An investigation on the perforation resistance of laminated CFRP beam and 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.

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Stability of a square plate with an elastic border

Journal of Mathematical Sciences ◽

10.1007/bf02431082 ◽

1995 ◽

Vol 74 (4) ◽

pp. 1154-1156

Author(s):

P. D. Levitskii ◽

G. I. Pshenichnov

Keyword(s):

Square Plate

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Elastic Shakedown in Pressure Vessel Components Under Non-Proportional Loading

Piping and Component Analysis and Diagnosis ◽

10.1115/pvp2002-1522 ◽

2002 ◽

Cited By ~ 3

Author(s):

Martin Muscat ◽

Robert Hamilton

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Pressure Vessel ◽

Proportional Loading ◽

Linear Superposition ◽

Element Analysis ◽

Mechanical Loads ◽

Bound Theorem ◽

Square Plate ◽

Elastic Shakedown

Bounding techniques for calculating shakedown loads are of great importance in design since this eliminates the need for performing full elasto-plastic cyclic loading analyses. The classical Melan’s lower bound theorem is widely used for calculating shakedown loads of pressure vessel components under proportional loading. Polizzotto extended the Melan’s theorem to the case of non-proportional loading acting on a structure. This paper presents a finite element method, based on Polizzotto’s theorem, to estimate the elastic shakedown load for a structure subjected to a combination of steady and cyclic mechanical loads. This method, called non-linear superposition, is then applied to investigate the shakedown behaviour of a pressure vessel component — a nozzle/cylinder intersection and that of a biaxially loaded square plate with a central hole. Results obtained for both problems are compared with those available in the literature and are verified by means of cyclic elasto-plastic finite element analysis.

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Thermal post-buckling of a square plate resting on an elastic foundation by finite element method

Computers & Structures ◽

10.1016/0045-7949(88)90039-9 ◽

1988 ◽

Vol 28 (2) ◽

pp. 195-199 ◽

Cited By ~ 38

Author(s):

K.Kanaka Raju ◽

G.Venkateswara Rao

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elastic Foundation ◽

Post Buckling ◽

Square Plate ◽

Element Method

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Plates in Unilateral Contact With Simple Supports: Pressure Loading

Journal of Applied Mechanics ◽

10.1115/1.3171701 ◽

1986 ◽

Vol 53 (1) ◽

pp. 141-145 ◽

Cited By ~ 3

Author(s):

N. J. Salamon ◽

T. P. Pawlak ◽

F. F. Mahmoud

Keyword(s):

Support System ◽

Unilateral Contact ◽

Response Mode ◽

Pressure Loading ◽

Analytical Work ◽

Simple Supports ◽

Square Plate ◽

Lift Off ◽

Good Agreement ◽

Shear Fields

The response of a square plate, simply and unilaterally supported, to pressure loading is numerically treated. The support system consists of discrete elastic springs whose stiffnesses range from near-rigid to compliant character. It is found that, except for rather low support stiffnesses, the plate will lift off the foundation. After demonstrating good agreement with a recent analytical work, the deflections and shear fields are provided. The response mode changes dramatically as the supports approach rigidity.

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Vibration of Rectangular Plates by the Ritz Method

Journal of Applied Mechanics ◽

10.1115/1.4010175 ◽

1950 ◽

Vol 17 (4) ◽

pp. 448-453 ◽

Cited By ~ 6

Author(s):

Dana Young

Keyword(s):

Ritz Method ◽

Normal Modes ◽

Approximate Solutions ◽

The Other ◽

Rectangular Plates ◽

Elastic Plates ◽

Modes Of Vibration ◽

Ritz’S Method ◽

Square Plate ◽

Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

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A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

Journal of the Royal Aeronautical Society ◽

10.1017/s0001924000063016 ◽

1962 ◽

Vol 66 (616) ◽

pp. 240-241 ◽

Cited By ~ 14

Author(s):

C. L. Kirk

Keyword(s):

Natural Frequency ◽

Natural Frequencies ◽

Present Note ◽

Flexural Vibration ◽

Approximate Solutions ◽

Mode Shapes ◽

Electronic Digital Computer ◽

Isotropic Plates ◽

Four Corners ◽

Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

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