Refined buckling and postbuckling analysis of two-dimensional delaminations—I. analysis and validation☆

Abstract An analytical procedure, based on the Rayleigh-Ritz method and von Karman's nonlinear theory of plates, is developed for computing the buckling loads and the postbuckling solutions of laminated anisotropic elliptical plates. Lengthy algebraic equations governing the expansion coefficients of the displacement functions are generated by a symbolic algorithm. Using polynomial displacement expansions of different orders, postbuckling solutions with increasing accuracy are systematically computed for isotropic and laminated elliptical plates. The deflections, the force and moment resultants and the energy release rates associated with the solutions of various orders arc compared to assess the trend of convergence. The comparison suggests the lowest order polynomial expansion needed to obtain reasonably accurate results for the force and moment resultants and the energy release rates. Previous Rayleigh-Ritz postbuckling solutions based on lower-order polynomial expansions of the displacements are found to yield results with significant errors.

[1]  W. J. Bottega,et al.  A growth law for propagation of arbitrary shaped delaminations in layered plates , 1983 .

[2]  C. Chia.  Nonlinear analysis of plates , 1980 .

[3]  Börje Andersson,et al.  Nonlinear plate theory applied to delamination in composites , 1988 .

[4]  C. D. Babcock,et al.  Two-Dimensional Modelling of Compressive Failure in Delaminated Laminates , 1985 .

[5]  Rakesh K. Kapania,et al.  Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling. , 1989 .

[6]  B. Storȧkers.  NONLINEAR ASPECTS OF DELAMINATION IN STRUCTURAL MEMBERS , 1989 .

[7]  John D. Whitcomb,et al.  Buckling of a Sublaminate in a Quasi-Isotropic Composite Laminate , 1985 .

[8]  Amar C. Garg,et al.  Delamination—a damage mode in composite structures , 1988 .

[9]  S. N. Sallam,et al.  Ultimate axial load capacity of a delaminated beam-plate , 1986 .

[10]  Yin Wan-Lee,et al.  Axisymmetric buckling and growth of a circular delamination in a compressed laminate , 1985 .

[11]  W. Knauss,et al.  One dimensional modelling of failure in laminated plates by delamination buckling , 1981 .

[12]  S. Bodner.  The post buckling behavior of a clamped circular plate , 1955 .

[13]  M. Feng,et al.  An energy theory for postbuckling of composite plates under combined loading , 1983 .

[14]  Wolfgang G. Knauss,et al.  Observation of damage growth in compressively loaded laminates , 1983 .

[15]  W.-L. Yin,et al.  The energy-release rate in the growth of a one-dimensional delamination , 1984 .

[16]  K. Friedrichs,et al.  The Non-Linear Boundary Value Problem of the Buckled Plate. , 1939, Proceedings of the National Academy of Sciences of the United States of America.