A THERMOELASTIC ANALYSIS USING THE BOUNDARY ELEMENTS, DIC AND THERMAL IMAGES

Authors

DOI:

https://doi.org/10.26512/ripe.v2i6.21474

Keywords:

Boundary elements. Thermoelasticity. Digital image correlation. Thermal images.

Abstract

The main goal of this work relies on developing an experimental procedure to verify a thermoelastic Boundary Elements Method (BEM) analysis using imaging techniques for obtaining the steady-state displacement and temperature fields on isotropic solids. The experimentally obtained temperature field is used as input for the numerical BEM analysis in order to represent the thermal expansion effect. The domain's temperature and consequent resultant thermoelastic displacement fields are carried into the BEM formulation using the Radial Integration Method (RIM). This method consists in a mathematical technique where the radial basis functions are applied to convert domain integrals to the boundary. The use of the RIM avoids the necessity of domain discretization and, therefore, preserves the BEM advantages. For this method to be effective, the experimentally obtained field that describes the temperature difference between the initial and final temperatures on the domain is described by a forth order polynomial. In the end, the resultant numerical displacement field, obtained from the experimental temperature field and the BEM analysis, is compared to the experimental displacement data in order to evaluate the numerical method efficacy. The verified proximity between the obtained numerical displacement curves and its experimental equivalents indicates the good performance of the proposed methodology. 

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References

Aliabadi, M.H., 2002. The Boundary Element Method, Volume 2, Applications in Solids and Structures. Wiley.

Banerjee, P., & Butterfield, R., 1981. Boundary elements method in engineering science. Mcgraw-hill.

Barranger, Y., Doumalin, P., Dupré, J.C., Germaneau, A., 2010. Digital image correlation accuracy: Influence of kind of speckle and recording setup. EPJ web of conferences Volume 6 - ICEM 14 ”“ 14th International Conference on Experimental Mechanics.

Bodelot, L., Sabatier, L., Charkaluk, E., & Dufrénoy, P., 2009. Experimental setup for fully coupled kinematic and thermal measurements at the microstructure scale of an AISI 316L steel. Materials Science and Engineering A, vol. 501, pp. 52-60.

Crammond, G., Boyd, S.W., & Dulieu-Barton, J.M., 2013. Speckle pattern assessment for digital image correlation. Optics and Lasers in Engineering, vol. 51 n. 12, pp. 1368-1378.

Cruse, T. A., 1975. Boundary integral equation method for three-dimensional elastic fracture mechanics. AFOSR-TR-75-0813, ADA 011660. Pratt and Whitney Aircraft-Connecticut.

Danson, D.J., 1981. A boundary element formulation for problems in linear isotropic elasticity with body forces. In Brebbia, C.A., ed, Boundary Element Methods, Berlin, pp. 105”“122. Springer-Berlin.

Dondero, A., Cisilino, A.P., Carella, J.M., & Tomba, J.P., 2011. Effective thermal conductivity of functionally graded random micro-heterogeneous materials using representative volume element and BEM. Intenational Journal of Heat and Mass Transfer, vol. 54 n. 17-18 pp. 3874-3881.

Gao, X.W., 2002. The radial integration method for evaluation of domain integrals with boundary-only discretization. Engineering Analysis with Boundary Elements, vol. 26, pp. 905-916.

Gao, X.W., 2003. Boundary element analysis in thermoelasticity with and without internal cells. International Journal for Numerical Methods in Engineering, vol. 57, n. 7, pp. 975-990.

Katsikadelis, J.T., 2002. Boundary elements: Theory and Applications. Elsevier, Oxford.

Lecompte, D., Sol, H., & Vantomme, J., 2006. Analysis of speckle patterns for deformation measurements by digital image correlation. Proceedings of SPIE vol. 6341, Speckle06, From Grains to Flowers.

Lecompte, D., Smits, A., Bossuyt, S., Sol, H., Vantomme, J., Van Hemelrijck, D., & Habraken, M.A., 2006. Quality assessment of speckle patterns for digital image correlation. Optics and Lasers in Engineering, vol. 44, n. 11, pp. 1132-1145.

Nardini, D., & Brebbia, C.A., 1983. A new approach for free vibration analysis using boundary elements. Applied Mathematical Modelling, vol. 7, n. 3, pp.157-162.

Neves, C.A., & Brebbia, C.A., 1991. The multiple reciprocity boundary element method in elasticity: a new approach for transforming domain integral to the boundary. International Journal for Numerical Methods in Engineering, vol. 31, n. 4, pp. 709”“27.

Nowak, J.A., & Brebbia, C.A., 1989. The multiple-reciprocity method. A new approach for transforming B.E.M. domain integrals to the boundary. Engineering Analysis with Boundary Elements, vol. 6, n. 3, pp. 164”“167.

Ochiai, Y., & Kobayashi, T., 1999. Initial stress formulation for elastoplastic analysis by improved multiple-reciprocity boundary element method. Engineering Analysis with Boundary Elements, vol. 23, pp. 167”“73.

Pan, B., Qian, K., Xie, H., & Asundi, A., 2008. On errors of digital image correlation due to speckle patterns. Proceedings of ICEM 2008: International Conference on Experimental Mechanics.

Pan, B., Qian, K., Xie, H., & Asundi, A., 2009. Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review. Measurement Science and Technology, vol. 20, n. 6, pp.1-17.

Partridge, P.W., Brebbia, C.A., & Wrobel, L.C., 1992. The Dual Reciprocity Boundary Element Method. Computational Mechanics Publications.

Silva, M.L., & Ravichandran, G., 2011. Combined thermoelastic stress analysis and digital image correlation with a single infrared camera. Journal of Strain Analysis for Engineering Design, vol. 46, n. 8, pp. 783-793.

Sládek, V., & Sládek, J., 1983. Boundary integral equation in thermoelasticity, Part I: General analysis. Applied Mathematical Modelling, vol. 7, n. 4, pp. 241-253.

Sládek, V., & Sládek, J., 1984. Boundary integral equation in thermoelasticity, Part III: Uncoupled thermoelasticity, Applied Mathematical Modelling, vol. 8, n. 6, pp. 413-418.

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Published

2017-01-19

How to Cite

Oberg, M. B. A. M., & Anflor, C. T. M. (2017). A THERMOELASTIC ANALYSIS USING THE BOUNDARY ELEMENTS, DIC AND THERMAL IMAGES. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(6), 99–111. https://doi.org/10.26512/ripe.v2i6.21474