The used matrix of Green type and algebra of matrix in the problem of static deformation of the circular plates with discrete-variable thickness

Based on classic theory of beams and certain modifications, a simple technique is derived in order to obtain an approximate value of the maximum bending moment in a rotationally symmetric circular plate with a variable thickness. It is assumed that one of the two concentric boundaries of the plate is clamped, and the other is free. Numerical examples for both cases of constant and variable thickness plates subject to uniform pressure or rim line loading are presented.

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

Building and reconstruction ◽

10.33979/2073-7416-2021-98-6-36-42 ◽

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.

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Collapse of Clamped Variable Thickness Circular Plates

Journal of the Engineering Mechanics Division ◽

10.1061/jmcea3.0001845 ◽

1973 ◽

Vol 99 (6) ◽

pp. 1309-1314

Author(s):

Helmut M. Haydl ◽

Archibald N. Sherbourne

Keyword(s):

Variable Thickness ◽

Circular Plates

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Large Deflections of Circular Plates of Variable Thickness

Journal of Applied Mechanics ◽

10.1115/1.3162046 ◽

1982 ◽

Vol 49 (1) ◽

pp. 243-245 ◽

Cited By ~ 9

Author(s):

B. Banerjee

Keyword(s):

Circular Plate ◽

Variable Thickness ◽

Large Deflection ◽

Numerical Results ◽

Large Deflections ◽

Circular Plates ◽

Uniform Load ◽

Plate Of Variable Thickness ◽

Plates Of Variable Thickness

The large deflection of a clamped circular plate of variable thickness under uniform load has been investigated using von Karman’s equations. Numerical results obtained for the deflections and stresses at the center of the plate have been given in tabular forms.

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