673-1684
Number of Pages12
Year2007
Place of PublicationNetherlands
ISSN0045-7825
Digital Object Identifier (DOI)https://doi.org/10.1016/j.cma.2006.09.017
Web Address (URL)https://www.sciencedirect.com/science/article/pii/S0045782506003264
Abstract

In this paper, a well-developed meshless numerical technique, local Kriging (LoKriging) method, is used to develop the LoKriging formulation for the large deformation problems, which are geometrically nonlinear. This is the first work for the geometrically nonlinear analyses by this meshless local weak-form method. In the LoKriging method, the Kriging interpolation is employed to construct the meshless shape functions. The spline function with high continuity is used as the weight function. The discrete equations of the large deformation analysis for two-dimensional solids are obtained using the local weak-forms, and based on the total Lagrangian (TL) approach. The presently developed LoKriging method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak-form. Several numerical examples of the two-dimensional geometrically nonlinear analysis are presented to illustrate the performance of the present LoKriging method. The present nonlinear LoKriging formulation is also used for the large deformation analysis of the microelectromechanical systems (MEMS) device. The numerical results are compared with the experimental results. Very good results are obtained. All these applications have demonstrated that the present LoKriging method is very effective for the large deformation analyses, because it avoids all mesh distortion issues.

KeywordsKriging interpolation; Large deformation; Local weak-form; MEMS; Meshless method; Nonlinear; Numerical computation
ANZSRC Field of Research 2020401706. Numerical modelling and mechanical characterisation
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Byline AffiliationsUniversity of Sydney
Institute of High Performance Computing, Singapore
Institution of OriginUniversity of Southern Queensland
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Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability
Thibbotuwawa, Namal, Oloyede, Adekunle, Senadeera, Wijitha, Li, Tong and Gu, YuanTong. 2015. "Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability." Journal of The Mechanical Behavior of Biomedical Materials. 51, pp. 248-259. https://doi.org/10.1016/j.jmbbm.2015.07.018
Analysis of strain-rate dependent mechanical behavior of single chondrocyte: a finite element study
Gu, YuanTong, Nguyen, Trung Dung, Oloyede, Adekunle and Senadeera, Wijitha. 2014. "Analysis of strain-rate dependent mechanical behavior of single chondrocyte: a finite element study." International Journal of Computational Methods. 11 (1 (Supplement)), pp. 1344005-1. https://doi.org/10.1142/S0219876213440052
A particle based model to simulate microscale morphological changes of plant tissues during drying
Karunasena, H. C. P., Senadeera, W., Brown, R. J. and Gu, Y. T.. 2014. "A particle based model to simulate microscale morphological changes of plant tissues during drying." Soft Matter. 10 (29), pp. 5249-5268. https://doi.org/10.1039/c4sm00526k
A mesh free model for plant tissue deformations during drying
Karunasena, H. C. P., Senadeera, W., Brown, R. J. and Gu, Y. T.. 2014. "A mesh free model for plant tissue deformations during drying." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 55 (EMAC2013), pp. C110-C137.
Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying
Karunasena, H. C. P., Gu, Y. T., Brown, R. J. and Senadeera, W.. 2015. "Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying." Biosystems Engineering. 132, pp. 71-87. https://doi.org/10.1016/j.biosystemseng.2015.02.002
Application of meshfree methods to numerically simulate microscale deformations of different plant food materials during drying
Karunasena, H. C. P., Brown, R. J., Gu, Y. T. and Senadeera, W.. 2015. "Application of meshfree methods to numerically simulate microscale deformations of different plant food materials during drying." Journal of Food Engineering. 146, pp. 209-226. https://doi.org/10.1016/j.jfoodeng.2014.09.011
Scanning electron microscopic study of microstructure of gala apples during hot air drying
Karunasena, H. C. P., Hesami, P., Senadeera, W., Gu, Y. T., Brown, R. J. and Oloyede, A.. 2014. "Scanning electron microscopic study of microstructure of gala apples during hot air drying." Drying Technology: an international journal. 32 (4), pp. 455-468. https://doi.org/10.1080/07373937.2013.837479
Numerical investigation of case hardening of plant tissue during drying and its influence on the cellular-level shrinkage
Karunasena, H. C. P., Gu, Y.T., Brown, R. J. and Senadeera, W.. 2015. "Numerical investigation of case hardening of plant tissue during drying and its influence on the cellular-level shrinkage." Drying Technology: an international journal. 33 (6), pp. 713-734. https://doi.org/10.1080/07373937.2014.982759
A constitutive model for mechanical response characterization of pumpkin peel and flesh tissues under tensile and compressive loadings
Shirmohammadi, Maryam, Yarlagadda, Prasad K. D. V. and Gu, YuanTong. 2015. "A constitutive model for mechanical response characterization of pumpkin peel and flesh tissues under tensile and compressive loadings ." Journal of Food Science and Technology. 52 (8), pp. 4874-4884. https://doi.org/10.1007/s13197-014-1605-2
Comprehensive Contribution of Filament Thickness and Crosslinker Failure to the Rheological Property of F-actin Cytoskeleton
Li, Tong, Liu, Ling, Hu, Dean, Oloyede, Adekunle, Xiao, Yin, Yarlagadda, Prasad and Gu, YuanTong. 2015. "Comprehensive Contribution of Filament Thickness and Crosslinker Failure to the Rheological Property of F-actin Cytoskeleton." Cellular and Molecular Bioengineering. 8 (2), pp. 278-284. https://doi.org/10.1007/s12195-015-0382-y
Trans-scale Granular Modelling of Cytoskeleton: a Mini-Review
Li, Tong, Yarlagadda, Prasad K. D. V., Oloyede, Adekunle, Thibbotuwawa, Namal and Gu, YuanTong. 2015. "Trans-scale Granular Modelling of Cytoskeleton: a Mini-Review." Molecular and Cellular Biomechanics. 12 (1), pp. 17-35. https://doi.org/10.3970/mcb.2015.012.017
Tensile properties of Si nanowires with faulted stacking layers
Zhan, Haifei, Gu, Yuantong, Yan, Cheng and Yarlagadda, Prasad K. D. V.. 2014. "Tensile properties of Si nanowires with faulted stacking layers." Science of Advanced Materials. 6 (7), pp. 1489-1492. https://doi.org/10.1166/sam.2014.1800
Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses
Li, Tong, Gu, Y. T., Oloyede, Adekunle and Yarlagadda, Prasad K. D. V.. 2014. "Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses." Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization. 17 (6), pp. 616-622. https://doi.org/10.1080/10255842.2012.706279
How to increase the accuracy of analysis and reduce the computational time in ANSYS in the case of deformation study of orthopedic bone plates
Malekani, Javad, Yarlagadda, Prasad K. D. V., Schmutz, Beat, Gu, YuanTong and Schuetz, Michael. 2014. "How to increase the accuracy of analysis and reduce the computational time in ANSYS in the case of deformation study of orthopedic bone plates." 3rd International Conference on Materials and Products Manufacturing Technology (ICMPMT 2013). China 25 - 26 Sep 2013 Scientific.Net. https://doi.org/10.4028/www.scientific.net/AMR.834-836.1592
Bending properties of Ag nanowires with pre-existing surface defects
Zhan, H. F., Gu, Y. T., Yan, C. and Yarlagadda, P. K. D. V.. 2014. "Bending properties of Ag nanowires with pre-existing surface defects." Computational Materials Science. 81, pp. 45-51. https://doi.org/10.1016/j.commatsci.2013.05.032
Studies on bending limitations for the optimal fit of orthopaedic bone plates
Malekani, J., Schmutz, B., Gudimetla, P., Gu, Y., Schuetz, M. and Yarlagadda, Prasad. 2013. "Studies on bending limitations for the optimal fit of orthopaedic bone plates." 2nd International Conference on Materials and Products Manufacturing Technology (ICMPMT 2012). 22 - 23 Sep 2012 Switzerland. https://doi.org/10.4028/www.scientific.net/AMR.602-604.1181
A coupled numerical approach for nonlinear dynamic fluid‐structure interaction analysis of a near‐bed submarine pipeline
Gu, Y.T. and Wang, Q.. 2008. "A coupled numerical approach for nonlinear dynamic fluid‐structure interaction analysis of a near‐bed submarine pipeline." Engineering Computations: international journal for computer-aided engineering and software. 25 (6), pp. 569-588. https://doi.org/10.1108/02644400810891553
A combined meshfree method and molecular dynamics in the multiscale length simulation
Wang, Q.X., Ng, T.Y., Kam, K.Y., Li, Hua and Fan, X.J.. 2002. "A combined meshfree method and molecular dynamics in the multiscale length simulation." Recent Advances In Computational Science And Engineering. Singapore. World Scientific Publishing. pp. 663–666