The elastic equilibrium of an unbounded body, weakened by a system of concentric cracks

1970 ◽  
Vol 6 (4) ◽  
pp. 433-436 ◽  
Author(s):  
A. E. Andreikiv ◽  
V. V. Panasyuk
Keyword(s):  
Elastic Equilibrium ◽  
Unbounded Body

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation

1999 ◽  
Vol 123 (4) ◽  
pp. 535-541 ◽  
Author(s):  
L. Saggere ◽  
S. Kota
Keyword(s):  
Compliant Mechanisms ◽  
Shape Change ◽  
Synthesis Method ◽  
Elastic Equilibrium ◽  
Body Motion ◽  
Motion Generation ◽  
Generation Task ◽  
Potential Applications ◽  
Flexible Segment ◽  
Definition Of

Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

STABILITY OF SPATIAL ELASTICA IN A GRAVITATIONAL FIELD

2012 ◽  
Vol 12 (02) ◽  
pp. 403-421 ◽  
Author(s):  
BOONCHAI PHUNGPAINGAM ◽  
LAWRENCE N. VIRGIN ◽  
SOMCHAI CHUCHEEPSAKUL
Keyword(s):  
Gravitational Field ◽  
Elastic Equilibrium ◽  
Experimental System ◽  
Primary Control ◽  
Arc Length ◽  
Euler Parameters ◽  
Reference Analysis ◽  
Horizontal Orientation ◽  
Equilibrium Configurations ◽  
Out Of Plane

This paper considers the behavior of a spatial elastica in a gravitational field. The slenderness of the system considered is such that the weight becomes an important consideration in determining elastic equilibrium configurations. Both ends of the elastica are clamped in an initially (planar) horizontal orientation at a fixed distance apart. However, one of the ends allows an increase in arc-length, that is, it is a sleeve joint. Thus, the total arc-length is the primary control parameter. This kind of elastica typically loses stability, resulting in out-of-plane deflections, when the total arc-length is increased beyond a critical value. A small mid-length torque can used to perturb a planar equilibrium configuration in order to test for stability. The aim of this study is to assess the effect of self-weight of the elastica (which is typically ignored) on promoting or delaying the loss of stability. To this end, it is useful to compare and contrast the results of orientation, that is, the system is configured in both an initial "upright" orientation and then in an "upside-down" orientation to highlight the influence of gravity. The results of the weightless elastica are used as a reference. Analysis is based on Kirchhoff's rod theory and Euler parameters, and the resulting set of governing differential equations are solved using a shooting method. The results from an experimental system using a slender superelastic wire made from Nitinol (Nickel Titanium Naval Ordnance Laboratory) exhibit close agreement with the analytical results.

The Solution of Boundary Value Problems of Various Types with Consideration of Volume Forces for Anisotropic Bodies of Revolution

2021 ◽  
pp. 57-70
Author(s):  
D.A. Ivanychev ◽  
E.Yu. Levina
Keyword(s):  
Elastic Equilibrium ◽  
Transversely Isotropic ◽  
The Body ◽  
Bodies Of Revolution ◽  
State Spaces ◽  
Elastic Fields ◽  
Boundary State ◽  
Boundary States ◽  
Anisotropic Bodies ◽  
The Given

In this work, we studied the axisymmetric elastic equilibrium of transversely isotropic bodies of revolution, which are simultaneously under the influence of surface and volume forces. The construction of the stress-strain state is carried out by means of the boundary state method. The method is based on the concepts of internal and boundary states conjugated by an isomorphism. The bases of state spaces are formed, orthonormalized, and the desired state is expanded in a series of elements of the orthonormal basis. The Fourier coefficients, which are quadratures, are calculated. In this work, we propose a method for forming bases of spaces of internal and boundary states, assigning a scalar product and forming a system of equations that allows one to determine the elastic state of anisotropic bodies. The peculiarity of the solution is that the obtained stresses simultaneously satisfy the conditions both on the boundary of the body and inside the region (volume forces), and they are not a simple superposition of elastic fields. Methods are presented for solving the first and second main problems of mechanics, the contact problem without friction and the main mixed problem of the elasticity theory for transversely isotropic finite solids of revolution that are simultaneously under the influence of volume forces. The given forces are distributed axisymmetrically with respect to the geometric axis of rotation. The solution of the first main problem for a non-canonical body of revolution is given, an analysis of accuracy is carried out and a graphic illustration of the result is given

Axisymmetric elastic equilibrium of finite hollow cylinders with deep grooves

1988 ◽  
Vol 24 (11) ◽  
pp. 1048-1054
Author(s):  
Yu. N. Nemish ◽  
E. I. Kryzhanovskii ◽  
N. M. Bloshko ◽  
D. I. Khoma
Keyword(s):  
Elastic Equilibrium ◽  
Hollow Cylinders
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