Axial Loading of Bonded Rubber Blocks

2002 ◽  
Vol 69 (6) ◽  
pp. 836-843 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme ◽  
M. J. C. Gover
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Closed Form ◽  
Cross Section ◽  
Shape Factor ◽  
Circular Cross Section ◽  
Axial Loading ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Lateral Profile

Axially loaded rubber blocks of long, thin rectangular and circular cross section whose ends are bonded to rigid plates are studied. Closed-form expressions, which satisfy exactly the governing equations and conditions based upon the classical theory of elasticity, are derived for the total axial deflection and stress distribution using a superposition approach. The corresponding relations are presented for readily calculating the apparent Young’s modulus, Ea, the modified modulus, Ea′, and the deformed lateral profiles of the blocks. From these, improved approximate elementary expressions for evaluating Ea and Ea′ are deduced. These estimates, and the precisely found values, agree for large values of the shape factor, S, with those previously suggested, but also fit the experimental data more closely for small values of S. Confirmation is provided that the assumption of a parabolic lateral profile is invalid for small values of S.

Axial Loading of Annular Bonded Rubber Blocks

2003 ◽  
Vol 76 (5) ◽  
pp. 1194-1211 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme ◽  
M. J. C. Gover
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Closed Form ◽  
Cross Section ◽  
Classical Theory ◽  
Cross Sections ◽  
Axial Loading ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Annular Cross Section

Abstract Closed-form expressions are derived using a superposition approach for the axial deflection and stress distribution of axially loaded rubber blocks of annular cross-section, whose ends are bonded to rigid plates. These satisfy exactly the governing equations and conditions based upon the classical theory of elasticity. Readily calculable relationships are derived for the corresponding apparent Young's modulus, Ea, and the modified modulus, Ea′, and their numerical values are compared with the available experimental data. Elementary expressions for evaluating Ea and Ea′ approximately are deduced from these, in forms which are closely analogous to those given previously for blocks of circular and long, thin rectangular cross-sections. The profiles of the deformed lateral surfaces of the block are discussed and it is confirmed that the assumption of parabolic lateral profiles is not valid generally.

Elastic–plastic deformation and residual stresses in helical springs

2019 ◽  
Vol 16 (3) ◽  
pp. 448-475
Author(s):  
Vladimir Kobelev
Keyword(s):  
Residual Stresses ◽  
Closed Form ◽  
Cross Section ◽  
Circular Cross Section ◽  
Content Type ◽  
Closed Form Solutions ◽  
Helical Springs ◽  
First Case ◽  
Setting Process ◽  
The Wire

Purpose The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs. Design/methodology/approach For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis. Findings For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws. Research limitations/implications The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses. Practical implications The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions. Social implications The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs. Originality/value Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation

2005 ◽  
Vol 363 (1832) ◽  
pp. 1551-1571 ◽  
Author(s):  
Shiva P Pudasaini ◽  
Yongqi Wang ◽  
Kolumban Hutter
Keyword(s):  
Numerical Simulation ◽  
Cross Section ◽  
Circular Cross Section ◽  
Hyperbolic Partial Differential Equations ◽  
Finite Mass ◽  
Governing Equations ◽  
Cross Sectional ◽  
Variation Diminishing ◽  
Cross Sectional Profile ◽  
Sectional Profile

This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech. 495 , 193–208). The intention was to be able to describe the flow of a finite mass of snow, gravel, debris or mud, down a curved and twisted corrie of nearly arbitrary cross-sectional profile. The governing equations for the distribution of the avalanche thickness and the topography-parallel depth-averaged velocity components are a set of hyperbolic partial differential equations. They are solved for different topographic configurations, from simple to complex, by applying a high-resolution non-oscillatory central differencing scheme with total variation diminishing limiter. Here we apply the model to a channel with circular cross-section and helical talweg that merges into a horizontal channel which may or may not become flat in cross-section. We show that run-out position and geometry depend strongly on the curvature and twist of the talweg and cross-sectional geometry of the channel, and how the topography is shaped close to run-out zones.

Torsion of Composite Elastic Bars of Arbitrary Cross Section

1968 ◽  
Vol 90 (3) ◽  
pp. 435-440 ◽  
Author(s):  
E. M. Sparrow ◽  
H. S. Yu
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Elastic Properties ◽  
Cross Section ◽  
Excellent Agreement ◽  
Solution Method ◽  
Circular Cross Section ◽  
High Accuracy ◽  
Arbitrary Cross Section ◽  
Closed Form Solutions

A method of analysis is presented for determining closed-form solutions for torsion of inhomogeneous prismatic bars of arbitrary cross section, the inhomogeneity stemming from the layering of materials of different elastic properties. It is demonstrated that the solution method is very easy to apply and provides results of high accuracy. As an application, solutions are obtained for the torsion of a bar of circular cross section consisting of two materials separated by a plane interface. The results are compared with those of various limiting cases and excellent agreement is found to exist. Among the limiting cases, an exact solution was derived by Green’s functions for the problem in which the interface between the materials coincides with a diameter of the circular cross section.

Design of Circular Cross-Section Corner-Filleted Flexure Hinges for Three-Dimensional Compliant Mechanisms

2002 ◽  
Vol 124 (3) ◽  
pp. 479-484 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Jeffrey S. N. Paine
Keyword(s):  
Cross Section ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Axial Loading ◽  
Flexure Hinge ◽  
Flexure Hinges ◽  
Element Simulation ◽  
The Right

The paper introduces the circular cross-section corner-filleted flexure hinges as connectors in three-dimensional compliant mechanism applications. Compliance factors are derived analytically for bending, axial loading and torsion. A circular cross-section corner-filleted flexure hinge belongs to a domain delimited by the cylinder (no fillet) and the right circular cross-section flexure hinge (maximum fillet radius). The analytical model predictions are confirmed by finite element simulation and experimental measurements. The circular cross-section corner-filleted flexure hinges are characterized in terms of their compliance, precision of rotation and stress levels.

Stresses in a Reinforced Monocoque Cylinder Under Concentrated Symmetric Transverse Loads

1944 ◽  
Vol 11 (4) ◽  
pp. A235-A239
Author(s):  
N. J. Hoff
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Cross Section ◽  
Maximum Shear Stress ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Normal Stress Distribution ◽  
Transverse Loads ◽  
Conventional Analysis ◽  
Analysis Application

Abstract The stresses in the sheet covering, stringers, and rings of a reinforced monocoque cylinder of circular cross section are calculated for the case of a loading consisting of concentrated symmetric forces applied to the rings in the planes of the rings. The conventional assumptions of a linear normal stress distribution and a corresponding shear-stress distribution in the bent cylinder are replaced by a least-work analysis. Application of the theory to the numerical example of a cantilever monocoque cylinder yields a maximum shear stress in the sheet covering and a maximum bending moment in the ring amounting to 900 per cent and 33 per cent, respectively, of the values obtained by the conventional analysis.

Stability of circular-section bonded rubber blocks subjected to compression and bending

2006 ◽  
Vol 220 (10) ◽  
pp. 1489-1496
Author(s):  
J M Horton ◽  
G E Tupholme
Keyword(s):  
Cross Section ◽  
Critical Loads ◽  
Circular Cross Section ◽  
Numerical Data ◽  
Theory Of Elasticity ◽  
Circular Section ◽  
Typical Representative ◽  
Parallel Surfaces ◽  
Explicit Representations ◽  
Implicit Expressions

Rubber blocks of circular cross-section whose ends are bonded to rigid plates are studied under compression between either flat parallel surfaces or central parallel knife-edges. Implicit expressions are derived exactly in each case for the critical values of the loads at which the blocks begin to bend, based upon the classical theory of elasticity. Convenient very good approximate explicit representations are additionally deduced for these first critical loads. Some typical representative numerical data are compared and presented graphically in both situations.

scholarly journals Accounting for the Scale Factor in Determining the Compressed Concrete Strength of Concrete-Filled Steel Tube Elements

2019 ◽  
Vol 278 ◽  
pp. 03003
Author(s):  
Elvira P. Chernyshova ◽  
Vladislav E. Chernyshov
Keyword(s):  
Experimental Data ◽  
Axial Compression ◽  
Cross Section ◽  
Concrete Strength ◽  
Circular Cross Section ◽  
Steel Tube ◽  
Scale Factor ◽  
Concrete Filled Steel Tube ◽  
New Formula

The published experimental data on the influence of the concrete samples dimensions on their strength under axial compression had been analyzed in the article. The mechanism of this influence is revealed from the positions of strength statistical theories. The known dependences are given and a new formula is proposed for taking into account the scale factor in determining the strength of compressed concrete. An algorithm for calculating the strength of centrally compressed concrete-filled steel tube elements (CFSTE) with a circular cross-section taking into account the scale factor is shown.

Analysis of Axially Loaded Annular Shells With Applications to Welded Bellows

1960 ◽  
Vol 82 (3) ◽  
pp. 741-753 ◽  
Author(s):  
M. Hetenyi ◽  
R. J. Timms
Keyword(s):  
Experimental Data ◽  
General Solution ◽  
Cross Section ◽  
Circular Cross Section ◽  
Radius Of Curvature ◽  
Approximate Design ◽  
Axial Forces ◽  
The Mean ◽  
Maximum Stresses ◽  
Toroidal Shells

A method is presented for the calculation of stresses and deflections in ring-shaped shells of circular cross section, subjected to axial forces. The solution is derived without the restriction imposed for toroidal shells by previous investigators, that the radius of curvature of the cross section is to be small in comparison with the mean radius of the torus. The range of applicability of the method is extended hereby to include the slightly arched convolutions used in the construction of welded bellows. By a rational reduction of the general solution approximate design formulas are obtained for the maximum stresses and deflections in bellows under axial forces and the calculated values are compared with experimental data.

Secondary Flows in Eccentric-Annular Tubes

2019 ◽  
Author(s):  
Mario Letelier ◽  
Dennis A. Siginer ◽  
Diego L. Almendra ◽  
Juan Stockle
Keyword(s):  
Cross Section ◽  
Shape Factor ◽  
Vortical Structure ◽  
Circular Cross Section ◽  
Weissenberg Number ◽  
Secondary Flows ◽  
Material Parameters ◽  
Annular Cross Section ◽  
Nonlinear Viscoelastic ◽  
Transversal Flow

Abstract In this paper, transversal flow field of nonlinear viscoelastic fluids abiding by the modified-Phan-Thien-Tanner (MPTT) constitutive model in straight tubes of eccentric-annular cross-section is investigated. An analytical solution is developed based on an asymptotic expansion in terms of the Weissenberg number coupled with the shape factor method a one-to-one mapping taking the circular cross-section into the eccentric annular cross section. The analysis reveals the formation of transversal flows due to elasticity and to the eccentricity parameter. The number of vortices in the cross-section depends on the ratio of the diameters in addition to the eccentricity parameter. The effect of these parameters on the vortical structure is explored for different values of the material parameters.

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