On the stress-strain state of toroidal shells of elliptical cross section formed from nonlinear elastic orthotropic materials

2000 ◽  
Vol 36 (1) ◽  
pp. 90-97 ◽  
Author(s):  
I. S. Chernyshenko ◽  
V. A. Maksimyuk
Keyword(s):  
Cross Section ◽  
Strain State ◽  
Elliptical Cross Section ◽  
Orthotropic Materials ◽  
Stress Strain ◽  
Elliptical Cross ◽  
Stress Strain State ◽  
Nonlinear Elastic ◽  
Toroidal Shells

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

Stress-Strain State Exploration of Stringer Made of Composite Materials Depending on Layers Stacking Structure

2018 ◽  
Vol 284 ◽  
pp. 71-76
Author(s):  
P.V. Solovyev ◽  
A.I. Gomzin ◽  
L.A. Ishbulatov ◽  
S.N. Galyshev ◽  
F.F. Musin
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Strain State ◽  
Stress Strain ◽  
Stress Strain State ◽  
Airplane Wing ◽  
External Loads ◽  
Stacking Structure ◽  
Composite Carbon ◽  
Shaped Cross Section

In this article the results of stress-strain state investigation for composite airplane wing stringer with different layers stacking structures are presented. As an object of research, a stringer made of composite carbon with V-shaped cross-section is considered. Due to the stress-strain state analysis of various stringer structures, the most effective structure for stringer layers stacking is selected, both in the view of providing the most rigidity and optimal perception by the stringer the field of external loads, which are most typical for the conditions of its operation.

The movement investigation of an axisymmetric rotation body under the action of electromagnetic fields

2020 ◽  
Vol 2 (103) ◽  
pp. 67-77
Author(s):  
O. Hrevtsev ◽  
N. Selivanova ◽  
P. Popovych ◽  
L. Poberezhny ◽  
O. Shevchuk ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Cross Section ◽  
Variable Thickness ◽  
Structural Damage ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Stress Strain ◽  
Coordinate Time ◽  
Stress Strain State ◽  
Natural Time

Purpose: To ensure an adequate level of accuracy, it is rational to study the ponderomotor forces of the ring, which drive a hollow disk of variable thickness, hung on the ring. Design/methodology/approach: The solution of the motion problem of a hollow disk of variable thickness suspended on a force ring of rectangular cross section is based on the method of solving the equations of the theory of thermoelasticity. The stress-strain state, as well as the motion of the specified body of rotation, the disk, in studies in a cylindrical coordinate system, under the action of ponderomotor forces. Findings: The motion equation of a hollow disk hung on a force ring-torus is made, exact solutions of the motion equations of a ring in the torus form of rectangular cross section are found. New component expressions of ponderomotor forces, which appear from the action of the ring's own electromagnetic field and cause the motion of a hollow disk, have been found on the basis of Maxwell's equations. It is proved that at high speeds and low natural accelerations the stress - strain state of the disk material does not cause the destruction of the structure. Research limitations/implications: Calculations of ponderomorphic forces are valid for the ring, which drives a hollow disk of variable thickness, hung on the ring. Practical implications: It is proved that at high velocities and small natural accelerations the stress-strain state of the disk medium does not cause structural damage. It is determined that the rotation in the direction of movement at an angle of 90 degrees changes only the direction of the acceleration vector without increasing its value. Originality/value: The dependences between own time and coordinate time are formulated. It is proved that a small change in the natural time for the studied disk can significantly change the coordinate time, and the pulsed electromagnetic field provides the ability to cover infinitely large distances over finite periods of time.

scholarly journals A transient dynamic process in a structural nonlinear system “beam – two-parameter foundation”

2020 ◽  
Vol 310 ◽  
pp. 00007
Author(s):  
Vladimir Gordon ◽  
Pavel Morrev ◽  
Olga Pilipenko
Keyword(s):  
Cross Section ◽  
Strain State ◽  
Shear Stiffness ◽  
Arbitrary Cross Section ◽  
Forced Oscillations ◽  
Stiffness Parameter ◽  
Stress Strain ◽  
Stress Strain State ◽  
Internal Forces ◽  
Two Parameter

A method for analytical assessment of dynamic added stress in elastic loaded beam resting on elastic two-parameter Pasternak’s foundation due to sudden destruction a part of foundation is proposed. Equations of static bending, natural and forced oscillations are written in a matrix form using state vectors including deflection, rotational angles, bending moments, and shear forces at arbitrary cross section of a beam and also using the matrices of the initial parameters influence on the stress-strain state in arbitrary cross section. The influence of foundation failure on beam’s stress-strain state, taking into account a relation between the stiffness parameters of foundation, is analyzed. The condition of smallness for the shear stiffness parameter (Pasternak’s parameter) in comparison with the stretching-compressing stiffness parameter (Vinkler’s parameter) is accepted. It is shown that the accounting of Pasternak’s parameter reduces the level of dynamic added stress in a beam when sudden destructing of a foundation. The factor of sudden defect occurrence in the system “beam – foundation” increases considerably the internal forces in a beam in comparison with quasistatic formation of the same defect.

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