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Thermal and thermo-mechanical solution of laminated composite beam based on a variables separation for arbitrary volume heat source locations. (English) Zbl 1443.74117

Summary: In this work, a method to compute explicit thermal solutions for laminated and sandwich beams with arbitrary heat source location is developed. The temperature is written as a sum of separated functions of the axial coordinate \(x\), the transverse coordinate \(z\) and the volumetric heat source location \(x_0\). The derived non-linear problem implies an iterative process in which three 1D problems are solved successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the axial description, classical Finite Element method is used. The presented approach is assessed on various laminated and sandwich beams and comparisons with reference solutions with a fixed heat source location are proposed. Based on the accurate results of the thermal analysis, thermo-mechanical response is also addressed using also a separated representation.

MSC:

74-10 Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids
80-10 Mathematical modeling or simulation for problems pertaining to classical thermodynamics
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[1] Drobez, H.; OHostis, G. L.; Gautier, K. B.; Laurent, F.; Durand, B., A new active composite, Smart Mater. Struct., 18, 2, 025020 (2009)
[2] Munoz, V.; Valès, B.; Perrin, M.; Pastor, M.; Welemane, H.; Cantarel, A.; Karama, M., Damage detection in CFRP by coupling acoustic emission and infrared thermography, Compos. Part B Eng. J., 85, 68-75 (2016)
[3] Tanigawa, Y.; Murakami, H.; Ootao, Y., Transient thermal stress analysis of a laminated composite beam., J. Thermal Stress., 12, 25-39 (1989)
[4] Blandford, G.; Tauchert, T.; Du, Y., Self-strained piezothermoelastic composite beam analysis using first-order shear deformation theory, Compos. Part B Eng. J., 30, 1, 51-63 (1999)
[5] Reddy, J., Mechanics of Laminated Composite Plates-Theory and Analysis. (1997), CRC Press: CRC Press Boca Raton, FL · Zbl 0899.73002
[6] Vidal, P.; Polit, O., A thermomechanical finite element for the analysis of rectangular laminated beams., Finite Elem. Anal. Des., 42, 10, 868-883 (2006)
[7] Lee, H.-J.; Saravanos, D., Coupled layerwise analysis of thermopiezoelectric composite beams, AIAA J., 34, 6, 1231-1237 (1996) · Zbl 0900.73263
[8] Carrera, E., An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates., J. Thermal Stress., 23, 797-831 (2000)
[9] Carrera, E.; Ciuffreda, A., Closed-form solutions to assess multilayered-plate theories for various thermal stress problems., J. Thermal Stress., 27, 1001-1031 (2004)
[10] Kapuria, S.; Dumir, P.; Ahmed, A., An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading., Int. J. Solids Struct., 40, 6613-6631 (2003) · Zbl 1042.74534
[11] Lezgy-Nazargah, M., Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach., Aerosp. Sci. Tech., 45, 154-164 (2015)
[12] Hetnarski, R.; Eslami, M., Thermal Stresses - Advanced Theory and Applications. (2009), Springer · Zbl 1165.74004
[13] Tauchert, T., Thermally induced flexure, buckling and vibration of plates., Appl. Mech. Rev., 44, 8, 347-360 (1991)
[14] Noor, A.; Burton, W., Computational models for high-temperature multilayered composite plates and shells., Appl. Mech. Rev., 45, 10, 419-446 (1992)
[15] Ammar, A.; Mokdada, B.; Chinesta, F.; Keunings, R., A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, J. Non Newton. Fluid Mech., 139, 153-176 (2006) · Zbl 1195.76337
[16] Bognet, B.; Bordeu, F.; Chinesta, F.; Leygue, A.; Poitou, A., Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity., Comput. Methods Appl. Mech. Eng., 201-204, 1-12 (2012) · Zbl 1239.74045
[17] Vidal, P.; Gallimard, L.; Polit, O., Assessment of a composite beam finite element based on the proper generalized decomposition., Compos. Struct., 94, 5, 1900-1910 (2012)
[18] Vidal, P.; Gallimard, L.; Polit, O., Thermo-mechanical analysis of laminated composite and sandwich beams based on a variables separation., Compos. Struct., 152, 755-766 (2016)
[19] Pruliere, E.; Chinesta, F.; Ammar, A.; Leygue, A.; Poitou, A., On the solution of the heat equation in very thin tapes., Int. J. Thermal Sci, 65, 148-157 (2013)
[20] Ghnatios, C.; Masson, F.; Huerta, A.; Leygue, A.; Cueto, E.; Chinesta, F., Proper generalized decomposition based dynamic data-driven control of thermal processes., Comput. Methods Appl. Mech. Eng., 213-216, 29-41 (2012)
[21] Aguado, J.; Huerta, A.; Chinesta, F.; Cueto, E., Real-time monitoring of thermal processes by reduced-order modeling., Int. J. Num. Meth. Eng., 102, 5, 991-1017 (2015) · Zbl 1352.80002
[22] Niroomandi, S.; Alfaro, I.; Cueto, E.; Chinesta, F., Model order reduction for hyperelastic materials, Int. J. Num. Meth. Eng., 81, 9, 1180 (2010) · Zbl 1183.74365
[23] Nouy, A., A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations, Comput. Methods Appl. Mech. Eng., 199, 23-24, 1603-1626 (2010) · Zbl 1231.76219
[24] Chinesta, F.; Ammar, A.; Leygue, A.; Keunings, R., An overview of the proper generalized decomposition with applications in computational rheology, J. Non- Newton. Fluid Mech., 166, 11, 578-592 (2011) · Zbl 1359.76219
[25] Vidal, P.; Gallimard, L.; Polit, O., Proper generalized decomposition and layer-wise approach for the modeling of composite plate structures., Int. J. Solids Struct., 50, 14-15, 2239-2250 (2013)
[26] Harshman, R. A., Foundations of the parafac procedure: Models and conditions for an explanatory multi-modal factor analysis., UCLA Work. Pap. Phon., 16, 1-84 (1970)
[27] Kiers, A. L., Towards a standardized notation and terminology in multiway analysis., J. Chemom., 14, 105-122 (2000)
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