Effect of Stress-Free Edges in Plane Shear of a Flat Body

1950 ◽  
Vol 17 (4) ◽  
pp. 349-352
Author(s):  
W. T. Read
Keyword(s):  
Pure Shear ◽  
Upper And Lower Bounds ◽  
Tangential Displacement ◽  
Slide Rule ◽  
Plane Shear ◽  
Numerical Work ◽  
Tangential Stiffness ◽  
State Of Stress ◽  
Energy Relations ◽  
Rectangular Body

Abstract This paper determines the tangential stiffness of a flat rectangular body, or shear pad, with a uniform relative tangential displacement on the upper and lower surfaces. The state of stress differs from pure shear in that the edges are stress-free. The correction to the stiffness in pure shear is obtained as a function of Poisson’s ratio and the length-to-thickness ratio. The paper also illustrates the power of energy methods in furnishing accurate approximations with a small amount of numerical work when only over-all quantities, such as stiffness, are investigated. By manipulating energy relations and using the Prager-Synge approximate method a few hours of slide-rule computation was sufficient to determine both upper and lower bounds for the stiffness.

Effect of Stress-Free Edges in Plane Shear of a Rectangular Orthotropic Region

1978 ◽  
Vol 45 (2) ◽  
pp. 307-312 ◽  
Author(s):  
S. Nair
Keyword(s):  
Lower Bounds ◽  
Elastic Problem ◽  
Upper And Lower Bounds ◽  
Tangential Displacement ◽  
Stiffness Coefficient ◽  
Shearing Force ◽  
Plane Shear ◽  
Zero Stresses ◽  
Plane Elastic Problem ◽  
Free Edges

The plane elastic problem of a rectangular orthotropic region is considered; subject to the boundary conditions of prescribed equal and opposite tangential displacements and zero normal displacements on the upper and lower edges and zero stresses on the remaining edges. The effect of the stress-free edges on the stiffness coefficient relating the tangential displacement and the corresponding shearing force is estimated in the form of upper and lower bounds for this coefficient.

Experimental Determination of the Two-Dimensional State of Stress and the Orthotropic Elasticity Coefficients for Coatings

1990 ◽  
Vol 203 ◽  
Author(s):  
Richard J. Farris ◽  
M. A. Maden ◽  
K. Tong
Keyword(s):  
Elastic Constants ◽  
Physical Property ◽  
The State ◽  
Normal Stresses ◽  
Free Standing ◽  
Vibrationally Excited ◽  
Plane Shear ◽  
Plane Normal ◽  
State Of Stress ◽  
The One

ABSTRACTThe state of stress for a uniform coating away from the edges reduces to that of plane stress, two in-plane normal stresses, and an in-plane shear stress. For this state, the interface between the coating and the substrate is totally stress free. Since the substrate and the coating are not interacting mechanically, an internal section of the substrate can be removed creating a tensioned drum-like membrane without altering the stress state. Holographic interferometry of vibrationally excited membranes is used to evaluate the stress. Using this technique, up to thirty vibrational modes can be obtained. This high degree of redundancy enables one to determine the one shear and two normal stresses that act in the plane of the coating. The only physical property requires is the coating density. The density is obtained from commonly reported literature values. Simple variations on the membrane vibration scheme, e.g., cutting the membrane to create a uniaxially tensioned ribbon, enables one to determine the in-plane Poisson's ratio and shearmodulus.In separate but related experiments on commercially made free-standing films with residual orientation, the above techniques, combined with special free and axially constrainedcompressibility experiments should enable all of the Poisson's ratios and elasticmoduli for an orthotropic material (nine elastic constants) to be determined. Methods for measuring the state of stress and the elastic constants are required to predict the state of stress in complex coating geometries.

A Comparison of Two Microslip Contact Models for Studying the Mechanics of Underplatform Dampers

2018 ◽  
Author(s):  
Chao Xu ◽  
Dongwu Li ◽  
Muzio M. Gola ◽  
Chiara Gastaldi
Keyword(s):  
Friction Coefficient ◽  
Friction Model ◽  
Tangential Displacement ◽  
Tangential Stiffness ◽  
Contact Loads ◽  
Contact Kinematics ◽  
Contact Models ◽  
Friction Models ◽  
Microslip Friction ◽  
Contact Parameters

In turbine blade systems, under-platform dampers are widely used to attenuate excessive resonant vibrations. Subjected to vibration excitation, the components with frictionally constrained interfaces can involve very complex contact kinematics induced by tangential and normal relative motions. To effectively calculate the dynamics of a blade-damper system, contact models which can accurately reproduce the interface normal and tangential motions are required. The large majority of works have been developed using macroslip friction models to model the friction damping at the contact interface. However, for those cases with small tangential displacement where high normal loads are applied, macroslip models are not enough to give accurate results. In this paper two recently published microslip models are compared, between them and against the simple macroslip spring-slider model. The aim is to find to which extent these models can accurately predict damper mechanics. One model is the so called GG array, where an array of macroslip elements is used. Each macroslip element of the GG array is assigned its own contact parameters and for each of them four parameters are needed: normal stiffness, tangential stiffness, normal gap and friction coefficient. The other one is a novel continuous microslip friction model. The model is based on a modification of the original classic IWAN model to couple normal and tangential contact loads. Like the GG array the model needs normal and tangential stiffness, and friction coefficient. Unlike the GG array the model is continuous and, instead of the normal gap required by the GG array, the Modified IWAN model needs a preload value. The two models are here applied to the study of the mechanics of a laboratory under-platform damper test rig. The results from the two models are compared and allow their difference, both for damper mechanics and for the complex-spring coefficients, to be assessed.

Notes and News

1914 ◽  
Vol 6 (3) ◽  
pp. 186-190
Keyword(s):  
Numerical Solution ◽  
Heuristic Method ◽  
Good Deal ◽  
Slide Rule ◽  
Numerical Work ◽  
The Way

Allyn and Bacon have just issued a trigonometry by E. J. Wilczynski which possesses some novel features. It is divided into two parts, the first being devoted to the theoretical and numerical solution of triangles, and the second to the treatment of the functions of the general angle. Other features are, its heuristic method, the way obtuse angles are introduced, carefully selected examples, careful detail in connection with numerical work, wide applications, explanation and use of slide rule, historical notes. It will undoubtedly be tried out with a good deal of interest.

Elastic Properties of Single-Walled Carbon Nanotubes in Axial and Transverse Directions: A First Principles Study

2005 ◽  
Author(s):  
X. Song ◽  
Q. Ge ◽  
S.-C. Yen
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Properties ◽  
First Principles ◽  
Pure Shear ◽  
Small Deformation ◽  
Single Walled Carbon Nanotubes ◽  
Elastic Behavior ◽  
Plane Shear ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

A first principles approach has been employed to study the elastic properties of ten zigzag and seven armchair types of single-walled carbon nanotubes (SWNTs) with the diameter varied from 0.551 to 1.358 nm. The linear elastic behavior of the SWNTs when subject to small deformation is studied by four virtual mechanical experiments: uniaxial strain, uniaxial stress, in-plane pure shear, and in-plane bi-axial tension tests. Assuming that a SWNT be transversely isotropic, a strain energy approach is used to calculate the Young’s moduli in axial and transverse directions, major Posson’s ratio, plain strain bulk, and in-plane shear moduli of the carbon nanotubes. It is found that the elastic constants are insensitive to the tube size, but show a slight dependence upon the helicity. However, the differences in the elastic moduli between zigzag and armchair nanotubes are within 10%.

Variational bounds and overall shear modulus of nano-composites with interfacial damage in anti-plane couple stress elasticity

2019 ◽  
Vol 29 (2) ◽  
pp. 246-271 ◽  
Author(s):  
Hossein M Shodja ◽  
Behdad Hashemian
Keyword(s):  
Shear Modulus ◽  
Couple Stress ◽  
Upper And Lower Bounds ◽  
Interface Conditions ◽  
Interfacial Damage ◽  
Plane Shear ◽  
Size Dependent ◽  
Couple Stress Elasticity ◽  
Nano Fiber ◽  
The Matrix

It is well known that classical continuum theory has certain deficiencies in capturing the size effects and predicting the nanoscopic behavior of materials in the vicinity of nano-inhomogeneities and nano-defects with reasonable accuracy. Couple stress theory which is associated with an internal length scale for the medium is one of the higher order continuum theories capable of overcoming such difficulties. In this work, the problem of a nano-size fiber embedded in an unbounded isotropic elastic body for three different types of interface conditions: perfect, imperfect (partially damaged), and pure sliding (completely damaged) subjected to remote anti-plane loading is examined in this framework. The physically realistic size-dependent elastic fields for the problem will be derived analytically. The discontinuities of the displacement and rotation fields at the imperfect interfaces are assumed to be proportional to the associated reduced traction and couple traction, respectively. The effect of the interfacial damage on the stress field around the nano-fiber is also examined. Subsequently, the elastic field of a single nano-fiber with a damaged interface condition is employed in conjunction with the Mori–Tanaka theory to estimate the size-dependent overall anti-plane shear modulus of such solids enriched with unidirectional circular cylindrical fibers severely damaged at their interfaces with the matrix. The dependence of the anti-plane elastic shear modulus on several important physical parameters such as size, interface conditions, rigidity of the fiber, and the characteristic length of the constituents is analyzed. Finally, a variational approach for the estimation of the upper and lower bounds of anti-plane shear modulus will be given within couple stress elasticity and, moreover, the dependence of the bounds on the matrix–fiber interface damage and the fiber to the matrix rigidity ratio is examined.

Cavitation and the state of stress in a flowing liquid

1998 ◽  
Vol 366 ◽  
pp. 367-378 ◽  
Author(s):  
DANIEL D. JOSEPH
Keyword(s):  
Atmospheric Pressure ◽  
Breaking Strength ◽  
Pure Shear ◽  
Amorphous Solids ◽  
Maximum Tensile Stress ◽  
Liquid Sample ◽  
Principal Stresses ◽  
Flowing Liquid ◽  
State Of Stress ◽  
Cavitation Threshold

The problem of the inception of cavitation is formulated in terms of a comparison of the breaking strength or cavitation threshold at each point in a liquid sample with the principal stresses there. A criterion of maximum tension is proposed which unifies the theory of cavitation, the theory of maximum tensile strength of liquid filaments and the theory of fracture of amorphous solids. Liquids at atmospheric pressure which cannot withstand tension will cavitate when and where tensile stresses due to motion exceed one atmosphere. A cavity will open in the direction of the maximum tensile stress which is 45° from the plane of shearing in pure shear of a Newtonian fluid. Experiments which support these ideas are discussed and some new experiments are proposed.

Interface Parameters of Composite Materials with an Elliptical Cross-Section Fiber Bundle

2013 ◽  
Vol 275-277 ◽  
pp. 1688-1692
Author(s):  
Zhi Min Xie ◽  
Dong Liang Chai ◽  
Hai Wen Du ◽  
Chang Qing Miao
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Fiber Bundle ◽  
Biaxial Tension ◽  
Pure Shear ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Plane Shear ◽  
Elliptical Cross ◽  
Interface Parameters

How to design the interfacial properties is a significant fundamental issue in the field of the composite materials, while little work was concerned with the mechanical design of the interface for the fiber reinforced polymer. In the present work, a fiber bundle embedded in the matrix was described as a transversely isotropic material. Based on the imperfect interface conditions, the interface parameters were derived to satisfy the neutral conditions for the composite materials reinforced by the elliptical cross-section fiber bundle. It is found that the interface parameter is not always associated with the applied loading in the case of the anti-plane shear. In the state of equal-biaxial tension, the normal interface parameter is merely related to the mechanical properties of components except for the shape of the fiber bundle, but independent of the loading magnitude. In the other cases of pure shear and uniaxial tension, the neutral interface does not exist except that the fiber bundle has a circular cross-section. It is also found that the interface parameters can be expressed in the forms similar to that for an isotropic inclusion by using Kolosov constant in the in-plane deformations.

scholarly journals In-plane shear modulus of cross-laminated timber by diagonal compression test

BioResources ◽  
2019 ◽  
Vol 14 (3) ◽  
pp. 5559-5572 ◽  
Author(s):  
Sven Berg ◽  
Jonas Turesson ◽  
Mats Ekevad ◽  
Anders Björnfot
Keyword(s):  
Shear Modulus ◽  
Compression Test ◽  
Pure Shear ◽  
Shear Stiffness ◽  
Least Square ◽  
Compression Tests ◽  
Plane Shear ◽  
Cross Laminated Timber ◽  
Fe Simulations ◽  
Diagonal Compression

Cross-laminated timber (CLT) is an engineered wood material that is used in the construction industry, e.g., for floors, walls, and beams. In cases where CLT-elements are used as shear walls, the in-plane-stiffness is an important property. For non-edge glued CLT, in-plane shear stiffness is lower than for edge-glued CLT. To evaluate the non-edge glued CLT panel’s in-plane shear modulus, the diagonal compression test and finite element (FE) simulation was used. FE-models with both isotropic and orthotropic material models were used to calculate the shear stiffness. The FE models using pure shear loads were used as a reference to determine the correct value of the shear modulus. To verify the FE simulations, diagonal compression tests were conducted on 30 CLT samples. A calibration formula was derived using the least square method for calculation of shear modulus. The formula gave accurate results. The results showed that FE simulations can reproduce the same shear stiffness as tests of non-edge glued 3-layer and 5-layer CLT panels.

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