An exact solution of the axisymmetric problem of the theory of elasticity for a hollow ellipsoid of revolution

1975 ◽  
Vol 11 (10) ◽  
pp. 1029-1032 ◽  
Author(s):  
G. V. Kutsenko ◽  
A. F. Ulitko
Keyword(s):  
Exact Solution ◽  
Axisymmetric Problem ◽  
Theory Of Elasticity ◽  
Ellipsoid Of Revolution

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

Inhomogeneous Problem of the Theory of Elasticity in a Half-Strip. Exact Solution

2020 ◽  
Vol 55 (6) ◽  
pp. 784-790
Author(s):  
M. D. Kovalenko ◽  
I. V. Menshova ◽  
A. P. Kerzhaev ◽  
G. Yu
Keyword(s):  
Exact Solution ◽  
Theory Of Elasticity ◽  
Inhomogeneous Problem ◽  
Half Strip

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

2019 ◽  
Vol 968 ◽  
pp. 475-485 ◽  
Author(s):  
Stanislav Koval’chuk ◽  
Alexey Goryk
Keyword(s):  
Exact Solution ◽  
General Solution ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Theory Of Elasticity ◽  
Transverse Shear Deformation ◽  
Uniform Load ◽  
Principle Of Superposition ◽  
Elastic Bending ◽  
Transverse Bending

An exact solution of the theory of elasticity is presented for the problem of a narrow multilayer bar section transverse bending under the action of a normal uniform load on longitudinal faces. The solution is built using the principle of superposition, by imposing common solutions to the problems of bending a multilayer cantilever with uniform loads on the longitudinal faces and an arbitrary load on the free end, and allows to take into account the orthotropy of the materials of the layers, as well as transverse shear deformation and compression. On the basis of a built-in general solution, a number of particular solutions are obtained for multi-layer beams with various ways of the ends fixing.

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