Cantilever Plate With Concentrated Edge Load

1937 ◽  
Vol 4 (1) ◽  
pp. A8-A10 ◽  
Author(s):  
D. L. Holl
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Finite Length ◽  
Finite Differences ◽  
Free Edge ◽  
Cantilever Plate ◽  
Transverse Stress ◽  
Longitudinal Stress ◽  
Concentrated Load ◽  
Clamped Edge

Abstract The author gives, by the method of finite differences, an approximate solution of the problem of a finite length of a cantilever plate which bears a concentrated load at the longitudinal free edge. All the boundary conditions are taken into account, and the plate action is determined approximately at all points of the plate. The author points out that a secondary maximum transverse stress occurs at the clamped edge nearest the loading point, and that the longitudinal stress is greatest directly under the loading point.

scholarly journals Buckling Of The Stiffened Flange Of The Thin-Walled Member At Longitudinal Stress Variation

2015 ◽  
Vol 61 (3) ◽  
pp. 149-168
Author(s):  
A. Szychowski
Keyword(s):  
Boundary Conditions ◽  
Free Edge ◽  
Cantilever Plate ◽  
Longitudinal Stress ◽  
Stress Variation ◽  
Buckling Modes ◽  
Load Distributions ◽  
Edge Stiffener ◽  
Thin Walled ◽  
Elastically Restrained

AbstractBuckling of the stiffened flange of a thin-walled member is reduced to the buckling analysis of the cantilever plate, elastically restrained against rotation, with the free edge stiffener, which is susceptible to deflection. Longitudinal stress variation is taken into account using a linear function and a 2nd degree parabola. Deflection functions for the plate and the stiffener, adopted in the study, made it possible to model boundary conditions and different buckling modes at the occurrence of longitudinal stress variation. Graphs of buckling coefficients are determined for different load distributions as a function of the elastic restraint coefficient and geometric details of the stiffener. Exemplary buckling modes are presented.

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.

Free-Edge Plastic Buckling of Axially Compressed Cylindrical Shells

1968 ◽  
Vol 35 (1) ◽  
pp. 73-79 ◽  
Author(s):  
S. C. Batterman
Keyword(s):  
Boundary Conditions ◽  
Finite Length ◽  
Cylindrical Shells ◽  
Free Edge ◽  
Numerical Results ◽  
Negligible Effect ◽  
Tangent Modulus ◽  
Plastic Buckling ◽  
Simple Support ◽  
Axisymmetric Plastic

Axisymmetric plastic buckling of axially compressed cylindrical shells is studied for semi-infinite shells and shells of finite length subject to free-edge boundary conditions. It is shown that the length of the cylinder has a negligible effect on the buckling load. Reductions in buckling stresses from the classical simple-support value are significant, with the amount of reduction dependent on the details of the variation of tangent modulus with stress. Numerical results are presented for cylinders composed of 2024-T4 aluminum and 3003-0 aluminum.

A Semianalytical Vibration Analysis of Partially Wet Square Cantilever Plate With Numerical and Experimental Verification: Partially Wet Modeshapes

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Y. Verma ◽  
N. Datta ◽  
R. Praharaj
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Free Edge ◽  
Cantilever Plate ◽  
Fluid Inertia ◽  
Commercial Code ◽  
Rigid Body Modes ◽  
Set Up ◽  
The Impact ◽  
Clamped Edge

A semianalytical study of a uniform homogenous partially submerged square cantilever plate vibration is presented. The structure is assumed to be a Kirchhoff's plate, clamped on one edge and free on the other edges. The lengthwise section of the plate is a cantilever clamped-free (CF) beam, while the widthwise section is a free-free (FF) beam. The plate modeshape is a weighted superposition of the product of the beam modeshapes, with unknown weights. The CF beam has only flexural modes. The FF beam has two rigid-body modes, i.e., translational and rotational modes. Rayleigh–Ritz method (RRM) is used to set up the free vibration eigenvalue problem. The eigenvector gives the unknown weights. The modeshapes generated are further used in the boundary element method (BEM) to calculate the fluid inertia, which participates in the vibration and leads to a consistent drop in frequencies. The dependence of this reduction on the submergence level is studied for the first six frequencies of the plate. The frequencies are also experimentally generated by the impact hammer test, both in the dry state, and under three distinct levels of submergence: 25%, 50%, and 75% from the free edge opposite to the clamped edge. The frequencies and modeshapes are also verified through numerical analysis using the commercial code ansys 16.0. Conclusions are drawn regarding the influence of fluid inertia distribution on the final plate modeshape, leading to insights into sound structural designs.

Deflections and Moments Due to a Concentrated Load on a Cantilever Plate of Infinite Length

1950 ◽  
Vol 17 (1) ◽  
pp. 67-72 ◽  
Author(s):  
T. J. Jaramillo
Keyword(s):  
Constant Width ◽  
Arbitrary Point ◽  
Free Edge ◽  
Practical Significance ◽  
Infinite Length ◽  
Cantilever Plate ◽  
Concentrated Load ◽  
Numerical Examples ◽  
Improper Integrals ◽  
Special Case

Abstract This paper contains an exact solution in terms of improper integrals for the deflections and moments due to a transverse concentrated load acting at an arbitrary point of an infinitely long cantilever plate of constant width and thickness. The solution is transformed into series form by means of contour integration, and is illustrated by numerical examples. In particular, comparisons are made with the known solution (1) for the special case where the load is applied at the free edge of the plate. The results obtained are of practical significance in connection with the design of certain types of monorail cranes.

Thermal Stresses in a Rectangular Plate Clamped Along an Edge

1949 ◽  
Vol 16 (2) ◽  
pp. 118-122 ◽  
Author(s):  
B. J. Aleck
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Rectangular Plate ◽  
Strain Energy ◽  
Thermal Stresses ◽  
Free Edge ◽  
Drop Out ◽  
Derivatives Of ◽  
Uniform Change ◽  
Clamped Edge

Abstract An approximate solution has been obtained for the stresses induced by a uniform change in temperature of a thin rectangular plate, clamped along an edge. The solution has been carried to completion for plates whose clamped edge is long, i.e., more than 5 times the length of the perpendicular free edge. The solution for smaller ratios of clamped to perpendicular lengths is expressed in terms of six determined functions whose coefficients are to be evaluated by satisfying two boundary conditions. The thermal-stress problem is first converted to one of specified boundary tractions. The normal stress, σx, parallel to the clamped edge is assumed of the form σx = f1 (x) + y f2(x) + y2f3(x), where fi(x) are as yet undetermined functions, and where y is the co-ordinate at right angles to the clamped edge. Using the equations of equilibrium and the boundary conditions, τxy and σy are expressed in terms of powers of y and the derivatives of fi(x). The integral representing the strain energy is then expressed in terms of the expressions for σx, σy, and τxy. In accordance with the principle of least work, the integral representing the strain energy is minimized, using the calculus of variations. The resulting simultaneous differential equations for fi(x) are solved as a linear combination of twelve functions (six of which drop out, by symmetry). Given f1(x), then f2(x) and f3(x) are determinate by virtue of the simultaneous equations. The six coefficients in the expression for f1 are evaluated by satisfying the boundary conditions along the free edges. The maximum normal stress concentration, over 10, occurs at the junction of the free and clamped edges.

BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

2021 ◽  
pp. 2-9
Author(s):  
M.V. Sukhoterin ◽  
◽  
A.M. Maslennikov ◽  
T.P. Knysh ◽  
I.V. Voytko ◽  
...  
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Trigonometric Series ◽  
Bending Moment ◽  
Partial Solution ◽  
Numerical Results ◽  
Cantilever Plate ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Beam Function

Abstract. An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

2021 ◽  
pp. 2150130
Author(s):  
G. Patel ◽  
A. N. Nayak ◽  
A. K. L. Srivastava
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Instability Region ◽  
Concentrated Load ◽  
Simply Supported ◽  
Finite Element Software ◽  
Design Charts ◽  
Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

scholarly journals Numerical solution of acoustic scattering by finite perforated elastic plates

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150767 ◽  
Author(s):  
A. V. G. Cavalieri ◽  
W. R. Wolf ◽  
J. W. Jaworski
Keyword(s):  
Boundary Conditions ◽  
Acoustic Scattering ◽  
Free Edge ◽  
Solution Procedure ◽  
Sound Level ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Beneficial Effects ◽  
Plate Length ◽  
Radiated Sound

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

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