Large Deflection of Stiffened Plates

1958 ◽  
Vol 25 (4) ◽  
pp. 444-448
Author(s):  
W. G. Soper
Keyword(s):  
Approximate Solution ◽  
Trigonometric Series ◽  
Large Deflection ◽  
Plate Boundary ◽  
Lateral Load ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Isotropic Plates ◽  
Simple Support

Abstract The problem of nonlinear deflection of orthogonally stiffened plates subjected to static lateral load is treated using the concept of equivalent orthotropic plates. Equations are derived which are the appropriate generalizations of von Karman’s equations for isotropic plates. Rectangular plates are considered in detail, and an approximate solution is obtained through trigonometric series. The solution allows for rotational constraint along the plate boundary. All cases from simple support to complete fixity of boundary can therefore be treated.

The Orthogonally Stiffened Plate Under Uniform Lateral Load

1940 ◽  
Vol 7 (4) ◽  
pp. A143-A146
Author(s):  
Henry A. Schade
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Transverse Dimension ◽  
Lateral Load ◽  
Lateral Loading ◽  
Stiffened Plates ◽  
Infinite Strip ◽  
Stiffened Plate ◽  
Longitudinal Dimension ◽  
Side Ratio

Abstract The problem of designing structures with orthogonally stiffened plates under lateral loading has been solved approximately by the infinite-strip method and has been applied, for example, to the double-bottom structure of a ship. Under certain conditions where the side ratio, that is, the ratio of the longitudinal dimension to the transverse dimension, is small, the approximate solution is inadequate. The author gives herein an exact solution applicable to all side ratios.

Large Deflections of Rectangular Orthotropic Plates under Combined Transverse and In-Plane Loads

1973 ◽  
Vol 15 (5) ◽  
pp. 346-350 ◽  
Author(s):  
M. K. Prabhakara ◽  
C. Y. Chia
Keyword(s):  
Large Deflection ◽  
Double Series ◽  
Composite Plates ◽  
Large Deflections ◽  
Orthotropic Plates ◽  
Reinforced Composite ◽  
Isotropic Plates ◽  
Transverse Pressure ◽  
Combined Action ◽  
Good Agreement

A theoretical analysis is presented for the problem of simply supported, rectangular, orthotropic plates undergoing large deflections due to the combined action of uniform transverse pressure and compressive in-plane loading. The solution of the von Kármán-type large deflection equations is obtained in the form of double series consisting of appropriate beam functions for the lateral deflection and the stress function. Numerical results are obtained for three types of fibre–reinforced composite plates with different values of aspect ratio. The effect of the material properties on the deflection and stresses is discussed. The results in the case of isotropic plates are in good agreement with the available solutions.

Analysis of large deflections for pressure loaded plates with rigid inclusions

1998 ◽  
Vol 33 (3) ◽  
pp. 217-222 ◽  
Author(s):  
K Kimura ◽  
M Okamoto
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Static Load ◽  
Numerical Solutions ◽  
Numerical Procedure ◽  
Rectangular Plates ◽  
Matching Method ◽  
Point Matching ◽  
Isotropic Plates ◽  
Out Of Plane

In the present paper, the non-linear Berger equation for large deflection problems of isotropic plates and the point-matching method are utilized to obtain solutions for out-of-plane deformations in rectangular isotropic plates with a circular rigid body at the centre. Numerical solutions are presented in order to illustrate the influence of the rigid body size on the deflection distribution in rectangular plates subjected to uniform static load. The numerical procedure is easier than other procedures based on the von Kármán theory, and reasonable results are obtained.

scholarly journals Vibrational Energy Flow Models of Finite Orthotropic Plates

2003 ◽  
Vol 10 (2) ◽  
pp. 97-113 ◽  
Author(s):  
Do-Hyun Park ◽  
Suk-Yoon Hong ◽  
Hyun-Gwon Kil
Keyword(s):  
Energy Flow ◽  
Vibrational Energy ◽  
Single Frequency ◽  
Field Energy ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Flow Models ◽  
Isotropic Plates ◽  
Classical Models ◽  
Field Energy Density

In this paper energy flow models for the transverse vibration of finite orthotropic plates are developed. These models are expressed with time- and locally space-averaged far-field energy density, and show more general forms than the conventional EFA models for isotropic plates. To verify the accuracy of the developed models, numerical analyses are performed for finite rectangular plates vibrating at a single frequency, and the calculated results expressed with the energy and intensity levels are compared with those of classical models by changing the frequency and the damping.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

Theoretical Determination of Rigidity Properties of Orthogonally Stiffened Plates

1956 ◽  
Vol 23 (1) ◽  
pp. 15-20
Author(s):  
N. J. Huffington
Keyword(s):  
Elastic Constants ◽  
Orthotropic Plate ◽  
Constant Thickness ◽  
Stiffened Plates ◽  
Geometrical Configuration ◽  
Orthotropic Plates ◽  
Theoretical Determination

Abstract The analysis of bending and buckling of orthogonally stiffened plates may be simplified by conceptually replacing the plate-stiffener combination by an “equivalent” homogeneous orthotropic plate of constant thickness. This procedure requires the determination of the four elastic rigidity constants which occur in the theory of thin orthotropic plates. Methods are presented whereby these quantities may be determined analytically in terms of the elastic constants and geometrical configuration of the component parts of the structure.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

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