THE CURVED BAR SUBJECTED TO AN ARBITRARILY DISTRIBUTED LOADING:ANOTHER PARADOX IN THE TWO-DIMENSIONAL THEORY OF ELASTICITY

The problem of the curved bar subjected to an arbitrarily distributed loading on the surfaces r=a and r=b is sp!ved by using the method of complex functions and expanding the boundary conditions at r=a and r=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bat is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 alpha is equal to 2 pi and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox ate obtained. Moreover, the modified classical solution which remains bounded as 2 alpha approaches 2 pi is provided.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

E-Cervix imaging displaying cervical elasticity characteristics of healthy adult nulliparous women at different age groups and different menstrual cycle stages

Objective To observe the cervical elasticity of healthy adult nulliparous women at different age groups and different stages of menstrual cycle with E-Cervix imaging technology.Methods A total of 218 healthy adult nulliparous women who underwent transvaginal ultrasound examination for routine physical examination were retrospectively enrolled,including 103 in follicular phase,78 in ovulation phase and 37 in luteal phase.Cervical canal length(CL)and E-Cervix elasticity parameters were compared among different age groups and different stages of menstrual cycle,including elasticity contrast index(ECI),hardness ratio(HR),cervical internal and external orifice strain values(IOS and EOS)and IOS/EOS ratio.Results No significant difference of CL nor cervical elasticity parameters was detected among healthy adult nulliparous women at different age groups(all P>0.05).There were significant differences of ECI,HR and IOS among different menstrual cycle stages(all P<0.05),among which women in follicular phase had higher ECI and IOS but lower HR than those in luteal phase(all P<0.05).Conclusion No significant difference of cervical elasticity existed among healthy adult nulliparous women at different age groups.Meanwhile,cervical elasticity of healthy adult nulliparous women changed during menstrual cycle,in follicular phase had higher ECI and IOS but lower HR than in luteal phase.

Anti-Plane Elasticity Problem and Mode Ⅲ Crack Problem of Cubic Quasicrystal

The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.

Comparative study on three dynamic modulus of elasticity and static modulus of elasticity for Lodgepole pine lumber

The dynamic and static modulus of elasticity （MOE） between bluestained and non-bluestained lumber of Lodgepole pine were tested and analyzed by using three methods of Non-destructive testing （NDT）, Portable Ultrasonic Non-destructive Digital Indicating Testing （Pundit）, Metriguard and Fast Fourier Transform （FFT） and the normal bending method. Results showed that the dynamic and static MOE of bluestained wood were higher than those of non-bluestained wood. The significant differences in dynamic MOE and static MOE were found between bulestained and non-bluestained wood, of which, the difference in each of three dynamic MOE （Ep. the ultrasonic wave modulus of elasticity, Ems, the stress wave modulus of elasticity and El, the longitudinal wave modulus of elasticity） between bulestained and non-bluestained wood arrived at the 0.01 significance level, whereas that in the static MOE at the 0.05 significance level. The differences in MOE between bulestained and non-bluestained wood were induced by the variation between sapwood and heartwood and the different densities of bulestained and non-bluestained wood. The correlation between dynamic MOE and static MOE was statistically significant at the 0.01 significance level. Although the dynamic MOE values of Ep, Em, Er were significantly different, there exists a close relationship between them （arriving at the 0.01 correlation level）. Comparative analysis among the three techniques indicated that the accurateness of FFT was higher than that of Pundit and Metriguard. Effect of tree knots on MOE was also investigated. Result showed that the dynamic and static MOE gradually decreased with the increase of knot number, indicating that knot number had significant effect on MOE value.

Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.

Correlation between the rock mass properties and maximum horizontal stress:A case study of overcoring stress measurements

Understanding the mechanical properties of the lithologies is crucial to accurately determine the horizontal stress magnitude.To investigate the correlation between the rock mass properties and maximum horizontal stress,the three-dimensional(3D)stress tensors at 89 measuring points determined using an improved overcoring technique in nine mines in China were adopted,a newly defined characteristic parameter C_(ERP)was proposed as an indicator for evaluating the structural properties of rock masses,and a fuzzy relation matrix was established using the information distribution method.The results indicate that both the vertical stress and horizontal stress exhibit a good linear growth relationship with depth.There is no remarkable correlation between the elastic modulus,Poisson's ratio and depth,and the distribution of data points is scattered and messy.Moreover,there is no obvious relationship between the rock quality designation(RQD)and depth.The maximum horizontal stress σ_(H) is a function of rock properties,showing a certain linear relationship with the C_(ERP)at the same depth.In addition,the overall change trend of σ_(H) determined by the established fuzzy identification method is to increase with the increase of C_(ERP).The fuzzy identification method also demonstrates a relatively detailed local relationship betweenσ_H and C_(ERP),and the predicted curve rises in a fluctuating way,which is in accord well with the measured stress data.

THE CALCULATION OF THE VOLUME INTEGRAL IN BEM OF TWO DIMENSIONAL ELASTICITY

In this paper, a method of transforming volume integrals to boundary integrals is given for complicated loadings such as a i(y)x i and b i(x)y i . In the present method the volume integrals are approximately transformed to boundary integrals.

Spectra of Off-diagonal Infinite-Dimensional Hamiltonian Operators and Their Applications to Plane Elasticity Problems

In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.

A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM

The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.

Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks

Uniaxial Compressive Strength (UCS) and modulus of elasticity (E) are the most important rock parameters required and determined for rock mechanical studies in most civil and mining projects. In this study, two mathematical methods, regression analysis and Artificial Neural Networks (ANNs), were used to predict the uniaxial compressive strength and modulus of elasticity. The P-wave velocity, the point load index, the Schmidt hammer rebound number and porosity were used as inputs for both meth-ods. The regression equations show that the relationship between P-wave velocity, point load index, Schmidt hammer rebound number and the porosity input sets with uniaxial compressive strength and modulus of elasticity under conditions of linear rela-tions obtained coefficients of determination of (R2) of 0.64 and 0.56, respectively. ANNs were used to improve the regression re-sults. The generalized regression and feed forward neural networks with two outputs (UCS and E) improved the coefficients of determination to more acceptable levels of 0.86 and 0.92 for UCS and to 0.77 and 0.82 for E. The results show that the proposed ANN methods could be applied as a new acceptable method for the prediction of uniaxial compressive strength and modulus of elasticity of intact rocks.

Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach

In this article, transverse free vibrations of axially moving nanobeams subjected to axial tension are studied based on nonlocal stress elasticity theory. A new higher-order differential equation of motion is derived from the variational principle with corresponding higher-order, non-classical boundary conditions. Two supporting conditions are investigated, i.e. simple supports and clamped supports. Effects of nonlocal nanoscale, dimensionless axial velocity, density and axial tension on natural frequencies are presented and discussed through numerical examples. It is found that these factors have great influence on the dynamic behaviour of an axially moving nanobeam. In particular, the nonlocal effect tends to induce higher vibration frequencies as compared to the results obtained from classical vibration theory. Analytical solutions for critical velocity of these nanobeams when the frequency vanishes are also derived and the influences of nonlocal nanoscale and axial tension on the critical velocity are discussed.

Generalized mixed finite element method for 3D elasticity problems

Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.

Value of shear wave elastography with maximal elasticity in differentiating benign and malignant solid focal liver lesions

BACKGROUND It is important to differentiate benign and malignant focal liver lesions(FLLs)accurately.Despite the wide use and acceptance of shear wave elastography(SWE),its value for assessing the elasticity of FLLs and differentiating benign and malignant FLLs is still investigational.Previous studies of SWE for FLLs used mean elasticity as the parameter to reflect the stiffness of FLLs.Considering the inhomogeneity of tumor stiffness,maximal elasticity(Emax)might be the suitable parameter to reflect the stiffness of FLLs and to differentiate malignant FLLs from benign ones.AIM To explore the value of SWE with Emax in differential diagnosis of solid FLLs.METHODS We included 104 solid FLLs in 95 patients and 50 healthy volunteers.All the subjects were examined using conventional ultrasound(US)and virtual touch tissue quantification(VTQ)imaging.A diagnosis of benign or malignant FLL was made using conventional US.Ten VTQ values were acquired after 10 consecutive measurements for each FLL and each normal liver,and the largest value was recorded as Emax.RESULTS There were 56 cases of malignant FLLs and 48 cases of benign FLLs in this study.Emax of malignant FLLs(3.29±0.88 m/s)was significantly higher than that of benign FLLs(1.30±0.46 m/s,P<0.01)and that of livers in healthy volunteers(1.15±0.17 m/s,P<0.01).The cut-off point of Emax was 1.945,and the area under the curve was 0.978.The sensitivity and specificity of Emax were 92.9%and 91.7%,respectively,higher(but not significantly)than those of conventional US(80.4%for sensitivity and 81.3%for specificity).Combined diagnosis of conventional US and Emax using parallel testing improved the sensitivity to 100%with specificity of 75%.CONCLUSION SWE is a convenient and easy method to obtain accurate stiffness information of solid FLLs.Emax is useful for differential diagnosis of FLLs,especially in combination with conventional US.

Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage

A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.

A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach

A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.

OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE

This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.

Symplectic eigenfunction expansion theorem for elasticity of rectangular planes with two simply-supported opposite sides

The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem.