Torsion of Cylinders With Shape Intrinsic Orthotropy

1987 ◽  
Vol 54 (4) ◽  
pp. 778-782 ◽  
Author(s):  
S. C. Cowin
Keyword(s):  
Shear Modulus ◽  
Tangent Plane ◽  
Material Symmetry ◽  
Torsion Problem ◽  
Growth Rings ◽  
Wood Tissue ◽  
Isotropic Cylinder ◽  
Linear Elastic ◽  
Elastic Cylinders ◽  
Tangential Directions

Shape intrinsic orthotropy may be thought of as the type of elastic material symmetry possessed by the wood tissue of a tree. Each year’s new growth rings form a laminate around a central core. The axes of material symmetry lie in the directions tangent and normal to the growth rings or laminates and along the axis of the cylinder. Let Gtz denote the linear elastic orthotropic shear modulus associated with the axial and tangential directions, the tangent plane of a laminate. It is shown here that, for a certain class of elastic cylinders with shape intrinsic orthotropy, the solution to the torsion problem is the same as the solution to the torsion problem for the isotropic cylinder of the same shape if the isotropic shear modulus G were replaced by the orthotropic shear modulus Gtz.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

scholarly journals Reconstructing the shear modulus contrast of linear elastic and isotropic media in quasi-static ultrasound elastography

2021 ◽  
Author(s):  
Elisabeth Brusseau ◽  
Lorena Petrusca ◽  
Elie Bretin ◽  
Pierre Millien ◽  
Laurent Seppecher
Keyword(s):  
Shear Modulus ◽  
Ultrasound Elastography ◽  
Linear Elastic ◽  
Isotropic Media

Moving Morphable Inclusion Approach: An Explicit Framework to Solve Inverse Problem in Elasticity

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Yue Mei ◽  
Zongliang Du ◽  
Dongmei Zhao ◽  
Weisheng Zhang ◽  
Chang Liu ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Shear Modulus ◽  
New Paradigm ◽  
Elastic Solids ◽  
Shear Moduli ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Inverse Approach ◽  
Optimization Parameters ◽  
Very High

Abstract In this work, we present a novel inverse approach to characterize the nonhomogeneous mechanical behavior of linear elastic solids. In this approach, we optimize the geometric parameters and shear modulus values of the predefined moving morphable inclusions (MMIs) to solve the inverse problem. Thereby, the total number of the optimization parameters is remarkably reduced compared with the conventional iterative inverse algorithms to identify the nonhomogeneous shear modulus distribution of solids. The proposed inverse approach is tested by multiple numerical examples, and we observe that this approach is capable of preserving the shape and the shear moduli of the inclusions well. In particular, this inverse approach performs well even without any regularization when the noise level is not very high. Overall, the proposed approach provides a new paradigm to solve the inverse problem in elasticity and has potential of addressing the issue of computational inefficacy existing in the conventional inverse approaches.

Modal Loss Factors of Thick Three-Layer Cylinders With Viscoelastic Core

1995 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Yanfei Jiang
Keyword(s):  
Shear Modulus ◽  
Natural Frequencies ◽  
Core Material ◽  
Constrained Layer Damping ◽  
Material Damping ◽  
The Core ◽  
Linear Viscoelastic Material ◽  
Wide Range ◽  
Elastic Cylinders ◽  
Loss Factors

Abstract An analytical solution to the free vibration of a damped three-layer thick sandwiched cylinder of infinite extend is presented. The constrained layer damping is accomplished by sandwiching a linear viscoelastic material between two isotropic elastic cylinders with the same properties. The governing equation is derived based on elasto-dynamic theory utilizing complex elastic moduli. Dimensionless natural frequencies and modal loss-factors are extracted. Special case for a three-layer sandwiched cylinder with similar elastic properties is considered. The computed dimensionless frequencies are compared with previously established results. The comparison indicates the validity of the proposed mathematical procedures. In addition, the effects of various values of material damping for the core layer and ratio of the core shear modulus to the shear modulus of the elastic cylinders on natural frequencies and modal loss-factors are studied. For a given configuration, modal information for the first two modes for n = 0, 1, 2, 3 and 4 are presented for a wide range of core material damping and G2/G1 ratio.

TORSION OF FUNCTIONALLY GRADED OPEN-SECTION MEMBERS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250020 ◽  
Author(s):  
M. R. HEMATIYAN ◽  
E. ESTAKHRIAN
Keyword(s):  
Shear Modulus ◽  
Cross Section ◽  
Analytical Method ◽  
Functionally Graded ◽  
Torsion Problem ◽  
Uniform Thickness ◽  
Analytical Formulation ◽  
Material Parameters ◽  
Open Section ◽  
Open Cross Section

There exist some approximate analytical methods for torsion analysis of homogeneous open cross-section members; however, no analytical formulation has been presented for solving a torsion problem of inhomogeneous open cross-section members yet. In this paper, an approximate analytical method for the torsion analysis of thin- to moderately thick-walled functionally graded open-section members with uniform thickness is presented. The shear modulus of rigidity is assumed to have a variation across the thickness. The cross-section is decomposed into some straight, curved and end segments. The torsion problem is then solved in each segment considering some appropriate approximations. By presenting three examples, accuracy of the presented method with respect to thickness, corner radius, and material parameters are investigated. The results show that the proposed method is useful for torsion analysis of thin- to moderately thick-walled functionally graded open-section members.

Effects of gravel content on liquefaction resistance and its assessment considering deformation characteristics in gravel – mixed sand

2019 ◽  
Vol 56 (12) ◽  
pp. 1743-1755
Author(s):  
Hirofumi Toyota ◽  
Susumu Takada
Keyword(s):  
Shear Modulus ◽  
Small Strain ◽  
Bender Element ◽  
Liquefaction Resistance ◽  
Liquefaction Potential ◽  
Shear Moduli ◽  
Linear Elastic ◽  
Undisturbed Samples ◽  
Strong Relation ◽  
Secant Shear Modulus

Many reports describe overestimation of liquefaction resistance based on sounding data related to ground materials containing coarse particles such as gravel and cobbles. Better methods of liquefaction potential estimation must be developed using investigation data other than those from sounding. Gathering perfect and undisturbed samples is difficult, but using seismic methods such as PS logging might be effective for assessing liquefaction potential. For this study, bender element (BE) tests and local small strain (LSS) tests were conducted, respectively, to measure the dynamic and static shear moduli of gravel – mixed sand specimens. Subsequently, relations between liquefaction strength and secant shear moduli were examined to provide reliable estimation of liquefaction in gravel – mixed sand. Although the liquefaction resistance increased considerably with overconsolidation, the initial shear modulus exhibited only a slight change with the same overconsolidation. The experimentally obtained results elucidated that the important shear strain level, for which secant shear modulus has a strong relation with liquefaction strength, was not a linear elastic region of 0.001%: it was about 0.01%.

scholarly journals Formulation of a Yield Surface for Sand Based on the Elastic Threshold Strain

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Sang Inn Woo
Keyword(s):  
Shear Modulus ◽  
Yield Surface ◽  
Void Ratio ◽  
Yield Function ◽  
Empirical Expression ◽  
Linear Elastic ◽  
Threshold Strain ◽  
Toyoura Sand ◽  
Yield Surfaces ◽  
Elastic Threshold

The present study proposes a rigorous expression of a yield function for sand based on the linear elastic threshold strain concept and empirical expression for the maximum shear modulus. The new yield function was calibrated for Toyoura sand. The calibration results show that the proposed yield surfaces are nonlinear curves that depend on the void ratio of sand in the p′-q plane, whereas the linear lines have been adopted in the bounding surface modeling of sand. This study also found that elliptic yield surfaces are the best fitted with the proposed yield surface and they can be used as alternatives to the proposed yield surface under the undrained shearing where the void ratio (or density) of sand is fixed.

Contact Stresses Between Elastic Cylinders: A Comprehensive Theoretical and Experimental Approach

1981 ◽  
Vol 103 (1) ◽  
pp. 40-45 ◽  
Author(s):  
M. J. Hartnett ◽  
J. W. Kannel
Keyword(s):  
Experimental Approach ◽  
Three Dimensional ◽  
Contact Stresses ◽  
Linear Elastic ◽  
Theoretical Predictions ◽  
Elastic Cylinders ◽  
Force Displacement ◽  
Contact Pressures ◽  
Two Bodies ◽  
Theory And Experiments

The purpose of the paper has been to present a comparison of theoretical predictions and experimental data for contact stresses between two bodies lubricated in contact. The theoretical analysis is based on a three-dimensional linear elastic solution to the problem and combines Boussinesq force-displacement relationships for a half-space with a modified flexibility method. The experimental approach involves the direct measurement of contact pressures between profiled rollers using a thin-film pressure transducer. Pressure measurements and predictions were made for three roller designs under various conditions of loads and misalignments. The agreement between theory and experiments is very good.

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