Abstract
The buckling and large deflection behaviors of axis-symmetric radially functionally graded (RFG) ring-stiffened circular plates are investigated by the dynamic relaxation (DR) method combined with the finite difference discretization technique. The material properties of the constituent components of the RFG plate are assumed to vary continuously according to the Mori-Tanaka distribution along the radial direction. The nonlinear governing equations are obtained in the incremental form based on the first-order shear deformation plate theory (FSDT) and the von Karman relations for large deflection. In the buckling analysis, an external in-plane load is applied to the plate incrementally so that, in each load-step, the incremental form of the governing equations can be solved by a numerical code prepared based on the DR method. After converging the DR code in the first increment, the latter load-step is added to the previous one, and the program is repeated again. The critical buckling load is determined from the compressive load-displacement curve obtained by solving the incremental form of the governing equa- tions. Based on the present incremental form of formulation, a bending analysis can also be conducted if the whole load is applied simultaneously. Finally, a detailed parametric study is carried out to investigate the influences of various boundary conditions, grading indices, thickness-to-radius ratios, stiffener’s positions and depths on the critical buckling load, and displacements and stresses resulted from the bending analysis. It is observed that the effect of the stiffener on the results is much greater in the functionally graded plate with higher material grading indices. The results also reveal that, by increasing the depth of the stiffer, the values of ascending the critical buckling load are approximately identical for both simply supported and clamped boundary conditions.
Similar content being viewed by others
References
Turvey, G. J. and Salehi, M. Elasto-plastic large deflection response of pressure loaded circular plates stiffened by a single diametral stiffener. Thin-Walled Structures, 46, 991–1002 (2008)
Nosier, A. and Fallah, F. Non-linear analysis of functionally graded circular plates under asymmetric transverse loading. International Journal of Non-Linear Mechanics, 44, 928–942 (2009)
Najafizadeh, M. M. and Eslami, M. R. Buckling analysis of circular plates of functionally graded materials under uniform radial compression. International Journal of Mechanical Sciences, 4, 2479–2493 (2002)
Prakash, T., Singha, M. K., and Ganapathi, M. Thermal postbuckling analysis of FGM skew plates. Engineering Structures, 30, 22–32 (2008)
Golmakani, M. E. and Kadkhodayan, M. Large deflection analysis of circular and annular FGM plates under thermo-mechanical loadings with temperature-dependent properties. Composites Part B: Engineering, 42, 614–625 (2011)
Golmakani, M. E. and Kadkhodayan, M. Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate theories. Computers and Structures, 93, 973–982 (2011)
Ma, L. S. and Wang, T. J. Relationship between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classicalplate theory. International Journal of Solids and Structures, 41, 85–101 (2004)
Ma, L. S. and Wang, T. J. Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings. International Journal of Solids and Structures, 40, 3311–3330 (2003)
Saidi, A. R., Rasouli, A., and Sahraee, S. Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory. Computers and Structures, 89, 110–119 (2009)
Bayat, M., Saleem, M., Sahari, B. B., Hamouda, A. M. S., and Mahdi, E. Thermo elastic analysis of a functionally graded rotating disk with small and large deflections. Thin-Walled Structures, 45, 677–691 (2007)
Golmakani, M. E. Large deflection thermo elastic analysis of shear deformable functionally gradedvariable thickness rotating disk. Composites Part B: Engineering, 45, 1143–1155 (2013)
Bayat, M., Sahari, B. B., Saleem, M., Ali, A., and Wong, S. V. Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory. Applied Mathematical Modelling, 33, 4215–4230 (2009)
Mousavi, S. M. and Tahani, M. Analytical solution for bending of moderately thick radially functionally graded sector plates with general boundary conditions using multi-term extended Kantorovich method. Composites Part B: Engineering, 43, 1405–1416 (2011)
Hosseini-Hashemi, S. H, Akhavan, H., Rokni-Damavandi-Taher, H., Daemi, D., and Alibeigloo, A. Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation. Material Design, 31, 1871–1880 (2010)
Hosseini-Hashemi, S. H., Rokni-Damavandi-Taher, H., and Akhavan, H. Vibration analysis of radially FGM sectorial plates of variable thickness on elasticfoundations. Computers and Structures, 92, 1734–1743 (2010)
Sepahi, O., Forouzan, M. R., and Malekzadeh, P. Thermal buckling and postbuckling analysis of functionally graded annular plates with temperature-dependent material properties. Material Design, 32, 4030–4041 (2011)
Golmakani, M. E. and Alamatian, J. Large defection analysis of shear deformable radially functionally graded sector plates on two-parameter elastic foundations. European Journal of Mechanics, Series A, Solids, 42, 251–265 (2013)
Turvey, G. J. and Salehi, M. Circular plates with one diametral stiffener an elastic large deflection analysis. Computers and Structures, 63, 775–783 (1997)
Turvey, G. J. Axisymmetric elastic large deflection behavior of stiffened composite plates. Computers and Structures, 6, 72–88 (1983)
Turvey, G. J. and Der Avanessian, N. G. V. Elastic large deflection analysis of ring-stiffened circular plates using graded finite differences. Proceedings of the NUMETA 85 Conference, Swansea, 875–884 (1985)
Turvey, G. J. and Der Avanessian, N. G. V. Axisymmetric elasto-plastic large deflection response of ring stiffened circular plates. International Journal of Mechanical Sciences, 31, 905–924 (1989)
Golmakani, M. E. Nonlinear bending analysis of ring-stiffened functionally graded circular plates under mechanical and thermal loadings. International Journal of Mechanical Sciences, 79, 130–142 (2014)
Golmakani, M. E. and Mehrabian, M. Nonlinear bending analysis of ring-stiffened circular and annular general angle-ply laminated plates with various boundary conditions. Mechanics Research Communications, 59, 42–50 (2014)
Shen, H. S. Nonlinear thermal bending response of FGM plates due to heat conduction. Composites Part B: Engineering, 38, 201–215 (2007)
Yang, J. and Shen, H. S. Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions. Composites Part B: Engineering, 34, 103–115 (2003)
Klusemann, B. and Svendsen, B. Homogenization methods for multi-phase elastic composites: comparisons and benchmarks. Technische Mechanik, 30, 374–386 (2010)
Prakash, T., Singha, M. K., and Ganapathi, M. Thermal postbuckling analysis of FGM skew plates. Engineering Structures, 30, 22–32 (2008)
Mori, T. and Tanaka, K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21, 571–574 (1973)
Asthana, R. and Singh, M. Evaluation of Pd-based brazes to join silicon nitride to copper-clad-molybdenum. Ceramics International, 35, 3511–3515 (2009)
He, P., Feng, J. C., and Xu, W. Microstructure and kinetics of induction brazing TiAl-based intermetallics to steel 35CrMo using AgCuTi filler metal. Materials Science and Engineering, 418, 53–60 (2006)
Walker, C. A. and Hodges, V. C. Comparing metal-ceramic brazing methods. Welding Journal, 87, 43–50 (2008)
Kadkhodayan, M., Zhang, L. C., and Sowerby, R. Analysis of wrinkling and buckling of elastic plates by DXDR method. Computers and Structures, 65, 561–574 (1997)
Turvey, G. J. and Salehi, M. Elasto-plastic large deflection response of pressure loaded circular plates stiffened by a single diametral stiffener. Thin-Walled Structures, 46, 991–1002 (2008)
Kirk, C. L. Vibration of centrally placed stiffened rectangular plates. Journal of the Royal Aeronautical Society, 65, 695–697 (1961)
Loughlan, J. The buckling performance of composite stiffened panel structures subjected to combined in-plane compression and shear loading. Computers and Structures, 29, 197–212 (1994)
Palani, G. S., Iyer, N. R., and Appa-Rao, T. V. S. R. An efficient finite element model for static and vibration analysis of eccentrically stiffened plates/shells. Computers and Structures, 43, 651–661 (1992)
Wah, T. Vibration of stiffened plates. Aero Quarterly, 15, 285–298 (1964)
Otter, J. R. H., Cassell, A. C., and Hobbs, R. E. Dynamic relaxation. Proceedings of the Institution of Civil Engineers, 35, 633–656 (1966)
Day, A. S. An introduction to dynamic relaxation. The Engineer, 219, 218–221 (1965)
Underwood, P. Dynamic Relaxation, in Computational Methods for Transient Analysis, Elsevier, Amsterdam (1983)
Zhang, L. C., Kadkhodayan, M., and Mai, Y. W. Development of the maDR method. Computers and Structures, 52, 1–8 (1994)
Zhang, L. C. and Yu, T. X. Modified adaptive dynamic relaxation method and application to elastic-plastic bending and wrinkling of circular plate. Computers and Structures, 33, 609–614 (1989)
Golmakani, M. E. and Kadkhodayan, M. Large deflection thermoelastic analysis of functionally graded stiffened annular sector plates. International Journal of Mechanical Sciences, 69, 94–106 (2013)
Kobayashi, H. and Turvey, G. J. On the application of a limiting process to the dynamic relaxation analysis of circular membranes, circular plates and spherical shells. Computers and Structures, 48, 1107–1116 (1993)
Jawad, M. H. Theory and Design of Plate and Shell Structures, Chapman & Hall, New York (1994)
Reddy, J. N., Wang, C. M., and Kitipornchai, S. Axisymmetric bending of functionally graded circular and annular plates. European Journal of Mechanics, Series A, Solids, 18, 185–199 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Golmakani, M.E., Emami, M. Buckling and large deflection behaviors of radially functionally graded ring-stiffened circular plates with various boundary conditions. Appl. Math. Mech.-Engl. Ed. 37, 1131–1152 (2016). https://doi.org/10.1007/s10483-016-2122-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-016-2122-6