Discussion. The Finite Strip Method in the Analysis of Elastic Plates With Two Opposite Simply Supported Ends.

Cheung, Y.K.; Nayak, Gopinatha

doi:10.1680/iicep.1969.7550

Cited by 32 publications

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“…"" Cheung (1968a) originally developed the finite strip method for the stress analysis of simply supported rectangular plates in bending. The method was also applied to plates with cla1!1Ped or free end boundary conditions (Cheung 1968b, Cheung andCheung 1971).…”

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Behaviour and Design of Cold-Formed Channel Columns

Young

Rasmussen

1999

Advances in Steel Structures (ICASS '99)

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Australia 1997 SYNOPSISThe behaviour of fixed-ended and pin-ended singly symmetric columns is investigated experimentally and theoretically in this thesis. It is shown that local buckling does not induce overall bending of fixed-ended singly symmetric columns, as it does of pin-ended singly symmetric columns. Consequently, local buckling has a fundamentally different effect on the behaviour of fixed-ended and pin-ended singly symmetric columns. These fundamentally different effects of local buckling lead to inconsistencies in traditional design approaches which account for support conditions solely by using effe.ctive lengths. Therefore, improved design recommendations for fixed-ended singly symmetric columns are proposed in this thesis.An experimental investigation on cold-formed channel columns compressed between fixed and pinned ends is presented in this thesis! A series of tests was performed on plain and lipped / channels brake-pressed from high strength structural steel sheets. Four different cross-section geometries were tested over a range of lengths which involved pure local buckling, distortional buckling as well as overall flexural buckling and flexural-torsional buckling. The different effects of local buckling on the behaviour of fixed-ended and pin-ended channels were investigated by comparing strengths, load-shortening and load-deflection curves, as well as longitudinal profiles of buckling deformations. Geometric imperfections were measured on nearly all test specimens oefore testing as well as the material properties and residual stresses were also measured. The experimental local buckling loads of the fixed-ended tests were determined and shown to be in excellent agreement with the theoretical local buckling loads obtained using an elastic finite strip buckling analysis .. A test rig was developed for the test program, such that detailed deformation profiles of the test specimens were succ~ssfully obtained during testing. Fixed-ended bearings were used which allowed measurements of the axial load and the bending moments about two perpendicular axes.A theory is described for the bifurcation analysis of locally buckled members by deriving the governing equations for the fundamental and bifurcated states. The analysis uses elastic and inelastic geometric nonlinear finite strip buckling analyses to determine the tangent rigidities of ,.,... the locally buckled section The tangent rigidities are substituted into the equations for overall flexural and flexural-torsional buckling to obtain the bifurcation loads. The effect of yield~g is highlighted through a parametric study. The members are subject to pure compression and assumed to be geometrically perfect in the overall sense. It is shown using the fundamental state equations that fixed-ended singly symmetric columns exhibit overall bifurcation behaviour while pin-ended columns do not. The overall bifurcation loads obtained from the analysis are compared with tests of fixed-ended channel columns. The variation of the bifurcation loads with the leng...

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“…Przemieniecki (1973) presented the stability matrix for plate flexural displacements used in conjunction with the finite strip method by Cheung (1968a) for the local buckling analysis of thin-walled cross-sections. The flexural stability matrix derived was for a combination of transverse and longitudinal compression in a plate strip.…”

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Behaviour and Design of Cold-Formed Channel Columns

Young

Rasmussen

1999

Advances in Steel Structures (ICASS '99)

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“…In comparison to exact method and numerical methods, such as the finite element method, the finite state machine (FSM) first introduced by Cheung [10] provides more efficient formulations for the investigation of plate buckling behavior under different load conditions. Ghannadpour [11] and his colleagues used the FSM to investigate the buckling of rectangular, functionally graded plates under three types of mechanical loading: uniaxial compression, biaxial compression, and biaxial compression and tension.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Cube Tanks’ Ceiling and Floor Plates Composed of FGMs when Subjected to Uniform Compression Perpendicular to the Mid-Plane

Abdolvahab¹

2017

MOJCE

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In recent years, a number of studies examined the application of composite cylindrical or cubic plates made of FGMs. FGMs are microscopically inhomogeneous materials in which both mechanical and thermal properties vary smoothly and continuously from one surface to the other, depending on the thickness of the material. This can be achieved by gradually changing the volume composition of constituent materials. Material properties vary according to a power law throughout the plate thickness. In this study, the displacement experienced by FGM cube tanks' ceiling and floor plates subjected to uniform compression perpendicular to the mid-plane was independent of the loading parameter and the plates' aspect ratios. Displacement was also the only function of the material gradient index. To obtain stability analysis of FGM plates, the Galerkin method was used to find the maximum displacement of FGM ceiling or floor plates of the cube tanks. The edges of the rectangular plates were fully simply supported. The accuracy of the proposed model was validated by comparing the results obtained in this study with prior results. Results obtained in this study showed that the Galerkin method reliably calculated the maximum displacement of the FGM plates.

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“…The method has been successfully applied to study the convergence of finite strips for rectangular plates [13,14]. In this paper, the method is further extended to study the vibration of cylindrical shells using the thin flat-plate finite strips; the latter was originally developed by Cheung [15] and remains as one of the most effective elements for analyzing prismatic structures [16]. By making use of the inherent cyclic symmetry of a cylindrical shell and the U-transformation method, explicit solutions for the cylindrical shell vibration problem using flat-shell finite strips were derived.…”

Section: Introductionmentioning

confidence: 99%

On the Validity of Flat-Plate Finite Strip Approximation of Circular Cylindrical Shells

Kong

2014

Journal of Computational Engineering

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The validity of modeling curved shell panels using flat-plate finite strips has been demonstrated in the past by comparing finite strip numerical results with analytical solutions of a few benchmark problems; to date, no mathematical exact solutions of the method or its explicit forms of error terms have been rigorously derived to demonstrate analytically its validity. Using a unitary transformation approach (abbreviated as the U-transformation herein), an attempt is made in this paper to derive mathematical exact solutions of flat-plate finite strips in cylindrical shell vibration analysis. Unlike the conventional finite strip method which involves assembly of the global system of matrix equation and its numerical solution, the U-transformation method makes use of the inherent cyclic symmetry of cylindrical shells to decouple the global matrix equation into one involving only a few unknowns, thus rendering explicit form of solutions for the flat-shell finite strip to be derived. Such explicit solutions can be subsequently expanded into Taylor's series whose results reveal directly their convergence to the exact solutions and the corresponding rate of convergence.

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Discussion. The Finite Strip Method in the Analysis of Elastic Plates With Two Opposite Simply Supported Ends.

Cited by 32 publications

References 0 publications

Behaviour and Design of Cold-Formed Channel Columns

Behaviour and Design of Cold-Formed Channel Columns

Stability Analysis of Cube Tanks’ Ceiling and Floor Plates Composed of FGMs when Subjected to Uniform Compression Perpendicular to the Mid-Plane

On the Validity of Flat-Plate Finite Strip Approximation of Circular Cylindrical Shells

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