Large Deflection of Unsymmetric Cross-Ply and Angle-Ply Plates

1976 ◽  
Vol 18 (4) ◽  
pp. 179-183 ◽  
Author(s):  
C. Y. Chia ◽  
M. K. Prabhakara
Keyword(s):  
Boundary Conditions ◽  
Large Deflection ◽  
Perturbation Technique ◽  
Transverse Load ◽  
Load Force ◽  
Rectangular Plates ◽  
Linear Partial Differential Equations ◽  
Transverse Deflection ◽  
Anisotropic Rectangular Plates ◽  
Good Agreement

An approximate solution to the von Karman-type large-deflection equations of unsymmetrically laminated, anisotropic, rectangular plates under uniform transverse load is formulated by the perturbation technique. The membrane boundary conditions are the zero normal and shear boundary forces. By expressing the load, force function and transverse deflection in the form of series, the governing equations and boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. In each approximation a solution is assumed in the form of polynomials which satisfy the associated boundary conditions and physical requirements for deflection and and three membrane forces in unsymmetric cross-ply and angle-ply plates. Taking the first three terms in the truncated series, numerical results are graphically presented for the load-deflection relations, bending moments and membrane forces in unsymmetric cross-ply and angle-ply plates with various values of aspect ratio and total number of layers. The present third approximation is in good agreement with the existing solutions for large deflections of isotropic and unsymmetric angle-ply plates having the ratio of central deflection to thickness up to the value of 2.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

Nonlinear Behaviour of Unsymmetric, Angle-Ply, Rectangular Plates under in-Plane Edge Shear

1979 ◽  
Vol 21 (3) ◽  
pp. 205-212 ◽  
Author(s):  
M. K. Prabhakara ◽  
J. B. Kennedy
Keyword(s):  
Large Deflection ◽  
Bending Moment ◽  
Double Series ◽  
Nonlinear Behaviour ◽  
Rectangular Plates ◽  
Bending Moments ◽  
High Modulus ◽  
Buckling Loads ◽  
Post Buckling ◽  
Transverse Deflection

A nonlinear analysis of unsymmetric, angle-ply, rectangular plates under uniform in-plane edge shear is presented. The solution is based on the von Kármán-type large-deflection equations, with the force function and the transverse deflection expressed as double series in terms of appropriate beam functions. The prescribed boundary conditions, including those for the vanishing of normal bending moment at the edges of simply supported plates, are satisfied. Numerical results for the buckling loads and for the post-buckling deflections, membrane forces and bending moments are presented for plates composed of high-modulus, fibre-reinforced epoxy composites.

scholarly journals LINEAR AND NONLINEAR FREE VIBRATION ANALYSIS OF RECTANGULAR PLATE

2021 ◽  
Vol 12 (1) ◽  
pp. 15-25
Author(s):  
Edward Adah ◽  
David Onwuka ◽  
Owus Ibearugbulem ◽  
Chinenye Okere
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Middle Surface ◽  
Rectangular Plates ◽  
Nonlinear Free Vibration ◽  
Surface Displacements ◽  
Linear And Nonlinear

The major assumption of the analysis of plates with large deflection is that the middle surface displacements are not zeros. The determination of the middle surface displacements, u0 and v0 along x- and y- axes respectively is the major challenge encountered in large deflection analysis of plate. Getting a closed-form solution to the long standing von Karman large deflection equations derived in 1910 have proven difficult over the years. The present work is aimed at deriving a new general linear and nonlinear free vibration equation for the analysis of thin rectangular plates. An elastic analysis approach is used. The new nonlinear strain displacement equations were substituted into the total potential energy functional equation of free vibration. This equation is minimized to obtain a new general equation for analyzing linear and nonlinear resonating frequencies of rectangular plates. This approach eliminates the use of Airy’s stress functions and the difficulties of solving von Karman's large deflection equations. A case study of a plate simply supported all-round (SSSS) is used to demonstrate the applicability of this equation. Both trigonometric and polynomial displacement shape functions were used to obtained specific equations for the SSSS plate. The numerical results for the coefficient of linear and nonlinear resonating frequencies obtained for these boundary conditions were 19.739 and 19.748 for trigonometric and polynomial displacement functions respectively. These values indicated a maximum percentage difference of 0.051% with those in the literature. It is observed that the resonating frequency increases as the ratio of out–of–plane displacement to the thickness of plate (w/t) increases. The conclusion is that this new approach is simple and the derived equation is adequate for predicting the linear and nonlinear resonating frequencies of a thin rectangular plate for various boundary conditions.

Post-Buckling Behaviour of Simply-Supported Cross-Ply Rectangular Plates

1976 ◽  
Vol 27 (4) ◽  
pp. 309-316 ◽  
Author(s):  
M K Prabhakara
Keyword(s):  
Large Deflection ◽  
Bending Moment ◽  
Double Series ◽  
Biaxial Compression ◽  
Rectangular Plates ◽  
Sine Series ◽  
Simply Supported ◽  
Unsymmetric Laminates ◽  
Post Buckling ◽  
Transverse Deflection

SummaryAn analysis is presented for the post-buckling behaviour of simply-supported, laminated cross-ply rectangular plates subjected to biaxial compression. The solution to von Kármán-type large deflection equations of the plate is expressed as a double sine series for the transverse deflection and a double series of clamped-clamped beam functions for the force function. All the boundary conditions, including those involving the normal bending moment at the edges, are satisfied exactly. The series solution is found to converge rapidly. Using only the first few terms in the series, numerical results for square graphite-epoxy unsymmetric laminates under uniaxial compression is presented graphically.

Nonlinear Analysis of Orthotropic Plates

1975 ◽  
Vol 17 (3) ◽  
pp. 133-138 ◽  
Author(s):  
C. Y. Chia ◽  
M. K. Prabhakara
Keyword(s):  
Large Deflection ◽  
Composite Plates ◽  
Double Fourier Series ◽  
Combined Loading ◽  
Transverse Load ◽  
Orthotropic Plates ◽  
Aspect Ratios ◽  
Patch Load ◽  
Combined Action ◽  
Transverse Deflection

The large deflection of a rectangular orthotropic plate subjected to the combined action of edge compression and transverse load is investigated on the basis of von Kármán-type large-deflection equations. The edges of the plate are assumed to be either all clamped or all simply supported. A solution is obtained in the form of double Fourier series consisting of beam eigenfunctions for both transverse deflection and force function. The postbuckling of the plate is treated as a special case. Taking the first nine terms in each truncated series, numerical results in load-deflection relations and bending moments are graphically presented for three types of fibre-reinforced composite plates with various aspect ratios. The three types of transverse load considered in the combined loading are central patch load, eccentric patch load and hydrostatic pressure. The present results for postbuckling and large deflection of isotropic and orthotropic plates are in good agreement with available data.

scholarly journals Free In-Plane Vibration of Super-Elliptical Plates

2011 ◽  
Vol 18 (3) ◽  
pp. 471-484 ◽  
Author(s):  
Murat Altekin
Keyword(s):  
Boundary Conditions ◽  
Lagrange Multipliers ◽  
Ritz Method ◽  
Rectangular Plates ◽  
Uniform Thickness ◽  
Plane Vibration ◽  
Good Agreement ◽  
Geometrical Boundary

Free in-plane vibration of super-elliptical plates of uniform thickness was investigated by the Ritz method. A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. The geometrical boundary conditions were satisfied by the Lagrange multipliers. The results were compared with those of rectangular plates. Basically good agreement was obtained. Matching results were reported, and the discrepancies were highlighted.

Large Deflection Theory for Orthotropic Rectangular Plates Subjected to Edge Compression

1952 ◽  
Vol 19 (4) ◽  
pp. 446-450
Author(s):  
Syed Yusuff
Keyword(s):  
Large Deflection ◽  
Polytechnic Institute ◽  
Large Deflections ◽  
Rectangular Plates ◽  
Compression Tests ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Theoretical Results ◽  
Anisotropic Rectangular Plates

Abstract A theory is presented of the large deflections of orthotropic (orthogonally anisotropic) rectangular plates when the plate is initially slightly curved and its boundaries are subjected to the conditions prevailing in edgewise compression tests. Results are given of computations carried out for four different combinations of load and lamination in Fiberglas panels. These theoretical results duplicate the substantial variations in the load-strain and load-deflection diagrams obtained earlier in experiments at the Polytechnic Institute of Brooklyn.

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