Use of the finite strip method in predicting the behaviour of composite laminated structures

Abstract A description is given of the use of the finite strip method (FSM) in determining the behaviour of composite laminated, prismatic plate and shell structures, with emphasis placed on relatively recent work conducted at The University of Birmingham. Both the semi-analytical and the spline variants of the method are described, and some attention is also paid to “exact” strips. Consideration is given to analyses conducted in the contexts of first-order shear deformation theory and of classical, or thin, theory. The calculation of buckling stresses and natural frequencies of vibration is discussed in detail for single span structures and then, using the spline finite strip approach with variable knot spacings, for multi-span structures and stepped structures. An account is given of the use of the FSM in predicting the post-buckling response of plate structures to progressive end-shortening strain. Brief description is given of the use of the method in predicting the thermal buckling and the transient response to dynamic loading of flat plates. Finally, the calculation of buckling stresses and natural frequencies of sandwich plate structures is considered, based on the adoption of a three-zone plate theory. Numerous examples of the application of the FSM are included in the paper.

[1]  Mahen Mahendran,et al.  Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method , 1986 .

[2]  D. J. Dawe,et al.  Buckling and vibration of thin laminated composite, prismatic shell structures , 1993 .

[3]  E. Hinton,et al.  STRUCTURAL SHAPE OPTIMIZATION OF VIBRATING SHELLS AND FOLDED PLATES USING TWO‐NODED FINITE STRIPS , 1993 .

[4]  D. J. Dawe,et al.  Buckling of composite shell structures using the spline finite strip method , 1999 .

[5]  李華煜.  Spline finite strip analysis of arbitrarily shaped plates and shells , 1988 .

[6]  Yew-Chaye Loo,et al.  THE FINITE STRIP METHOD IN BRIDGE ENGINEERING , 1978 .

[7]  J. S. Przemieniecki.  Finite Element Structural Analysis of Local Instability , 1972 .

[8]  Y. K. Cheung,et al.  Postbuckling analysis of shells by spline finite strip method , 1989 .

[9]  D. J. Dawe,et al.  Buckling of composite plates and plate structures using the spline finite strip method , 1994 .

[10]  D. J. Dawe,et al.  Postbuckling analysis of thin rectangular laminated plates by spline FSM , 1998 .

[11]  F. W. Williams,et al.  Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings , 1974 .

[12]  H. C. Chan,et al.  Buckling of multi-layer sandwich plates by the finite strip method , 1977 .

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

[14]  D. J. Dawe,et al.  Finite strip buckling analysis of curved plate assemblies under biaxial loading , 1977 .

[15]  Jiye Chen,et al.  Linear transient analysis of rectangular laminated plates by a finite strip-mode superposition method , 1996 .

[16]  D. J. Dawe,et al.  Buckling and vibration of shear deformable prismatic plate structures by a complex finite strip method , 1988 .

[17]  Gregory J. Hancock,et al.  A nonlinear elastic spline finite strip analysis for thin-walled sections , 1991 .

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

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

[20]  T. R. Graves Smith,et al.  A finite strip method for the post-locally-buckled analysis of plate structures , 1978 .

[21]  D. J. Dawe,et al.  Spline finite strip analysis of the buckling and vibration of composite prismatic plate structures , 1997 .

[22]  Srinivasan Sridharan,et al.  Doubly symmetric interactive buckling of plate structures , 1983 .

[23]  I. H. Marshall,et al.  Composite structures 5 , 1989 .

[24]  D. J. Dawe,et al.  Linear transient analysis of rectangular laminates using spline finite strips , 1998 .

[25]  Srinivasan Sridharan,et al.  Mode Interaction in Thin-Walled Structural Members∗ , 1984 .

[26]  D. J. Dawe,et al.  Postbuckling Analysis of Composite Laminated Panels , 2000 .

[27]  D. J. Dawe,et al.  Buckling and vibration analysis of composite plate and shell structures using the PASSAS software package , 1997 .

[28]  Y. K. Cheung,et al.  Static and dynamic analysis of multi-layered sandwich plates , 1972 .

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

[30]  Analysis of the post-buckling behaviour of rectangular laminates , 1992 .

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

[32]  D. J. Dawe,et al.  Vibration of shear-deformable laminated plate structures by the finite strip method , 1987 .

[33]  Maurice Petyt,et al.  Finite strip analysis of singly curved skin-stringer structures , 1981 .

[34]  Mark A. Bradford,et al.  INTERACTION OF LOCAL AND LATERAL BUCKLING IN BEAMS , 1982 .

[35]  Gregory J. Hancock,et al.  Nonlinear Analysis of Thin Sections in Compression , 1979 .

[36]  D. J. Dawe,et al.  Vibration of curved plate assemblies subjected to membrane stresses , 1982 .

[37]  D. J. Dawe,et al.  Buckling and vibration of long plate structures by complex finite strip methods , 1990 .

[38]  C S Smith,et al.  ELASTIC BENDING, BUCKLING, AND VIBRATION OF ORTHOTROPIC PLATE-BEAM STRUCTURES , 1968 .

[39]  D. J. Dawe,et al.  Finite strip large deflection and post-overall-buckling analysis of diaphragm-supported plate structures , 1996 .

[40]  D. J. Dawe,et al.  Buckling and vibration analysis of composite laminated plates and shells using general spline function , 1997 .

[41]  S. Sridharan,et al.  A finite strip method for the buckling of plate structures under arbitrary loading , 1978 .

[42]  J. Loughlan,et al.  The buckling performance of composite stiffened panel structures subjected to combined in-plane compression and shear loading , 1994 .

[43]  B. Barsky,et al.  An Introduction to Splines for Use in Computer Graphics and Geometric Modeling , 1987 .

[44]  Mo Shing Cheung,et al.  Natural vibrations of thin, flat-walled structures with different boundary conditions , 1971 .

[45]  I. Sheinman,et al.  Mechanical performance of thin-walled tubular composite elements under uniaxial loading part 2: compressive behavior , 1995 .

[46]  Bo Edlund,et al.  Buckling analysis of trapezoidally corrugated panels using spline finite strip method , 1994 .

[47]  D. J. Dawe,et al.  Dynamic instability of composite laminated rectangular plates and prismatic plate structures , 2002 .

[48]  W. H. Wittrick.  A Unified Approach to the Initial Buckling of Stiffened Panels in Compression , 1968 .

[49]  D. J. Dawe,et al.  Free vibration of curved-plate assemblies with diaphragm ends , 1980 .

[50]  Maurice Petyt.  Finite strip analysis of flat skin-stringer structures , 1977 .

[51]  D. J. Dawe,et al.  Buckling and Vibration Analysis of Composite Prismatic Plate Structures , 1989 .

[52]  D. J. Dawe,et al.  Finite strip vibration analysis of composite prismatic shell structures with diaphragm ends , 1993 .

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

[54]  Y K Cheung,et al.  THE FINITE STRIP METHOD IN THE ANALYS OF ELASTIC PLATES WITH TWO OPPOSITE SIMPLY SUPPORTED ENDS. , 1968 .

[55]  Jay A. Puckett,et al.  Plate bending analysis by unequally spaced splines , 1991 .

[56]  D. J. Dawe,et al.  A note on finite strip buckling analysis of composite plate structures , 1996 .

[57]  W. H. Wittrick,et al.  The Influence of Orthotropy on the Stability of some Multi-plate Structures in Compression , 1973 .

[58]  D. J. Dawe,et al.  Free vibration of sandwich plates with laminated faces , 2002 .

[59]  A. R. Cusens,et al.  A finite strip method for the geometrically nonlinear analysis of plate structures , 1983 .

[61]  W. H. Wittrick.  General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures , 1968 .

[62]  D. J. Dawe,et al.  Overall and local buckling of sandwich plates with laminated faceplates, part II: Applications , 2001 .

[63]  D. J. Dawe,et al.  Finite strip buckling and free vibration analysis of stepped rectangular composite laminated plates , 1999 .

[64]  D. J. Dawe,et al.  Spline FSM postbuckling analysis of shear-deformable rectangular laminates , 1999 .

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

[66]  R. J. Plank,et al.  Buckling under combined loading of thin, flat‐walled structures by a complex finite strip method , 1974 .

[67]  D. J. Dawe,et al.  Non-linear finite strip analysis of rectangular laminates under end shortening, using classical plate theory , 1992 .

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

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

[71]  D. J. Dawe,et al.  Finite strip analysis of imperfect laminated plates under end shortening and normal pressure , 1995 .

[72]  Y. K. Cheung,et al.  Free vibration of formed sandwich panel , 1982 .

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

[74]  A. V. Viswanathan,et al.  Elastic buckling analysis for composite stiffened panels and other structures subjected to biaxial inplane loads , 1973 .

[75]  Kim J.R. Rasmussen,et al.  Recent developments in the buckling and nonlinear analysis of thin-walled structural members , 1990 .

[76]  M. S. Anderson,et al.  Buckling and vibration of any prismatic assembly of shear and compression loaded anisotropic plates with an arbitrary supporting structure , 1983 .

[77]  W. J. Stroud,et al.  Buckling loads of stiffened panels subjected to combined longitudinal compression and shear: Results obtained with PASCO, EAL, and STAGS computer programs , 1984 .

[78]  D. J. Dawe,et al.  Finite strip post-local-buckling analysis of composite prismatic plate structures , 1993 .

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

[80]  D. J. Dawe,et al.  Nonlinear transient analysis of rectangular composite laminated plates , 2000 .

[81]  D. Dawe,et al.  Thermal buckling of shear-deformable composite laminated plates by the spline finite strip method , 2000 .

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

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

[84]  J Bruneau,et al.  THE FINITE STRIP METHOD , 1976 .

[85]  E. Hinton,et al.  Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells , 1995 .

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

[87]  D. J. Dawe,et al.  General spline finite strip analysis for buckling and vibration of prismatic composite laminated plate and shell structures , 1998 .

[88]  Analysis of plated structures with rectangular cutouts and internal supports using the spline finite strip method , 1994 .

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

[90]  David Kennedy,et al.  Analysis Features of VICONOPT, An Exact Buckling and Vibration Program for Prismatic Assemblies of Anisotropic Plates , 1990 .

[91]  J. Loughlan.  A finite strip analysis of the buckling characteristics of some composite stiffened shear panels , 1994 .

[92]  J. Webber,et al.  Experimental Buckling Loads of Sandwich Panels with Carbon Fibre Faceplates , 1973 .

[93]  J. T. Gierlinski,et al.  The geometric non-linear analysis of thin-walled structures by finite strips , 1984 .

[94]  D. J. Dawe,et al.  Finite strip buckling and postbuckling analysis , 1995 .

[95]  A. V. Viswanathan,et al.  Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads , 1974 .

[96]  R. Dhanaraj,et al.  Thermal buckling of laminated composite plates , 1994 .

[97]  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 .

[98]  R. Houlston,et al.  Finite strip analysis of plates and stiffened panels subjected to air-blast loads , 1989 .

[99]  M. D. Olson,et al.  Nonlinear dynamic analysis of stiffened plates , 1988 .