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AN APPLICATION OF THE MODIFIED FINITE ELEMENT TRANSFER MATRIX METHOD FOR A HEAT TRANSFER PROBLEM

Year 2019, Volume: 5 Issue: 1, 15 - 28, 30.06.2019
https://doi.org/10.34186/klujes.564004

Abstract

The Transfer Matrix Method is an effective method which is used in
mechanics and provides a great advantage especially in solving some mechanical
problems. The most important advantage of the Transfer Matrix Method is
reducing the dimensions of the matrix used in the analysis. The most important
consequence of this is the saving the time.



In this study, firstly studies in recent years in relation with the
Transfer Matrix Method have been briefly summarized. Then the Modified Finite
Element Transfer Matrix Method is explained briefly. At the end of the study,
the application of the Modified Finite Element Transfer Matrix Method to the
heat transfer problem has been demonstrated.

References

  • [1] Holzer, H. Analysis of Torsional Vibration, Springer, Berlin, 1921.
  • [2] Myklestad, N.O. New Method of Calculating Natural Modes of Coupled Bending-Torsion Vibration of Beams. Trans. ASME., 61-67.
  • [3] Thompson, W. T. Matrix Solution for The Vibration of Non-Uniform Beams. J. App. Mech .17(1950), 337–339.
  • [4] Thompson, W. T. Transmission of Elastic Waves Through a Stratified Solid Media, J. Appl. Phys. 21(1950),89-93
  • [5] Haskel, N.A. The Dispersion of Surface Waves on Multilayered Media. Bull. seism. Soc. Am. 43 (1953),17-34.
  • [6] Pestel, E.C., Leckie, F. A. Matrix Methods in Elastomechanics. New York: McGraw-Hill,1963.
  • [7] İnan, M. The Method of Initial Values and the Carry-over Matrix in Elastomechanics, Middle East Technical University,1968.
  • [8] Hoerner, G.C. The Rıccati Transfer Matrix Method. Ph.D. Thesis, University of virginia, Charlottesvile, VA.,1975.
  • [9] Dokanish, M.A. A New Approach for Plate Vibration: Combination of Transfer Matrix and Finite Element Technique. Trans. ASME J. Eng. Ind. 94(1972), 526-530.
  • [10] Mcdaniel, T. J., Eversole, K. B. A Combined Finite Element-Transfer Matrix Structural Analysis Method.J. Sound Vibr. 51(1977), 157-169.
  • [11] Ghiatti, G., Sestieri, A. Analysis of Static and Dynamic Structural Problems by a Combined Finite Element-Transfer Matrix Method. J. Sound Vibr. 67 (1979),35-42.
  • [12] Ohga, M., Shigematsu, T., Hara, T. (1984) A Combined Finite Element-Transfer Matrix Method. J. Engng Mech.Div., Am. Sot. Ciu. Engrs 110(1984), 1335-1349.
  • [13] Degen, E.E., Shepbhard, M.S., Loewy, R.G. Combined Finite Element-Transfer Matrix Method Based on a Finite Mixed Formulation. Comput. Struct., 20(1985), 173-180.
  • [14] Chen, Y. H., Xue, H. Y. Dynamic Large Deflection Analysis of Structures by a Combined Finite Element Riccati Transfer Matrix Method on a Microcomputer. Comput. Struct. 39(1991), No 6., 699–703.
  • [15] Xue, H.Y. A Combined Dynamic Finite Element-Ricatti Transfer Matrix Method for Solving Non-Linear Eigenproblems of Vibrations. Comp. Struct., 53(1994), No.6, 1257-1261.
  • [16] Yuhua, C. Large Deflection Analysis of Structures by an Improved Combined Finite Element-Transfer Matrix Method. Comput Struct 55(1995), 167–171.
  • [17] Bhutani, N., Loewy, R.G. Combined Finite Element-Transfer Matrix Method. J. Sound Vib., 226 (1999), No.5,1048-1052.
  • [18] Alimonti, L.,Atalla,N.,Sgard,F. Assessment of a hybrid finite element-transfer matrix model for flat structures with homogeneous acoustic treatments. J Acoust Soc Am.135(2014), No.5,2694-2705.
  • [19] Fan ,S.,Barber,J.R. Solution of Periodic Heating Problems by the Transfer Matrix Method.Heat and Mass Trans. 45(2002),1155-1158.
  • ([20] Choi, M.S. Free Vibration Analysis of Plate Structures Using Finite Element Transfer Stiffness Coefficient Method. J. Mech. Sci. Tech., 17(2003), No. (6), 805-815.
  • [21] RUI, X., WANG, G., LU, Y. Transfer Matrix Method for Linear Multibody System. Multibody Syst. Dyn. 19(2008), No.3,179-207.
  • [22] Rong, B., Rui, X.T., Wang, G.P. Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures. J. Appl. Mech., ASCE, 78(2011), No.2, 021016.
  • [23] He, B., Rui, X., Zhang, H. Transfer Matrix Method for Natural Vibration Analysis of Tree System. Math. Prob. Eng, Article ID 393204, 19 pages, 2012.
  • [24] Ozturk, D., Bozdogan, K., Nuhoglu, A. Modified Finite Element-Transfer Matrix Method for The Static Analysis of Structures. Struct. Eng. Mech., 43(2012), No.6, 761-769.
  • [25] Ozturk, D., Bozdogan, K. B. A Method for Determination of the Fundamental Period of Layered Soil Profiles. J Appl.Comp.Mech.3(2017),No.4,267-273.
  • [26] Demirkan, E.,Artan R.Buckling Analysis of Nanobeams Based on Nonlocal Timoshenko Beam Model by the Method of Initial Values, Int J Struct Stab Dy, 19(2019), No.3, 17 p.
  • [27] Xu, P., Jiang, G. Calculation of Natural Frequencies of Retaining Walls Using the Transfer Matrix Method. Adv. Civ Eng.(2019), Article ID 2156475, 8 pages.
  • [28] Kang, S.,Nanfang, J., Han, K., Shen, X., Wang, W. Theoretical modelling of periodic graphene structures. Physica B Condens Matter.563 (2019), No.15,36-40.
  • [29] Reddy, J.N. An Introduction to The Fınite Element Method,3, McGraw-Hill, New York, 2005.
  • [30] Abaqus, Dassault Systemes Simulia Corp, Providence (2014)
Year 2019, Volume: 5 Issue: 1, 15 - 28, 30.06.2019
https://doi.org/10.34186/klujes.564004

Abstract

References

  • [1] Holzer, H. Analysis of Torsional Vibration, Springer, Berlin, 1921.
  • [2] Myklestad, N.O. New Method of Calculating Natural Modes of Coupled Bending-Torsion Vibration of Beams. Trans. ASME., 61-67.
  • [3] Thompson, W. T. Matrix Solution for The Vibration of Non-Uniform Beams. J. App. Mech .17(1950), 337–339.
  • [4] Thompson, W. T. Transmission of Elastic Waves Through a Stratified Solid Media, J. Appl. Phys. 21(1950),89-93
  • [5] Haskel, N.A. The Dispersion of Surface Waves on Multilayered Media. Bull. seism. Soc. Am. 43 (1953),17-34.
  • [6] Pestel, E.C., Leckie, F. A. Matrix Methods in Elastomechanics. New York: McGraw-Hill,1963.
  • [7] İnan, M. The Method of Initial Values and the Carry-over Matrix in Elastomechanics, Middle East Technical University,1968.
  • [8] Hoerner, G.C. The Rıccati Transfer Matrix Method. Ph.D. Thesis, University of virginia, Charlottesvile, VA.,1975.
  • [9] Dokanish, M.A. A New Approach for Plate Vibration: Combination of Transfer Matrix and Finite Element Technique. Trans. ASME J. Eng. Ind. 94(1972), 526-530.
  • [10] Mcdaniel, T. J., Eversole, K. B. A Combined Finite Element-Transfer Matrix Structural Analysis Method.J. Sound Vibr. 51(1977), 157-169.
  • [11] Ghiatti, G., Sestieri, A. Analysis of Static and Dynamic Structural Problems by a Combined Finite Element-Transfer Matrix Method. J. Sound Vibr. 67 (1979),35-42.
  • [12] Ohga, M., Shigematsu, T., Hara, T. (1984) A Combined Finite Element-Transfer Matrix Method. J. Engng Mech.Div., Am. Sot. Ciu. Engrs 110(1984), 1335-1349.
  • [13] Degen, E.E., Shepbhard, M.S., Loewy, R.G. Combined Finite Element-Transfer Matrix Method Based on a Finite Mixed Formulation. Comput. Struct., 20(1985), 173-180.
  • [14] Chen, Y. H., Xue, H. Y. Dynamic Large Deflection Analysis of Structures by a Combined Finite Element Riccati Transfer Matrix Method on a Microcomputer. Comput. Struct. 39(1991), No 6., 699–703.
  • [15] Xue, H.Y. A Combined Dynamic Finite Element-Ricatti Transfer Matrix Method for Solving Non-Linear Eigenproblems of Vibrations. Comp. Struct., 53(1994), No.6, 1257-1261.
  • [16] Yuhua, C. Large Deflection Analysis of Structures by an Improved Combined Finite Element-Transfer Matrix Method. Comput Struct 55(1995), 167–171.
  • [17] Bhutani, N., Loewy, R.G. Combined Finite Element-Transfer Matrix Method. J. Sound Vib., 226 (1999), No.5,1048-1052.
  • [18] Alimonti, L.,Atalla,N.,Sgard,F. Assessment of a hybrid finite element-transfer matrix model for flat structures with homogeneous acoustic treatments. J Acoust Soc Am.135(2014), No.5,2694-2705.
  • [19] Fan ,S.,Barber,J.R. Solution of Periodic Heating Problems by the Transfer Matrix Method.Heat and Mass Trans. 45(2002),1155-1158.
  • ([20] Choi, M.S. Free Vibration Analysis of Plate Structures Using Finite Element Transfer Stiffness Coefficient Method. J. Mech. Sci. Tech., 17(2003), No. (6), 805-815.
  • [21] RUI, X., WANG, G., LU, Y. Transfer Matrix Method for Linear Multibody System. Multibody Syst. Dyn. 19(2008), No.3,179-207.
  • [22] Rong, B., Rui, X.T., Wang, G.P. Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures. J. Appl. Mech., ASCE, 78(2011), No.2, 021016.
  • [23] He, B., Rui, X., Zhang, H. Transfer Matrix Method for Natural Vibration Analysis of Tree System. Math. Prob. Eng, Article ID 393204, 19 pages, 2012.
  • [24] Ozturk, D., Bozdogan, K., Nuhoglu, A. Modified Finite Element-Transfer Matrix Method for The Static Analysis of Structures. Struct. Eng. Mech., 43(2012), No.6, 761-769.
  • [25] Ozturk, D., Bozdogan, K. B. A Method for Determination of the Fundamental Period of Layered Soil Profiles. J Appl.Comp.Mech.3(2017),No.4,267-273.
  • [26] Demirkan, E.,Artan R.Buckling Analysis of Nanobeams Based on Nonlocal Timoshenko Beam Model by the Method of Initial Values, Int J Struct Stab Dy, 19(2019), No.3, 17 p.
  • [27] Xu, P., Jiang, G. Calculation of Natural Frequencies of Retaining Walls Using the Transfer Matrix Method. Adv. Civ Eng.(2019), Article ID 2156475, 8 pages.
  • [28] Kang, S.,Nanfang, J., Han, K., Shen, X., Wang, W. Theoretical modelling of periodic graphene structures. Physica B Condens Matter.563 (2019), No.15,36-40.
  • [29] Reddy, J.N. An Introduction to The Fınite Element Method,3, McGraw-Hill, New York, 2005.
  • [30] Abaqus, Dassault Systemes Simulia Corp, Providence (2014)
There are 30 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Issue
Authors

Kanat Burak Bozdoğan 0000-0001-7528-2418

Farshid Khosravı Malekı This is me 0000-0002-8866-114X

Publication Date June 30, 2019
Published in Issue Year 2019 Volume: 5 Issue: 1

Cite

APA Bozdoğan, K. B., & Khosravı Malekı, F. (2019). AN APPLICATION OF THE MODIFIED FINITE ELEMENT TRANSFER MATRIX METHOD FOR A HEAT TRANSFER PROBLEM. Kirklareli University Journal of Engineering and Science, 5(1), 15-28. https://doi.org/10.34186/klujes.564004