Bending of Orthogonally Stiffened Plates

1955 ◽  
Vol 22 (2) ◽  
pp. 267-271
Author(s):  
W. H. Hoppmann
Keyword(s):  
Boundary Conditions ◽  
Experimental Method ◽  
Circular Plate ◽  
Elastic Constants ◽  
Orthotropic Material ◽  
Elastic Moduli ◽  
Unit Area ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Clamped Edge

Abstract In this paper the flexure theory for plates of orthotropic material is applied in the case of orthogonally stiffened plates using an experimental method to determine plate stiffnesses in bending and in twisting. Once these stiffnesses, or elastic moduli, have been determined by test they may be used in calculating bending deflections for plates of identical stiffened construction but any given boundary conditions. As an example, calculated deflections of a stiffened circular plate with clamped edge are compared with those which were determined experimentally. It is also demonstrated that the theory can be applied to the case of vibration of a stiffened plate if in addition to the orthotropic elastic constants the weight per unit area of the plate is determined. The various experimental results show considerable promise for use of the proposed combination of theory and experimental method in the analysis of both statically and dynamically loaded plates with attached stiffeners.

Bending of a Cylindrically Aeolotropic Circular Plate With Eccentric Load

1952 ◽  
Vol 19 (1) ◽  
pp. 9-12
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Uniform Thickness ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Different Boundary Conditions ◽  
Small Deflection ◽  
Deflection Theory ◽  
Clamped Edge

Abstract The problem of small-deflection theory applicable to plates of cylindrically aeolotropic material has been developed, and expressions for moments and deflections produced have been found by Carrier in some symmetrical cases under uniform lateral loadings and with different boundary conditions. The author has also found the moments and deflection in the case of an unsymmetrical bending of a plate loaded by a distribution of pressure of the form p = p0r cos θ, with clamped edge. The object of the present paper is to investigate the problem of the bending of a cylindrically aeolotropic circular plate of uniform thickness under a concentrated load P applied at a point A at a distance b from the center, the edge being clamped.

Stability Analysis of the Stiffened Plate with Rids under the Longitudinal Loads

2011 ◽  
Vol 243-249 ◽  
pp. 279-283
Author(s):  
Yu Zhang
Keyword(s):  
Potential Energy ◽  
Boundary Conditions ◽  
Critical Loads ◽  
Minimum Condition ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Simply Supported ◽  
Total Potential ◽  
The Stability ◽  
Work Done

The stiffened plate with rids was considered as a whole structure. Using energy method the stability of stiffened plates with rids under the longitudinal forces was analyzed. Calculating the potential energy of deformation of plate and that of rids and the work done by the neutral plane forces of plate when the plates were buckled, the formulas of critical loads of the stiffened plate with rids under longitudinal forces were derived from the minimum condition of total potential energy. Using the formulas in this paper engineers can easily calculate the critical loads of the stiffened plate with rids under the boundary conditions: the opposite sides are fixed and the other opposite sides are simply supported, four sides are simply supported. The formula of critical loads of the stiffened plate with rids under other boundary conditions can be derived using the method in this paper.

Transient Interaction of a Circular Plate and a Fluid Medium

1979 ◽  
Vol 46 (1) ◽  
pp. 26-30 ◽  
Author(s):  
J. W. Berglund
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Fluid Medium ◽  
Fluid Field ◽  
Elastic Circular Plate ◽  
Unstrained State ◽  
State Of Rest ◽  
Acoustic Fluid

The transient dynamic response of an elastic circular plate subjected to a suddenly applied pressure is determined for several edge boundary conditions. The plate boundary is attached to a semi-infinite, radially rigid tube which is filled with an acoustic fluid, and pressure is applied to the in-vacuo side of the plate. The transient solution is determined by using a technique in which the plate is subjected to a periodic pressure function constructed of appropriately signed and time-shifted Heaviside step functions, and by relying on a physical mechanism which returns the plate and fluid near the plate to an unstrained state of rest between pulses. The plate response is presented for a number of radius-to-thickness ratios and edge boundary conditions when interacting with water. Comparisons are also made with solutions obtained using a plane wave approximation to the fluid field.

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.

Numerical Investigation of Ultimate Strength of Stiffened Plates With Various Cross-Section Forms

2018 ◽  
Author(s):  
Huilong Ren ◽  
Yifu Liu ◽  
Chenfeng Li ◽  
Xin Zhang ◽  
Zhaonian Wu
Keyword(s):  
Aluminum Alloy ◽  
Ultimate Strength ◽  
Cross Section ◽  
High Performance ◽  
Lightweight Design ◽  
Offshore Structures ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Element Analysis ◽  
Hull Structure

There is an increasing interest in the lightweight design of ship and offshore structures, more specifically, choosing aluminum alloys or other lightweight high-performance materials to build structure components and ship equipments. Due to its better mechanical properties and easy assembly nature, extruded aluminum alloy stiffened plates are widely used in hull structures. When the load on the hull reaches a certain level during sailing, partial or overall instability of stiffened plate makes significant contribution in an event of collapse of the hull structure. It is very necessary to investigate the ultimate strength of aluminum alloy stiffened plate to ensure the ultimate bearing capacity of large aluminum alloy hull structure. Most of studies of the ultimate strength of stiffened plates deal with stiffened plates with T–shaped stiffeners. Stiffeners of other shapes have seldom been explored. In this research, the ultimate strength of six different cross–section aluminum alloy stiffened plates and one steel stiffened plate was studied based on the non–linear finite element analysis (FEA). Taking into account stiffness, weight and other issues, the new cross–section aluminum stiffener has finally been concluded for replacing the original steel stiffener in upper deck of a warship.

scholarly journals Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

2018 ◽  
Vol 38 (2) ◽  
pp. 558-573 ◽  
Author(s):  
Yongqiang Yang ◽  
Zhongmin Wang ◽  
Yongqin Wang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Coupling Coefficient ◽  
Inertial Force ◽  
Angular Speed ◽  
Circular Plates ◽  
Thermoelastic Coupling ◽  
Coupling Vibration ◽  
Friction Clutch

Rotating friction circular plates are the main components of a friction clutch. The vibration and temperature field of these friction circular plates in high speed affect the clutch operation. This study investigates the thermoelastic coupling vibration and stability of rotating friction circular plates. Firstly, based on the middle internal forces resulting from the action of normal inertial force, the differential equation of transverse vibration with variable coefficients for an axisymmetric rotating circular plate is established by thin plate theory and thermal conduction equation considering deformation effect. Secondly, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the thermoelastic coupling transverse vibrations with three different boundary conditions are calculated. In this case, the change curve of the first two-order dimensionless complex frequencies of the rotating circular plate with the dimensionless angular speed and thermoelastic coupling coefficient are analyzed. The effects of the critical dimensionless thermoelastic coupling coefficient and the critical angular speed on the stability of the rotating circular plate with simply supported and clamped edges are discussed. Finally, the relation between the critical divergence speed and the dimensionless thermoelastic coupling coefficient is obtained. The results provide the theoretical basis for optimizing the structure and improving the dynamic stability of friction clutches.

Approximated Fundamental Frequency for Thin Circular Plates Clamped or Pinned at the Edge

2007 ◽  
Author(s):  
George Weiss
Keyword(s):  
Circular Plate ◽  
Fundamental Frequency ◽  
Bessel Functions ◽  
Unit Area ◽  
Continuous System ◽  
Modified Bessel Functions ◽  
Circular Plates ◽  
Numerical Parameter ◽  
Elliptical Plate ◽  
Distributed Load

Calculating the exact solution to the differential equations that describe the motion of a circular plate clamped or pinned at the edge, is laborious. The calculations include the Bessel functions and modified Bessel functions. In this paper, we present a brief method for calculating with approximation, the fundamental frequency of a circular plate clamped or pinned at the edge. We’ll use the Dunkerley’s estimate to determine the fundamental frequency of the plates. A plate is a continuous system and will assume it is loaded with a uniform distributed load, including the weight of the plate itself. Considering the mass per unit area of the plate, and substituting it in Dunkerley’s equation rearranged, we obtain a numerical parameter K02, related to the fundamental frequency of the plate, which has to be evaluated for each particular case. In this paper, have been evaluated the values of K02 for thin circular plates clamped or pinned at edge. An elliptical plate clamped at edge is also presented for several ratios of the semi–axes, one of which is identical with a circular plate.

Sign in / Sign up

Export Citation Format

Share Document