Geometrically nonlinear analysis of rectangular mindlin plates using the finite strip method

Abstract A general finite strip method of analysis is presented for the geometrically nonlinear analysis of laterally loaded, rectangular, isotropic plates. The analysis is based on the use of Mindlin plate theory and therefore includes the effects of transverse shear deformation. The nonlinearity is introduced via the strain-displacement equations and correspondingly the analysis pertains to problems involving moderate displacements but small rotations. The principle of minimum potential energy is used in the development of the strip and the complete plate stiffness equations and the latter equations are solved using the Newton-Raphson method. In numerical applications a particular type of finite strip is used in which all five reference quantities (three displacements and two rotations) are represented by cubic polynomial interpolation across the strip whilst the ends of the strip are simply supported for bending/shearing behaviour and immovable for membrane behaviour. These applications are concerned with uniformly loaded plates of both thin and moderately-thick geometry and detailed presentation is given of both displacement- and force-type quantities.

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

[2]  E. Hinton,et al.  Finite element analysis of geometrically nonlinear plate behaviour using a mindlin formulation , 1980 .

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

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

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

[6]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[7]  D. J. Dawe.  Static analysis of diaphragm‐supported cylindrical shells using a curved finite strip , 1977 .

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

[9]  Samuel Levy,et al.  Bending of Rectangular Plates With Large Deflections , 1942 .

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

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

[12]  Srinivasan Sridharan,et al.  Postbuckling Analyses with Finite Strips , 1981 .

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

[14]  Mo Shing Cheung,et al.  Static and dynamic behaviour of rectangular plates using higher order finite strips , 1972 .

[15]  Yau-Kai Choung,et al.  Finite Strip Method Analysis of Elastic Slabs , 1968 .

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

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

[18]  A. Mawenya,et al.  Finite strip analysis of plate bending including transverse shear effects , 1974 .

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

[20]  J. N. Reddy,et al.  Large-deflection and large-amplitude free vibrations of laminated composite-material plates , 1981 .

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

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