Spline finite strip analysis of the buckling and vibration of rectangular composite laminated plates

Abstract A spline finite strip capability is presented for predicting the buckling stresses and natural frequencies of rectangular laminated plates. The plates may have arbitrary lay-ups and general boundary conditions. The spline finite strip method is first developed in the context of first-order shear deformation plate theory and then, by reduction, the method is also developed in the context of classical plate theory. In both approaches the superstrip concept is incorporated into the solution procedure. A considerable range of types of application is described and it is demonstrated that the spline finite strip method is versatile, with good convergence characteristics and accuracy. In these applications, frequent comparison is made with the results of other approaches which comprise a spline Rayleigh-Ritz method, a finite element method, an analytical Rayleigh-Ritz method and a semi-analytical finite strip method.

[1]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[2]  J. Whitney,et al.  Shear Correction Factors for Orthotropic Laminates Under Static Load , 1973 .

[3]  J. E. Harding,et al.  Aspects of the analysis of plate structures: Edited by D. J. Dawe, R. W. Horsington, A. G. Kamtekar and G. H. Little. 1985. Oxford University Press, Oxford. 323 pp. Price: £45·00 hardback. (ISBN 0 19 856168 7) , 1986 .

[4]  E. Hinton,et al.  A thick finite strip solution for static, free vibration and stability problems , 1976 .

[5]  D. J. Dawe,et al.  Flexural vibration of symmetrically laminated composite rectangular plates including transverse shear effects , 1986 .

[6]  Y. K. Cheung,et al.  Flexural free vibrations of rectangular plates with complex support conditions , 1984 .

[7]  I. H. Marshall,et al.  Composite Structures 4 , 1987 .

[8]  D. Dawe,et al.  Vibration of shear-deformable rectangular plates using a spline-function Rayleigh-Ritz approach , 1993 .

[9]  Ashwini Kumar,et al.  Buckling of antisymmetric angle- and cross-ply rectangular plates under shear and compression , 1991 .

[10]  P. M. Prenter Splines and variational methods , 1975 .

[11]  Heinz Antes Bicubic fundamental splines in plate bending , 1974 .

[12]  D. J. Dawe,et al.  Buckling and vibration of finite-length composite prismatic plate structures with diaphragm ends, Part II: computer programs and buckling application , 1990 .

[13]  S. Timoshenko Theory of Elastic Stability , 1936 .

[14]  J. Ashton,et al.  Analysis of Anisotropic Plates II , 1969 .

[15]  Gregory J. Hancock,et al.  Buckling of thin flat-walled structures by a spline finite strip method , 1986 .

[16]  D. Dawe,et al.  The Influence of Shear Deformation on the Natural Frequencies of Laminated Rectangular Plates , 1985 .

[17]  D. J. Dawe,et al.  Finite strip models for vibration of mindlin plates , 1978 .

[18]  Y. K. Cheung,et al.  FINITE STRIP METHOD IN STRUCTURAL ANALYSIS , 1976 .

[19]  D. J. Dawe,et al.  A buckling analysis capability for use in the design of composite prismatic plate structures , 1990 .

[20]  F. W. Williams,et al.  A GENERAL ALGORITHM FOR COMPUTING NATURAL FREQUENCIES OF ELASTIC STRUCTURES , 1971 .

[21]  D. J. Dawe,et al.  Free vibration of generally-laminated, shear-deformable, composite rectangular plates using a spline Rayleigh-Ritz method , 1993 .

[22]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[23]  Shen Pengcheng,et al.  Static, vibration and stability analysis of stiffened plates using B spline functions , 1987 .

[24]  D. J. Dawe,et al.  Buckling and vibration of finite-length composite prismatic plate structures with diaphragm ends, part I: finite strip formulation , 1989 .

[25]  Tomisaku Mizusawa,et al.  Vibration of stiffened skew plates by using B-spline functions , 1979 .

[26]  Tomisaku Mizusawa,et al.  Buckling of skew plate structures using B‐spline functions , 1980 .

[27]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

[28]  D. J. Dawe,et al.  Vibration of shear-deformable beams using a spline-function approach , 1992 .

[29]  I. H. Marshall Composite structures 3 , 1985 .

[30]  D. Dawe,et al.  The vibration and stability of symmetrically-laminated composite rectangular plates subjected to in-plane stresses , 1986 .

[31]  D. J. Dawe,et al.  Non-linear analysis of rectangular laminates under end shortening, using shear deformation plate theory , 1993 .

[32]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[33]  Y. K. Cheung,et al.  STATIC ANALYSIS OF RIGHT BOX GIRDER BRIDGES BY SPLINE FINITE STRIP METHOD , 1983 .

[34]  D. Dawe,et al.  Buckling of rectangular mindlin plates , 1982 .

[35]  T. A. Weisshaar,et al.  Optimum design of composite structures , 1989 .

[36]  J. L. Walsh,et al.  The theory of splines and their applications , 1969 .

[37]  D. J. Dawe,et al.  Vibration analysis of rectangular mindlin plates by the finite strip method , 1980 .

[38]  J. Whitney Structural Analysis of Laminated Anisotropic Plates , 1987 .

[39]  D. Dawe,et al.  The Use of Spline Functions in Calculating the Natural Frequencies of Anisotropic Rectangular Laminates , 1987 .

[40]  E. Reissner The effect of transverse shear deformation on the bending of elastic plates , 1945 .