Saint-Venant torsion of orthotropic bars with inhomogeneous rectangular cross section

This work presents an exact solution of the Saint-Venant torsion of a straight bar with an orthotropic and inhomogeneous rectangular cross section whose material properties obey the exponential law in one direction. An approximate solution is also obtained for the material properties being arbitrarily distributed in one direction by using a layerwise model, in which the inhomogeneous rectangle is simulated by a composite rectangle composed of multiple rigidly connected homogeneous rectangular regions. The warping function, stresses and torsional rigidity are analytically expressed in terms of Fourier series for both solutions, in which the hyperbolic functions are not directly employed to avoid numerical difficulties. Some numerical examples are finally presented to verify the proposed method and the parametrical study is also performed.     

Method for determining the thermophysical characteristics of orthotropic bodies

The solution for the inverse coefficient problem of heat conduction for an orthotropic body is proposed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 4, pp. 596–600, April, 1988.     

Certain asymptotic relations for the dynamic moduli in superposed oscillatory shear

We consider the incompressible BKZ fluid subjected to small in-line and transverse oscillations superposed on steady shearing flow. Investigations are made of the asymptotic behavior of the storage and loss moduli at ultrasonic frequencies. Asymptotic formulae for both shear and normal stress moduli are obtained. We also point out the relationships between the ultrasonic storage moduli and acceleration waves.     

Differences in shear strengths of orthotropic bodies

Summary The failure strengths of anisotropic bodies and especially those of fiber reinforced materials are generally studied at the principal directions of their strength and loading of the bodies. For the most reliable criteria, based on failure functions having the form of a general tensorial polynomial, the modes of failure of anisotropic (orthotropic, transversely isotropic) bodies were studied primarily on the principal stress (₁, ₂, ₃). The elliptic paraboloid failure surface, (EPFS), being one of them, was based on the phenomenological assumption that even the anisotropic media do not fail under the influence of any hydrostatic pressure superimposed with an elementary loading, taking care of the anisotropy.Modes of failure of orthotropic media under the influence of shear loading, which are very important especially for the transfer of loading between fibers and matrix in a single lamina, as well as in the theory of failure of laminates, was up-to-now neglected.In this paper the effect of shear is studied for transversely isotropic and orthotropic materials. The dependence of the pure shear loading on the sign of shear, as well as on the parameters of anisotropy of the medium, is established. Interesting results are revealed, having a direct application on a well-founded theory of strength of laminates.     

Part-circular surface cracks in round bars under tension,bending and twisting

Circular-fronted cracks in round bars subject to tension, bending and twisting are considered. Numerical expressions are given allowing the calculation of stress intensity factors K _I, K _II, K _III at every point on the crack front for a wide range of crack geometries. Comparisons are made with analytical, experimental and numerical results abailable in the literature. Crack shapes satisfying the iso-K _I criterion are also determined, making it possible to investigate the problem of crack growth behaviour under tensile or bending fatigue loads.     

Locking-free finite elements for shear deformable orthotropic thin-walled beams

Numerical models for finite element analyses of assemblages of thin-walled open-section profiles are presented. The assumed kinematical model is based on Timoshenko–Reissner theory so as to take shear strain effects of non-uniform bending and torsion into account. Hence, strain elastic-energy coupling terms arise between bending in the two principal planes and between bending and torsion. The adopted model holds for both isotropic and orthotropic beams. Several displacement interpolation fields are compared with the available numerical examples. In particular, some shape functions are obtained from ‘modified’ Hermitian polynomials that produce a locking-free Timoshenko beam element. Analogously, numerical interpolation for torsional rotation and cross-section warping are proposed resorting to one Hermitian and six Lagrangian formulation. Analyses of beams with mono-symmetric and non-symmetric cross-sections are performed to verify convergence rate and accuracy of the proposed formulations, especially in the presence of coupling terms due to shear deformations, pointing out the decay length of end effects. Profiles made of both isotropic and fibre-reinforced plastic materials are considered. The presented beam models are compared with results given by plate-shell models. Copyright © 2007 John Wiley & Sons, Ltd.     

Material tailoring and moduli homogenization for finite twisting deformations of functionally graded Mooney-Rivlin hollow cylinders

We analytically analyze finite plane strain twisting deformations of a hollow cylinder made of an isotropic and inhomogeneous Mooney-Rivlin material with material moduli varying in the radial direction. The cylinder is deformed by applying either tangential tractions on the inner surface and tangential displacements on the outer surface or vice versa. The radial variation of the moduli is found that will minimize the tangential displacement of the bounding surface where tangential traction is specified. Furthermore, the modulus of a homogeneous neo-Hookean cylinder is found that is energetically equivalent to the inhomogeneous cylinder.     

Effective Young's moduli of quasilayered bars using bar resonance frequencies

Rectangular-bar specimens with nonhomogeneous (quasilayered) porosity distribution were prepared from an iron powder. Using these specimens, differences were observed in effective Young's modulus values determined experimentally by means of specimen flexural vibrations with bending in the plane of quasilayers and in the plane perpendicular to quasilayers. To account for these differences, general expressions for resonance frequencies of flexural vibrations of model quasilayered bars were derived in a theoretical way. The model quasilayered bar means a prismatic bar of rectangular cross section, with material Young's modulus varying continuously only along one of transverse directions. Substituting theoretical resonance frequencies, instead of experimentally measured ones, into the routine evaluation procedure of the dynamical resonant method, theoretical values of effective Young's modulus were calculated. In majority of theoretically investigated simple model examples with lowered modulus of surface regions the effective modulus determined by means of the frequency of sample flexural vibration perpendicular to layers is lower than the effective modulus determined by means of the vibration parallel to the layers. These theoretical results explain qualitatively the effective modulus differences obtained for our quasilayered samples in an experimental way.     

Appraisement of planar,bending and twisting cracks in 3D with isotropic and orthotropic damage models

This paper discusses the modeling of cracking in quasi-brittle materials using isotropic and orthotropic damage constitutive laws. A mixed strain/displacement finite element formulation is used, taking advantage of its enhanced precision and its enforced interelemental strain continuity. On the one hand, this formulation avoids the spurious mesh dependency of the computed solution associated to standard elements and does not require the use of tracking techniques. On the other hand, it greatly alleviates the spurious stress locking associated to the use of orthotropic models on standard finite elements. The performance of several isotropic and orthotropic damage constitutive laws is assessed through an extensive comparison with analytical solutions, numerical tests and experimental evidence reported in the literature. The behavior of the different damage models in terms of crack surface, collapse mechanism and force displacement curves is investigated performing 3D analyses in several conditions including Mode I, Mixed Mode and Mode III fracture. When performing the appraisement of planar, bending and twisting cracks, the enhanced accuracy of the mixed formulation allows for a distinct assessment of the several damage models considered. Aspects related to the behavior of damage models, such as the influence of Poisson’s ratio, the shape of the damage surface and the adoption of isotropic and orthotropic models are investigated and noteworthy conclusions are drawn.     

Neural network modelling for shear strength of concrete members reinforced with FRP bars

This paper investigates the feasibility of using artificial neural networks (NNs) to predict the shear capacity of concrete members reinforced longitudinally with fibre reinforced polymer (FRP) bars, and without any shear reinforcement. An experimental database of 138 test specimens failed in shear is created and used to train and test NNs as well as to assess the accuracy of three existing shear design methods. The created NN predicted to a high level of accuracy the shear capacity of FRP reinforced concrete members.Garson index was employed to identify the relative importance of the influencing parameters on the shear capacity based on the trained NNs weightings. A parametric analysis was also conducted using the trained NN to establish the trend of the main influencing variables on the shear capacity. Many of the assumptions made by the shear design methods are predicted by the NN developed; however, few are inconsistent with the NN predictions.     

Displacement discontinuity formulation for modeling cracks in orthotropic shear deformable plates

A displacement discontinuity formulation is presented for modeling cracks in orthotropic Reisnner plates. Fundamental solutions for displacement discontinuity are derived for the first time using a Fourier transform method. Boundary integral equations are presented in terms of discontinuity rotations on the crack surfaces for opening mode problems. As the fundamental solutions have singularity of O (1/r ²), Chebyshev polynomials of the second kind are used to evaluate the integral equations. By solving for coefficients of the Chebyshev polynomials, the stress intensity factors at the crack tips are obtained directly. Comparisons are made with solutions using the finite element method to demonstrate that the displacement discontinuity method is an efficient and accurate method for solving crack problems in orthotropic Reissner plates.     

An orthotropic shear specimen in computerised stress analysis

The Iosipescu specimen, invented for investigation of shear strength of orthotropic materials, in its original shape did not meet expectations, producing a complex stress pattern. In the present investigation a improved shape of the specimen is presented, which depends sharply on tested material properties. Resulting relations both for the shape of the specimen (1) and calculation of shear strength (2) are given. The research has shown a strong dependence of the shape of the specimen on elastic properties of the tested material.     

Equilibrium equations for plane slender bars undergoing large shear deformations

Summary Equilibrium equations for plane slender bars are derived using the principles of Continuum Solid Mechanics. Large shear deformations are accounted for. The equations are derived in an explicit form, yielding upon introduction of a constitutive law (not given here) a system of differential equations to be integrated on the undeformed length. Within certain limitations, the equations, derived in an exact form, incorporate expressions for finite strain. The stress distribution along a deformed section is studied.

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Gleichgewichtsbedingungen ebener schlanker Stäbe bei großen Schubverformungen

Zusammenfassung Gleichgewichtsbedingungen ebener schlanker Stäbe werden unter Verwendung der Sätze der Kontinuumstechnik hergeleitet. Große Schubverformungen werden berücksichtigt. Die Gleichungen werden in expliziter Form angegeben, sie führen mit einem hier nicht angegebenen Werkstoffgesetz auf ein System von Differentialgleichungen. Mit gewissen Einschränkungen schließen diese in exakter Form angegebenen Gleichungen die für endliche Verformungen ein. Die Spannungsverteilung in einem verformten Abschnitt wird untersucht.

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Notation position vector of material point in undeformed state - position vector of material point in deformed state - displacement vector of material point - u displacement component inx-direction - w displacement component inz-direction - covariant base vector in deformed state (i=1,2) - G _ij metric tensor in deformed state - g _ij metric tensor in undeformed state - slope of geometrical axis (elastic line) - shear deformation angle - rotation of plane section of bar - K curvature of geometrical axis - curvature of geometrical axis due to bending only - unit tangent vector to geometrical axis - unit normal vector to geometrical axis - _(ij) Lagrangian strain tensor - ^ij stress tensor - ^(ij) physical stress tensor - N normal force (parallel to geometrical axis) acting on plane section - S shear force (parallel to deformed section) acting on plane section - M bending moment - H horizontal external force acting on plane section - V vertical external force acting on plane section - vector of conservative body forces uniformly distributed along geometrical axis - f _x component of inx-direction - f _z component of inz-direction - unit normal vector to plane section - F _i force component on distorted plane section - F _(i) physical force component on distorted plane section - F _ij component ofF ⁱ inj-direction - inclination angle ofF ¹¹ toF ¹ (see Fig. 8) With 8 Figures     

Anti-plane shear problem for an edge crack in a finite orthotropic plate

The problem of an edge crack in a finite orthotropic plate under anti-plane shear is considered. The boundary collocation method is used to calculate the mode III stress intensity factor (SIF). For the case in which the material is isotropic, the present results agree very well with those obtained by using the integral equation method. Furthermore, the method can be extended readily for general cases with arbitrary geometrical and boundary loading conditions and material properties.     

Evolution of ultrasonic velocity and dynamic elastic moduli with shear strain in granular layers

Ultrasonic wave transmission has been used to investigate processes that influence frictional strength, strain localization, fabric development, porosity evolution, and friction constitutive properties in granular materials under a wide range of conditions. We present results from a novel technique using ultrasonic wave propagation to observe the evolution of elastic properties during shear in laboratory experiments conducted at stresses applicable to tectonic faults in Earth’s crust. Elastic properties were measured continuously during loading, compaction, and subsequent shear using piezoelectric transducers fixed within shear forcing blocks in the double-direct-shear configuration. We report high-fidelity measurements of elastic wave properties for normal stresses up to 20 MPa and shear strains up to 500 % in layers of granular quartz, smectite clay, and a quartz-clay mixture. Layers were 0.1–1 cm thick and had nominal contact area of $5 \mathrm{cm} \!\times \! 5 \mathrm{cm}$ . We investigate relationships among frictional strength, granular layer thickness, and ultrasonic wave velocity and amplitude as a function of shear strain and normal stress. For layers of granular quartz, P-wave velocity and amplitude decrease by 20–70 % after a shear strain of 0.5. We find that P-wave velocity increases upon application of shear load for layers of pure clay and for the quartz-clay mixture. The P-wave amplitude of pure clay and quart-clay mixtures first decreases by $\sim $ 50 and 30 %, respectively, and then increases with additional shear strain. Changes in P-wave speed and wave amplitude result from changes in grain contact stiffness, crack density and disruption of granular force chains. Our data indicate that sample dilation and shear localization influence acoustic velocity and amplitude during granular shear.     

Young's and shear moduli of ceramic particle filled polyethylene

Tensile and shear properties were determined for hydroxyapatite reinforced poly-ethylene composites (HAPEXTM) for medical applications. Properties of talc or alumina filled polyethylene were also obtained. Hydroxyapatite particles of different median sizes and morphologies were used to reinforce the polyethylene. Furthermore, chemical coupling of hydroxyapatite to polyethylene was investigated. The obtained results are discussed in terms of possible use as orthodontic materials. © 1998 Kluwer Academic Publishers     

Investigation on the shear moduli and damping ratios of silica gel

Silica gel, a typical desiccant widely used in industry to absorb moisture, is a porous inert colloid with different sizes in beaded or angular shape. The mixture of silica gel and pore fluid of matched refractive index has been used as transparent media to mimic the behavior of sand. Previous studies have been focused on the static properties of transparent soil. In the current study, the dynamic properties of silica gel, including small-strain shear modulus and damping ratio, were examined through a series of resonant column tests. Four different gradations of silica gel were tested under confining pressures of 50, 100, 200, 300, and 400 kPa. The test results fully displayed the dynamic behavior of the silica gel. The test data also revealed that silica gel has a certain similar dynamic behavior as those of natural soils. With the test findings, silica gel could be used as a surrogate for natural soils in dynamic transparent soil model tests.