Abstract
In order to avoid using C1 interpolation functions in finite element implementation of the previous zig–zag theories, artificial constraints, in which the first derivatives of transverse displacement will be replaced by the assumed variables, are usually employed. However, such assumption will violate continuity conditions of transverse shear stresses at interfaces. Differing from previous work, this paper will propose a C0-type zig–zag theory for buckling analysis of laminated composite and sandwich plates with general configurations. The first derivatives of transverse displacement have been taken out from a displacement field of the proposed zig–zag theory. Thus, the C0 interpolation functions are only required in finite element implementations of the proposed model. Without use of any artificial constraints, an eight-node quadrilateral element based on the proposed model is presented by incorporating the terms associated with the geometric stiffness matrix. In order to verify performance of the proposed model, several buckling problems of sandwich plates with soft core have been analyzed. Numerical results show that the proposed model is able to predict accurately buckling loads of the soft-core sandwich plates with varying fiber orientations of face sheets.
Similar content being viewed by others
References
Hu H.T., Tzeng W.L.: Buckling analysis of skew laminate plates subjected to uniaxial in-plane loads. Thin-Walled Struct. 38, 53–77 (2000)
Hwang S.F., Liu G.H.: Buckling behavior of composite laminates with multiple delaminations under uniaxial compression. Compos. Struct. 53, 235–243 (2001)
Aslan Z., Sahin M.: Buckling behavior and compressive failure of composite laminates containing multiple large delaminations. Compos. Struct. 89, 382–390 (2009)
Wang S.: Buckling analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory. Compos. Struct. 37, 5–19 (1997)
Kyoung W.M., Kim C.G., Hong C.S.: Buckling and postbuckling behavior of composite cross-ply laminates with multiple delaminations. Compos. Struct. 43, 257–274 (1999)
Kabir H.R.H., Askar H., Chaudhuri R.A.: Thermal buckling response of shear flexible laminated anisotropic plates using a three-node isoparametric element. Compos. Struct. 59, 173–187 (2003)
Sahin O.S.: Thermal buckling of hybrid angle-ply laminated composite plates with a hole. Compos. Sci. Technol. 65, 1780–1790 (2005)
Reddy J.N., Phan N.D.: Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J. Sound Vib. 98, 157–170 (1985)
Frostig Y.: Buckling of sandwich panels with a flexible core-Higher-order theory. Int. J. Solids Struct. 35, 183–204 (1998)
Babu C.S., Kant T.: Two shear deformable finite element models for buckling analysis of skew fibre-reinforced composite and sandwich panels. Compos. Struct. 46, 115–124 (1999)
Kant T., Babu C.S.: Thermal buckling analysis of skew fibre-reinforced composite and sandwich plates using shear deformable finite element models. Compos. Struct. 49, 77–85 (2000)
Dawe D.J., Yuan W.X.: Overall and local buckling of sandwich plates with laminated faceplates, part I: analysis. Comput. Methods Appl. Mech. Eng. 190, 5197–5213 (2001)
Zou G.P., Lam S.S.E.: Buckling analysis of composite laminates under end shortening by higher-order shear deformable finite strips. Int. J. Numer. Methods Eng. 55, 1239–1254 (2002)
Reddy J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51, 745–752 (1984)
Nayak A.K., Moy S.S.J., Shenoi R.A.: A higher order finite element theory for buckling and vibration analysis of initially stressed composite sandwich plates. J. Sound Vib. 286, 763–780 (2005)
Kharazi M., Ovesy H.R., Taghizadeh M.: Buckling of the composite laminates containing through-the-width delaminations using different plate theories. Compos. Struct. 92, 1176–1183 (2010)
Matsunaga H.: Buckling instabilities of thick elastic plates subjected to in-plane stresses. Comput. Struct. 62, 205–214 (1997)
Matsunaga H.: Vibration and stability of cross-ply laminated composite plates according to a global higher order plate theory. Compos. Struct. 48, 231–244 (2000)
Matsunaga H.: Vibration and buckling of multilayered composite beams according to higher order deformation theories.. J. Sound. Vib. 246, 47–62 (2001)
Matsunaga H.: Vibration and stability of cross-ply laminated composite shallow shells subjected to in-plane stresses. Compos. Struct. 78, 377–391 (2007)
Matsunaga H.: Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory. Compos. Struct. 68, 439–454 (2005)
Matsunaga H.: Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory. Compos. Struct. 72, 177–192 (2006)
Matsunaga H.: Thermal buckling of cross-ply laminated composite shallow shells according to a global higher-order deformation theory. Compos. Struct. 81, 210–221 (2007)
Dafedar J.B., Desai Y.M., Mufti A.A.: Stability of sandwich plates by mixed, higher-order analytical formulation. Int. J. Solids Struct. 40, 4501–4517 (2003)
Kant T., Swaminathan K.: Analytical solutions using a higher order refined theory for the stability analysis of laminated composite and sandwich plates. Struct. Eng. Mech. 10, 337–357 (2000)
Wu Z., Chen W.J.: An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams. Compos. Struct. 84, 337–349 (2008)
Cho M., Kim J.S.: Higher-order zig–zag theory for laminated composite with multiple delaminations. J. Appl. Mech. 68, 869–877 (2001)
Kim J.S., Cho M.: Buckling analysis for delaminated composite using plate bending elements based on higher-order zig–zag theory. Int. J. Numer. Methods Eng. 55, 1323–1343 (2002)
Kapuria S., Dumir P.C., Jain N.K.: Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams. Compos. Struct. 64, 317–327 (2004)
Pandit M.K., Singh B.N., Sheikh A.H.: Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory.. Thin-Walled Struct. 46, 1183–1191 (2008)
Batoz J.L., Tahar M.B.: Evaluation of a new quadrilateral thin plate bending element. Int. J. Numer. Methods Eng. 18, 1655–1677 (1982)
Khandelwal R.P., Chakrabarti A., Bhargava P.: An efficient FE model and Least Square Error method for accurate calculation of transverse shear stresses in composites and sandwich laminates. Compos. Part B 43, 1695–1704 (2012)
Dafedar J.B., Desai Y.M.: Stability of composite and sandwich struts by mixed formulation. J. Eng. Mech. 130, 762–770 (2004)
Yuan W.X., Dawe D.J.: Overall and local buckling of sandwich plates with laminated faceplates, part II: applications. Comput. Methods Appl. Mech. Eng. 190, 5215–5231 (2001)
Khatua T.P., Cheung Y.K.: Stability analysis of multilayer sandwich plates. AIAA J. 11, 1233–1234 (1973)
Chen W.J., Wu Z.: A selective review on recent development of displacement-based laminated plate theories.. Recent Patents Mech. Eng. 1, 29–44 (2008)
Kant T., Patil H.S.: Buckling loads of sandwich columns with a higher-order theory. J. Reinf. Plast. Compos. 10, 102–109 (1991)
Kant T., Swaminathan K.: Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Compos. Struct. 56, 329–344 (2002)
Rao K.M.: Buckling analysis of anisotropic sandwich plates faced with fibre-reinforced plastics. AIAA J. 23, 1247–1253 (1985)
Kim C.G., Hong C.S.: Buckling of unbalanced anisotropic sandwich plates with finite bonding stiffness. AIAA J. 26, 982–988 (1988)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xiaohui, R., Zhen, W. Buckling of soft-core sandwich plates with angle-ply face sheets by means of a C0 finite element formulation. Arch Appl Mech 84, 1173–1188 (2014). https://doi.org/10.1007/s00419-014-0876-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-014-0876-4