Deformations and Stresses in Symmetrically Loaded Circular Plates of Varying Thickness

1953 ◽  
Vol 57 (511) ◽  
pp. 449-454 ◽  
Author(s):  
D. C. Boston
Keyword(s):  
Temperature Gradient ◽  
Gas Turbine ◽  
Variable Thickness ◽  
Material Properties ◽  
Simple Function ◽  
Constant Thickness ◽  
Circular Plates ◽  
Strength Of Materials ◽  
Varying Thickness

The problem of symmetrically loaded circular plates of constant thickness is covered adequately in several of the standard textbooks on the strength of materials. Formulae are derived enabling the deflections and stresses to be readily calculated in any portion of the plate. The problem is complicated by the introduction of a variable thickness and by a variation of material properties due to a temperature gradient down the radius of the plate; conditions such as are encountered in gas turbine wheels, bearing support diaphragms and flexible disc couplings. Methods exist whereby the plate can be solved if the thickness is a simple function of the plate radius, but in practice this is not always so, the profile often being complicated by flanges and spigots.

Axi-Symmetric Buckling of Orthotopic Circular Plates with Variable Thickness

1967 ◽  
Vol 71 (675) ◽  
pp. 218-223 ◽  
Author(s):  
Sharad A. Patel ◽  
Franklin J. Broth
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Material Properties ◽  
Radial Direction ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Edge ◽  
Simply Supported

Axi-symmetric buckling of a circular plate having different material properties in the radial and circumferential directions was analysed in ref. 1. A plate with constant thickness and subjected to a uniform edge compression was considered. The plate edge was assumed clamped or simply-supported. The analysis of ref. 1 is extended to include plates with thickness variation in the radial direction.

A Method of Calculating Stresses in a Non-Uniformly Thick Disc Subjected to Asymmetric Loads, Adapted to a Tabular Computation

1953 ◽  
Vol 57 (514) ◽  
pp. 658-660
Author(s):  
B. A. Hodson
Keyword(s):  
Circular Plate ◽  
Constant Thickness ◽  
Circular Plates ◽  
Strength Of Materials ◽  
Thick Plates ◽  
Thick Disc ◽  
Varying Thickness ◽  
Tabular Method ◽  
Symmetric Loading ◽  
Asymmetric Load

Symmetrically loaded circular plates of constant thickness are dealt with adequately in several of the standard textbooks on the strength of materials. The problem of non-uniformly thick plates subjected to symmetric loading has been discussed by M. Donath and, more recently, by D. C. Boston. So far very little has been done on the problem of a circular plate of varying thickness subjected to an asymmetric load. A tabular method approximating to the solution is outlined in this note. A typical example of the problem arises in certain manoeuvres of a jet aircraft in flight, the rotor discs of the engine being then subject to gyroscopic moments.

Axially Symmetrical Plates With Linearly Varying Thickness

1951 ◽  
Vol 18 (2) ◽  
pp. 140-142
Author(s):  
H. D. Conway
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Variable Thickness ◽  
Practical Problem ◽  
Constant Thickness ◽  
Circular Plates ◽  
Varying Thickness ◽  
Small Deflection ◽  
Special Case ◽  
Plates Of Variable Thickness

Abstract The most practical problem in the bending of symmetrically loaded circular plates of variable thickness is probably that in which the thickness decreases linearly with the distance from the center of the plate. A general solution of the small-deflection problem of such plates is given here in closed form for the special case when Poisson’s ratio is 1/3. Numerical results are given for two particular examples, and these are compared with the results for corresponding plates of constant thickness.

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

2020 ◽  
pp. 146442072098049
Author(s):  
V Kumar ◽  
SJ Singh ◽  
VH Saran ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Engineering Structures ◽  
Property Variation ◽  
Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

RELATIONSHIP OF MAXIMUM DEFLECTIONS AND NATURAL FREQUENCIES VIBRATIONS OF ISOTROPIC CIRCULAR PLATES WITH INHOMOGENEOUS RESISTANCE CONDITIONS ON THE OUTER AND INNER CONTOUR

2021 ◽  
Vol 98 (6) ◽  
pp. 36-42
Author(s):  
A.V. TURKOV ◽  
◽  
S.I. POLESHKO ◽  
E.A. FINADEEVA ◽  
K.V. MARFIN ◽  
...  
Keyword(s):  
Variable Thickness ◽  
Constant Thickness ◽  
Circular Plates ◽  
Outer Contour ◽  
Numerical Studies ◽  
The Difference ◽  
Relationship Of ◽  
The Relationship ◽  
Hinged Support ◽  
Natural Transverse

The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

The Bending of Symmetrically Loaded Circular Plates of Variable Thickness under Uniform Compression

1968 ◽  
Vol 19 (1) ◽  
pp. 59-70
Author(s):  
R. S. Dhaliwal
Keyword(s):  
Variable Thickness ◽  
Circular Ring ◽  
Maximum Deflection ◽  
Circular Plates ◽  
Uniform Compression ◽  
Varying Thickness ◽  
Ring Plate ◽  
Plates Of Variable Thickness

SummaryThe solution has been obtained for the problem of a uniformly compressed and symmetrically loaded circular ring plate of linearly varying thickness. Four particular cases have been discussed and numerical values of the maximum deflection have been obtained for various sizes of the hole of the ring.

The Bending of Symmetrically Loaded Circular Plates of Variable Thickness

1948 ◽  
Vol 15 (1) ◽  
pp. 1-6
Author(s):  
H. D. Conway
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Maximum Stress ◽  
Central Hole ◽  
Constant Thickness ◽  
External Diameter ◽  
Circular Plates ◽  
Plates Of Variable Thickness

Abstract This investigation was carried out with the object of obtaining a solution to the problem of a symmetrically loaded circular plate with a central hole, the thickness of the plate at any section being proportional to the distance of the section from the center of the plate. Six particular cases were investigated, and the values of the maximum stress and deflection calculated for various ratios of the external diameter of the plate to the diameter of the central hole. These values were compared with the corresponding values obtained for plates of constant thickness by A. M. Wahl and G. Lobo (1).

scholarly journals Optimization on the Production of Variable Thickness Aluminium Tubes

2010 ◽  
Author(s):  
Reza Bihamta ◽  
Guillaume D’Amours ◽  
Quang-Hien Bui ◽  
Ahmed Rahem ◽  
Michel Guillot ◽  
...  
Keyword(s):  
Variable Thickness ◽  
Constant Thickness ◽  
Outer Diameter ◽  
Minimum Thickness ◽  
Mechanical Parts ◽  
Tube Drawing ◽  
Matlab Code ◽  
Mechanical Assemblies ◽  
Optimization Study ◽  
One Step

The variable thickness tube drawing is a new modification in the tube drawing methods which enables production of axially variable thickness tubes faster and easier in comparison with other similar methods like radial forging or indentation forging. The production of this type of tubes can be used in optimum design of mechanical parts which do not necessarily need constant thickness along the axis of tube and this method can strikingly reduce the overall weight of parts and mechanical assemblies like cars. In this paper, the variable thickness tube drawing were parameterized in a MATLAB code and optimized with the Ls-Opt software as an optimization engine and Ls-Dyna as a FE solver. The final objective of this optimization study is to determine the minimum thickness which can be produced in one step by this method with various tube dimensions (tube thickness and outer diameter). For verification of results, some experiments were performed in the tube drawing machine which was fabricated by this research group and acceptable correspondence was observed between numerical and experimental results.

Sign in / Sign up

Export Citation Format

Share Document