Structural Analysis of Stiffened FGM Thick Walled Cylinders by Application of a New Cylindrical Super Element
Structural behavior of ring stiffened thick walled
cylinders made of functionally graded materials (FGMs) is
investigated in this paper. Functionally graded materials are inhomogeneous composites which are usually made from a mixture
of metal and ceramic. The gradient compositional variation of the
constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are
induced when two dissimilar materials with large differences in material properties are bonded. FGM formation of the cylinder is
modeled by power-law exponent and the variation of characteristics is supposed to be in radial direction.
A finite element formulation is derived for the analysis. According to the property variation of the constituent materials in the radial
direction of the wall, it is not convenient to use conventional elements to model and analyze the structure of the stiffened FGM
cylinders. In this paper a new cylindrical super-element is used to model the finite element formulation and analyze the static and
modal behavior of stiffened FGM thick walled cylinders. By using
this super-element the number of elements, which are needed for
modeling, will reduce significantly and the process time is less in comparison with conventional finite element formulations. Results for static and modal analysis are evaluated and verified by
comparison to finite element formulation with conventional
elements. Comparison indicates a good conformity between results.
[1] M. Koizumi, "The concept of FGM", Ceramic Trans., Functionally Gradient Materials, 1993, 34, pp 3-10.
[2] M. Yamanouchi, M. Koizumi, T. Hirai, I. Shiota, "Proceeding of the first
international symposium on functionally gradient materials", Japan,
1990.
[3] C.T. Loy, K.Y. Larn, J.N. Reddy, "Vibration of functionally graded
cylindrical shells", Int. Journal of Mechanical Science,1999 , vol. 41 , pp 309-324.
[4] S.C. Pradhan, C.T. Loy, K.Y. Lam, J. N. Reddy, "Vibration of functionally graded cylindrical shells under various boundary
conditions" Applied Acoustics, 2000, vol. 61 , pp. 111-129.
[5] ChenW.Q. Chen, Z .G. Bian, H.J. Ding, "Three-dimensional vibration
analysis of a fluid-filled orthotropic FGM cylinder shells ", Int. Journal
of Mechanical Sciences, 2004, vol. 46 , pp 159-171.
[6] W.H. Hoppmann, "Some characteristics of the flexural vibrations of orthogonally stiffened cylindrical shells", J. of Acoustical Society of
America, 1958, vol. 30 , pp 77-82.
[7] M.M. Mikulas, J.A. McElman, "On the free vibration of eccentrically
stiffened cylindrical shells and plates", NASA TN-D 3010, 1965.
[8] D.M. Egle, J.L. Sewall, "Analysis of free vibration of orthogonally
stiffened cylindrical shells with stiffeners treated as discrete elements", AIAA J., 1968, vol. 6 (3), pp 518-526.
[9] S. Parthan, D.J. Johns, "Effects of in-plane and rotary inertia on the
frequencies of eccentrically stiffened cylindrical shells", AIAAJ., 1970, vol. 8 , pp 253-261.
[10] B. A. J. Mustafa, R. Ali, "An energy method for free vibration analysis
of stiffened circular cylindrical shells", J. Computer & Structures, 1989,
vol. 32(2), pp 335-363.
[11] C.M. Wang, S. Swaddiwudhipong, J. Tian, "Ritz method for vibration
analysis of cylindrical shell with ring stiffeners", J. Eng. Mech., 1997,
vol. 123, pp 134-42.
[12] Moeini, S.A., Rahaeifard, M.T. Ahmadian, M.R. Movahhedy, "Free
vibration analysis of functionally graded cylindrical shells stiffened by
uniformly and non-uniformly distributed ring stiffeners", (Accepted for
publication), In Proc. of IMECE Conf., 2009, to be published.
[13] F. Ju, Y.S. Choo, "Superelement approach to cable passing through
multiple pulleys. International journal of solids and structures", 2005,
vol. 42, pp 3533-3547.
[14] J. Jiang, M.D. Olson, "Nonlinear analysis of orthogonally stiffened
cylindrical shells by a superelement approach", Finite Elements in
Analysis and Design, 1994, vol. 18, pp 99-110.
[15] S.A. Lukasiewics "Geometrical super-elements for elasto-plastic shells
with large deformation " Finite Elements in Analysis and Design, 1987,
vol. 3, pp 199-211.
[16] M.T. Ahmadian, M. Bonakdar, " A new cylindrical element formulation
and its application to structural analysis of laminated hollow cylinders"
Finite Element in Analysis and Design, 2008.
[17] J.N. Reddy, "Theory and analysis of elastic plates", Taylor and Francis,
PA 1999.
[18] S. Suresh, A. Mortensen, "Fundamentals of functionally graded
materials ", Cambridge Publication, London, 1998.
[19] F.L. Satasa, "Applied finite element analysis for engineer", CBS
publishing, Japan, 1986.
[1] M. Koizumi, "The concept of FGM", Ceramic Trans., Functionally Gradient Materials, 1993, 34, pp 3-10.
[2] M. Yamanouchi, M. Koizumi, T. Hirai, I. Shiota, "Proceeding of the first
international symposium on functionally gradient materials", Japan,
1990.
[3] C.T. Loy, K.Y. Larn, J.N. Reddy, "Vibration of functionally graded
cylindrical shells", Int. Journal of Mechanical Science,1999 , vol. 41 , pp 309-324.
[4] S.C. Pradhan, C.T. Loy, K.Y. Lam, J. N. Reddy, "Vibration of functionally graded cylindrical shells under various boundary
conditions" Applied Acoustics, 2000, vol. 61 , pp. 111-129.
[5] ChenW.Q. Chen, Z .G. Bian, H.J. Ding, "Three-dimensional vibration
analysis of a fluid-filled orthotropic FGM cylinder shells ", Int. Journal
of Mechanical Sciences, 2004, vol. 46 , pp 159-171.
[6] W.H. Hoppmann, "Some characteristics of the flexural vibrations of orthogonally stiffened cylindrical shells", J. of Acoustical Society of
America, 1958, vol. 30 , pp 77-82.
[7] M.M. Mikulas, J.A. McElman, "On the free vibration of eccentrically
stiffened cylindrical shells and plates", NASA TN-D 3010, 1965.
[8] D.M. Egle, J.L. Sewall, "Analysis of free vibration of orthogonally
stiffened cylindrical shells with stiffeners treated as discrete elements", AIAA J., 1968, vol. 6 (3), pp 518-526.
[9] S. Parthan, D.J. Johns, "Effects of in-plane and rotary inertia on the
frequencies of eccentrically stiffened cylindrical shells", AIAAJ., 1970, vol. 8 , pp 253-261.
[10] B. A. J. Mustafa, R. Ali, "An energy method for free vibration analysis
of stiffened circular cylindrical shells", J. Computer & Structures, 1989,
vol. 32(2), pp 335-363.
[11] C.M. Wang, S. Swaddiwudhipong, J. Tian, "Ritz method for vibration
analysis of cylindrical shell with ring stiffeners", J. Eng. Mech., 1997,
vol. 123, pp 134-42.
[12] Moeini, S.A., Rahaeifard, M.T. Ahmadian, M.R. Movahhedy, "Free
vibration analysis of functionally graded cylindrical shells stiffened by
uniformly and non-uniformly distributed ring stiffeners", (Accepted for
publication), In Proc. of IMECE Conf., 2009, to be published.
[13] F. Ju, Y.S. Choo, "Superelement approach to cable passing through
multiple pulleys. International journal of solids and structures", 2005,
vol. 42, pp 3533-3547.
[14] J. Jiang, M.D. Olson, "Nonlinear analysis of orthogonally stiffened
cylindrical shells by a superelement approach", Finite Elements in
Analysis and Design, 1994, vol. 18, pp 99-110.
[15] S.A. Lukasiewics "Geometrical super-elements for elasto-plastic shells
with large deformation " Finite Elements in Analysis and Design, 1987,
vol. 3, pp 199-211.
[16] M.T. Ahmadian, M. Bonakdar, " A new cylindrical element formulation
and its application to structural analysis of laminated hollow cylinders"
Finite Element in Analysis and Design, 2008.
[17] J.N. Reddy, "Theory and analysis of elastic plates", Taylor and Francis,
PA 1999.
[18] S. Suresh, A. Mortensen, "Fundamentals of functionally graded
materials ", Cambridge Publication, London, 1998.
[19] F.L. Satasa, "Applied finite element analysis for engineer", CBS
publishing, Japan, 1986.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:49682", author = "S. A. Moeini and M. T.Ahmadian", title = "Structural Analysis of Stiffened FGM Thick Walled Cylinders by Application of a New Cylindrical Super Element", abstract = "Structural behavior of ring stiffened thick walled
cylinders made of functionally graded materials (FGMs) is
investigated in this paper. Functionally graded materials are inhomogeneous composites which are usually made from a mixture
of metal and ceramic. The gradient compositional variation of the
constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are
induced when two dissimilar materials with large differences in material properties are bonded. FGM formation of the cylinder is
modeled by power-law exponent and the variation of characteristics is supposed to be in radial direction.
A finite element formulation is derived for the analysis. According to the property variation of the constituent materials in the radial
direction of the wall, it is not convenient to use conventional elements to model and analyze the structure of the stiffened FGM
cylinders. In this paper a new cylindrical super-element is used to model the finite element formulation and analyze the static and
modal behavior of stiffened FGM thick walled cylinders. By using
this super-element the number of elements, which are needed for
modeling, will reduce significantly and the process time is less in comparison with conventional finite element formulations. Results for static and modal analysis are evaluated and verified by
comparison to finite element formulation with conventional
elements. Comparison indicates a good conformity between results.", keywords = "FGMs, Modal analysis, Static analysis, Stiffened cylinders.", volume = "3", number = "10", pages = "1148-6", }