Year 2025,
Volume: 13 Issue: 2, 510 - 523, 01.06.2025
Osman Ayaz
,
Ahmad Reshad Noorı
,
Burkay Sivri
,
Beytullah Temel
References
-
P. E. Grafton and D. R. Strome, “Analysis of axisymmetrical shells by the direct stiffness method,” AIAA Journal, vol. 1, no. 10, pp. 2342–2347, 1963, doi: 10.2514/3.2064.
-
Garnet, H and J. Kempner, “Axisymmetric Free Vibrations of Conical Shells,” AIAA Journal, vol. 2, no. 3, pp. 458–466, 1964.
-
D. A. Godfrey and M. M. Moussa, “Dynamic analysis of axisymmetric shells under arbitrary transient pressures,” Nuclear Engineering and Design, vol. 23, no. 2, pp. 187–194, 1972.
-
A. Tessler, “An efficient, conforming axisymmetric shell element including transverse shear and rotary inertia,” Computers & Structures, vol. 15, no. 5, pp. 567–574, 1982.
-
B. Suarez, M. Canet, and E. Onate, “Free vibration analysis of plates, bridges and axisymmetric shells using a thick finite strip method,” Engineering Computations, vol. 5, no. 3, pp. 123–130, 1988, doi: 10.1108/eb023734
-
A. F. Loula, I. Miranda, T. J. Hughes, and L. P. Franca, “On mixed finite element methods for axisymmetric shell analysis,” Computer Methods Appl. Mech. Eng., vol. 72, no. 2, pp. 201–231, 1989.
-
D. P. Thambiratnam, “A simple finite element analysis of hyperboloidal shell structures,” Computers & Structures, vol. 48, no. 2, pp. 249–254, Jul. 1993, doi: 10.1016/0045-7949(93)90417-C.
-
D. P. Thambiratnam and V. Thevendran, “Axisymmetric free vibration analysis of cylindrical shell structures using BEF analogy,” Computers & Structures, vol. 43, no. 1, pp. 145–150, 1992.
-
D. P. Thambiratnam and Y. Zhuge, “Axisymmetric free vibration analysis of conical shells,” Engineering Structure, vol. 15, no. 2, 1993.
-
M. Ozakqa and E. Hinton, “Free vibration analysis and optimisation of axisymmetric plates and shells—I. Finite element formulation,” Computers & Structures, vol. 52, no. 6, pp. 1181–1197, 1994.
-
M. Özakça and E. Hinton, “Free vibration analysis and optimisation of axisymmetric plates and shells—II. Shape optimisation,” Computers & Structures, vol. 52, no. 6, pp. 1199–1211, 1994.
-
A. R. Noori and B. Temel, “Dynamic analysis of axisymmetric shells in the Laplace domain,” in Proc. 1st Int. Mediterranean Science and Engineering Congress (IMSEC), Adana, Turkey, Oct. 2016. [Online]. Available: https://www.researchgate.net/publication/316922251
-
A. Filippidis and A. J. Sadowski, “Modern analysis of axisymmetric shells with AQUINAS: A MATLAB finite element toolbox,” SoftwareX, vol. 23, 101434, 2023.
-
H. Guo and H. Zheng, “The linear analysis of thin shell problems using the numerical manifold method,” Thin-Walled Structures, vol. 124, pp. 366–383, 2018, doi: 10.1016/j.tws.2017.12.027.
-
P. Das, M. A. Islam, S. Somadder, and M. A. Hasib, “Analytical and numerical analysis of functionally graded (FGM) axisymmetric cylinders under thermo-mechanical loadings,” Materials Today: Communications, vol. 33, 104405, 2022, doi: 10.1016/j.mtcomm.2022.104405.
-
Y. V. Tokovyy, “Integration of the equations of plane axisymmetric problems of the theory of elasticity and thermoelasticity for layered solid cylinders,” Journal of Mathematical Sciences, vol. 282, no. 5, pp. 769–779, 2024, doi: 10.1007/s10958-024-07215-9.
-
A. H. Sofiyev, A. Deniz, M. Avcar, P. Özyigit, and M. H. Omurtag, “Effects of the non-homogeneity and elastic medium on the critical torsional load of the orthotropic cylindrical shell,” Acta Physica Polonica A, vol. 123, no. 4, pp. 728–730, 2013, doi: 10.12693/APhysPolA.123.728.
-
F. Gu et al., “Theoretical study on 3D elastic response and first layer failure strength of composite cylinders subjected to axisymmetric loadings,” International Journal of Pressure Vessels and Piping, vol. 210, 105245 , 2024, doi: 10.1016/j.ijpvp.2024.105245.
-
M. H. Samadzadeh, M. Arefi, and A. Loghman, “Static bending analysis of pressurized cylindrical shell made of graphene origami auxetic metamaterials based on higher-order shear deformation theory,” Heliyon, vol. 10, no. 16, 2024, doi: 10.1016/j.heliyon.2024.e36319.
-
I. D. Breslavsky, M. Amabili, and M. Legrand, “Static and dynamic behavior of circular cylindrical shell made of hyperelastic arterial material,” Journal of Applied Mechanics, vol. 83, no. 5, 051002 , 2016, doi: 10.1115/1.4032549.
-
C. U. Nwoji, D. G. Ani, O. A. Oguaghamba, and V. T. Ibeabuchi, “Static bending of isotropic circular cylindrical shells based on the higher order shear deformation theory of Reddy and Liu,” International Journal of Applied Mechanics and Engineering, vol. 26, no. 3, pp. 141–162, 2021, doi: 10.2478/ijame-2021-0041.
-
B. Temel, S. Yildirim, and N. Tutuncu, “Elastic and viscoelastic response of heterogeneous annular structures under arbitrary transient pressure,” International Journal of Mechanical Sciences, vol. 89, pp. 78–83, 2014, doi: 10.1016/j.ijmecsci.2014.08.021.
-
S. Yildirim and N. Tutuncu, “Radial vibration analysis of heterogeneous and non-uniform disks via complementary functions method,” Journal of Strain Analysis for Engineering Design, vol. 53, no. 5, pp. 332–337, 2018, doi: 10.1177/0309324718765006.
-
A. R. Noori and B. Temel, “On the vibration analysis of laminated composite parabolic arches with variable cross-section of various ply stacking sequences,” Mechanics of Advanced Materials and Structures, vol. 27, no. 19, pp. 1658–1672, 2020, doi: 10.1080/15376494.2018.1524949.
-
B. Temel, T. A. Aslan, and A. R. Noori, “In-plane vibration analysis of parabolic arches having a variable thickness,” International Journal of Dynamics and Control, vol. 9, no. 3, pp. 910–921, 2021, doi: 10.1007/s40435-020-00727-7.
-
A. R. Noori, T. A. Aslan, and B. Temel, “Dynamic analysis of functionally graded porous beams using complementary functions method in the Laplace domain,” Composite Structures, vol. 256, 113094, 2021, doi: 10.1016/j.compstruct.2020.113094.
-
B. Temel, T. A. Aslan, and A. R. Noori, “An efficient dynamic analysis of planar arches,” European Mechanical Science, 1(3), 82-88, 2017.
-
T. A. Aslan, A. R. Noori, and B. Temel, “Dynamic response of viscoelastic tapered cycloidal rods,” Mechanics Research Communications, vol. 92, pp. 8–14, 2018, doi: 10.1016/j.mechrescom.2018.06.006.
-
K. Sayar, “Dönel kabuk sistemlerin diferansiyel geçiş matrisleriyle çözümü,” Doçentlik Tezi, 1970.
-
Y. Mengi, Numerical Methods in Engineering, Adana, Turkey: Çukurova University, 1993.
-
S. Chapra and R. Canale, Numerical Methods for Engineers, 7th ed., 2011.
-
Wolfram Research Inc., Mathematica, Wolfram Research, Inc., 2024.
STATIC ANALYSIS OF AXISYMMETRIC THIN CYLINDRICAL SHELL USING THE COMPLEMENTARY FUNCTIONS METHOD
Year 2025,
Volume: 13 Issue: 2, 510 - 523, 01.06.2025
Osman Ayaz
,
Ahmad Reshad Noorı
,
Burkay Sivri
,
Beytullah Temel
Abstract
The analysis of thin cylindrical shells is essential for a wide range of engineering applications, making it critical to understand their static behavior under various loading conditions. In this study, the static analysis of axisymmetric thin cylindrical shells is performed using the Complementary Functions Method (CFM). The research focuses on examining the static behavior of cylindrical shells made of homogeneous, isotropic, and linear elastic materials under various loading conditions. The governing differential equations for the static response of these structural elements are derived based on thin shell theory, utilizing the principle of minimum total potential energy. These equations are solved using CFM, an efficient numerical solution method. In this context, the CFM is coded in Wolfram Mathematica. To validate the accuracy and reliability of the proposed solution method, the results are compared with existing studies in the literature, demonstrating a high degree of consistency and confirming the effectiveness of the method. It has been observed that the type of loading significantly impacts the behavior of the shell.
References
-
P. E. Grafton and D. R. Strome, “Analysis of axisymmetrical shells by the direct stiffness method,” AIAA Journal, vol. 1, no. 10, pp. 2342–2347, 1963, doi: 10.2514/3.2064.
-
Garnet, H and J. Kempner, “Axisymmetric Free Vibrations of Conical Shells,” AIAA Journal, vol. 2, no. 3, pp. 458–466, 1964.
-
D. A. Godfrey and M. M. Moussa, “Dynamic analysis of axisymmetric shells under arbitrary transient pressures,” Nuclear Engineering and Design, vol. 23, no. 2, pp. 187–194, 1972.
-
A. Tessler, “An efficient, conforming axisymmetric shell element including transverse shear and rotary inertia,” Computers & Structures, vol. 15, no. 5, pp. 567–574, 1982.
-
B. Suarez, M. Canet, and E. Onate, “Free vibration analysis of plates, bridges and axisymmetric shells using a thick finite strip method,” Engineering Computations, vol. 5, no. 3, pp. 123–130, 1988, doi: 10.1108/eb023734
-
A. F. Loula, I. Miranda, T. J. Hughes, and L. P. Franca, “On mixed finite element methods for axisymmetric shell analysis,” Computer Methods Appl. Mech. Eng., vol. 72, no. 2, pp. 201–231, 1989.
-
D. P. Thambiratnam, “A simple finite element analysis of hyperboloidal shell structures,” Computers & Structures, vol. 48, no. 2, pp. 249–254, Jul. 1993, doi: 10.1016/0045-7949(93)90417-C.
-
D. P. Thambiratnam and V. Thevendran, “Axisymmetric free vibration analysis of cylindrical shell structures using BEF analogy,” Computers & Structures, vol. 43, no. 1, pp. 145–150, 1992.
-
D. P. Thambiratnam and Y. Zhuge, “Axisymmetric free vibration analysis of conical shells,” Engineering Structure, vol. 15, no. 2, 1993.
-
M. Ozakqa and E. Hinton, “Free vibration analysis and optimisation of axisymmetric plates and shells—I. Finite element formulation,” Computers & Structures, vol. 52, no. 6, pp. 1181–1197, 1994.
-
M. Özakça and E. Hinton, “Free vibration analysis and optimisation of axisymmetric plates and shells—II. Shape optimisation,” Computers & Structures, vol. 52, no. 6, pp. 1199–1211, 1994.
-
A. R. Noori and B. Temel, “Dynamic analysis of axisymmetric shells in the Laplace domain,” in Proc. 1st Int. Mediterranean Science and Engineering Congress (IMSEC), Adana, Turkey, Oct. 2016. [Online]. Available: https://www.researchgate.net/publication/316922251
-
A. Filippidis and A. J. Sadowski, “Modern analysis of axisymmetric shells with AQUINAS: A MATLAB finite element toolbox,” SoftwareX, vol. 23, 101434, 2023.
-
H. Guo and H. Zheng, “The linear analysis of thin shell problems using the numerical manifold method,” Thin-Walled Structures, vol. 124, pp. 366–383, 2018, doi: 10.1016/j.tws.2017.12.027.
-
P. Das, M. A. Islam, S. Somadder, and M. A. Hasib, “Analytical and numerical analysis of functionally graded (FGM) axisymmetric cylinders under thermo-mechanical loadings,” Materials Today: Communications, vol. 33, 104405, 2022, doi: 10.1016/j.mtcomm.2022.104405.
-
Y. V. Tokovyy, “Integration of the equations of plane axisymmetric problems of the theory of elasticity and thermoelasticity for layered solid cylinders,” Journal of Mathematical Sciences, vol. 282, no. 5, pp. 769–779, 2024, doi: 10.1007/s10958-024-07215-9.
-
A. H. Sofiyev, A. Deniz, M. Avcar, P. Özyigit, and M. H. Omurtag, “Effects of the non-homogeneity and elastic medium on the critical torsional load of the orthotropic cylindrical shell,” Acta Physica Polonica A, vol. 123, no. 4, pp. 728–730, 2013, doi: 10.12693/APhysPolA.123.728.
-
F. Gu et al., “Theoretical study on 3D elastic response and first layer failure strength of composite cylinders subjected to axisymmetric loadings,” International Journal of Pressure Vessels and Piping, vol. 210, 105245 , 2024, doi: 10.1016/j.ijpvp.2024.105245.
-
M. H. Samadzadeh, M. Arefi, and A. Loghman, “Static bending analysis of pressurized cylindrical shell made of graphene origami auxetic metamaterials based on higher-order shear deformation theory,” Heliyon, vol. 10, no. 16, 2024, doi: 10.1016/j.heliyon.2024.e36319.
-
I. D. Breslavsky, M. Amabili, and M. Legrand, “Static and dynamic behavior of circular cylindrical shell made of hyperelastic arterial material,” Journal of Applied Mechanics, vol. 83, no. 5, 051002 , 2016, doi: 10.1115/1.4032549.
-
C. U. Nwoji, D. G. Ani, O. A. Oguaghamba, and V. T. Ibeabuchi, “Static bending of isotropic circular cylindrical shells based on the higher order shear deformation theory of Reddy and Liu,” International Journal of Applied Mechanics and Engineering, vol. 26, no. 3, pp. 141–162, 2021, doi: 10.2478/ijame-2021-0041.
-
B. Temel, S. Yildirim, and N. Tutuncu, “Elastic and viscoelastic response of heterogeneous annular structures under arbitrary transient pressure,” International Journal of Mechanical Sciences, vol. 89, pp. 78–83, 2014, doi: 10.1016/j.ijmecsci.2014.08.021.
-
S. Yildirim and N. Tutuncu, “Radial vibration analysis of heterogeneous and non-uniform disks via complementary functions method,” Journal of Strain Analysis for Engineering Design, vol. 53, no. 5, pp. 332–337, 2018, doi: 10.1177/0309324718765006.
-
A. R. Noori and B. Temel, “On the vibration analysis of laminated composite parabolic arches with variable cross-section of various ply stacking sequences,” Mechanics of Advanced Materials and Structures, vol. 27, no. 19, pp. 1658–1672, 2020, doi: 10.1080/15376494.2018.1524949.
-
B. Temel, T. A. Aslan, and A. R. Noori, “In-plane vibration analysis of parabolic arches having a variable thickness,” International Journal of Dynamics and Control, vol. 9, no. 3, pp. 910–921, 2021, doi: 10.1007/s40435-020-00727-7.
-
A. R. Noori, T. A. Aslan, and B. Temel, “Dynamic analysis of functionally graded porous beams using complementary functions method in the Laplace domain,” Composite Structures, vol. 256, 113094, 2021, doi: 10.1016/j.compstruct.2020.113094.
-
B. Temel, T. A. Aslan, and A. R. Noori, “An efficient dynamic analysis of planar arches,” European Mechanical Science, 1(3), 82-88, 2017.
-
T. A. Aslan, A. R. Noori, and B. Temel, “Dynamic response of viscoelastic tapered cycloidal rods,” Mechanics Research Communications, vol. 92, pp. 8–14, 2018, doi: 10.1016/j.mechrescom.2018.06.006.
-
K. Sayar, “Dönel kabuk sistemlerin diferansiyel geçiş matrisleriyle çözümü,” Doçentlik Tezi, 1970.
-
Y. Mengi, Numerical Methods in Engineering, Adana, Turkey: Çukurova University, 1993.
-
S. Chapra and R. Canale, Numerical Methods for Engineers, 7th ed., 2011.
-
Wolfram Research Inc., Mathematica, Wolfram Research, Inc., 2024.