弹性力学中平衡微分方程推导方法的一点小改进

许多《弹性力学》教材在应用泰勒公式推导平衡微分方程的过程中表述不够清楚,让学生感到困惑。本文明确了泰勒公式展开点,对平衡微分方程进行了重新推导。

《弹塑性力学》硕士课程内容的优化设计

本文以长期以来国内硕士研究生弹塑性力学课程内容为研究对象,以安徽理工大学土木工程、采矿工程、弹爆工程专业硕士研究生教学为研究背景,对目前该领域的教材进行了深入地研究。从国内大多数高校工科研究生力学知识的状况、目前教材编写的思路、目前教材内容特征等提出了一系列优化建议,相应的做法在我校《弹塑性力学》硕士课程的教学中产生了很好的效果。

应力分量坐标变换的矩阵解法

应用正交坐标系间矢量分量的变换关系 ,导出了直角坐标与极坐标系下应力分量之间变换的关系式 ,形式规整 ,便于记忆。

Dynamic Phase Field Description on Ductile Fracture Process

In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simplification.An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids.This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity,embracing plasticization,cracks initiation,propagation,branching and merging while fulfilling the basic principle of thermodynamics.Herein,we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code.The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks,and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.

First principles investigation of binary intermetallics in Mg-Al-Ca-Sn alloy:Stability,electronic structures,elastic properties and thermodynamic properties

The structural stability, electronic structures, elastic properties and thermodynamic properties of the main binary phases Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca in Mg-Al-Ca-Sn alloy were determined from the first-principles calculation. The calculated lattice parameters are in good agreement with the experimental and literature values. The calculated heats of formation and cohesive energies show that Al_2Ca has the strongest alloying ability and structural stability. The densities of states（DOS）, Mulliken electron occupation number, metallicity and charge density difference of these compounds are given. The elastic constants of Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca phases are calculated, and the bulk moduli, shear moduli, elastic moduli and Poisson ratio are derived. The calculations of thermodynamic properties show that the Gibbs free energies of Al_2Ca and Mg_2 Sn are lower than that of Mg_（17）Al_（12）, which indicates that Al_2Ca and Mg_2 Sn are more stable than Mg_（17）Al_（12） phase. Hence, the heat resistance of Mg-Al-based alloys can be improved by adding Ca and Sn additions.

First-principle calculations of ductile CeAg intermetallic compound

The first-principle calculations were performed to investigate the structural,mechanical,electronic and thermal properties of the binary ductile intermetallic compound CeAg with B2（CsCl） structure.The calculated value of lattice constant a0 for CeAg with generalized gradient approximation is 3.713-,which is in better agreement with experimental data than local spin density approximation.The negative energy of formation implies that CeAg with B2 structure is thermodynamically stable phase.The greater separation between the d bands of Ce and Ag results in weaker bond hybridization of Ce d—Ag d,which prevents formation of directional covalent bonding.The three independent elastic constants（C11,C12 and C44） are derived and the bulk modulus,shear modulus,elastic modulus,anisotropy factor,and Poisson ratio are determined to be 57.6 GPa,15.8 GPa,43.4 GPa,3.15 and 0.374,respectively.The elastic constants meet all the mechanical stability criteria.The value of Pugh＇s criterion is 3.65.The ductility of CeAg is predicted if Pugh＇s criterion is greater than 1.75.Furthermore,the variations of volume,bulk modulus,heat capacity,and thermal expansion coefficient with temperature and/or pressure were calculated and discussed.

Elastic and thermodynamic properties of Re_2N at high pressure and high temperature

First principles calculations are preformed to systematically investigate the elastic and thermodynamic properties of Re2N at high pressure and high temperature. The Re2N exhibits a clear elastic anisotropy and the elastic constants C11 and C33 vary rapidly in comparison with the variations in C12, C13 and C44 at high pressure. In addition, bulk modulus B, elastic modulus E, and shear modulus Gas a function of crystal orientations for Re2N are also investigated for the first time. The tensile directional dependences of the elastic modulus obey the following trend： [0001] [1211] [1010] [1011]EEEE〉〉〉 . The shear moduli of Re2N within the （0001） basal plane are the smallest and greatly reduce the resistance of against large shear deformations. Based on the quasi-harmonic Debye model, the dependences of Debye temperature, Grüneisen parameter, heat capacity and thermal expansion coefficient on the temperature and pressure are explored in the whole pressure range from 0 to 50 GPa and temperature range from 0 to 1600 K.

MULTI-BODY AEROELASTIC STABILITY ANALYSIS OF TILTROTOR AIRCRAFT IN HELICOPTER MODE

The muhi-body analysis of the aeroelastic stability of the tiltrotor aircraft is presented. Muhi-body dynamic differential equations are combined with the equations of the unsteady dynamic inflow model to establish the complete unsteadily aeroelastic coupling analytical model of the tiltrotor. The stability of the tiltrotor in the helicopter mode is analyzed aiming at a semi span soft-inplane tihrotor model with an elastic wing. Parametric effects of the lag stiffness of blades and the flight speed are analyzed. Numerical simulations demonstrate that the multibody analytical model can analyze the aeroelastic stability of the tiltrotor aircraft in the helicopter mode.

Influence of Zr content on microstructure and mechanical properties of implant Ti-35Nb-4Sn-6Mo-xZr alloys

The influence of Zr content on the microstructure and mechanical properties of implant Ti-35Nb-4Sn-6Mo-xZr （x=0, 3, 6, 9, 12, 15; mass fraction） alloys was investigated. It is shown that Ti-35Nb-4Sn-6Mo-xZr alloys appear to have equiaxed single β microstructure after solution treatment at 1023 K. It is found that the grains are refined first and then coarsened with the increase of Zr content. It is also found that Zr element added to titanium alloys has both the solution strengthening and fine-grain strengthening effect, and affects the lattice parameters. With increasing the Zr content of the alloys, the strength increases, the elongation decreases, whereas the elastic modulus firstly increases and then decreases. The mechanical properties of Ti-35Nb-4Sn-6Mo-9Zr alloy are as follows： σb=785 MPa, δ=11%, E=68 GPa, which is more suitable for acting as human implant materials compared to the traditional implant Ti-6Al-4V alloy.

Study on conveyor non-linear dynamics and its effect on dynamic behavior

A conveyor linear system assumption is based on an approximate description of belt mechanics behavior and constant elastic moduli. It produces analysis errors and improper dynamics simulation in large conveyors. The belt non-linear characteristics based on sag are described and the belt equivalent elastic moduli expression is deduced. The relationship between belt-equivalent elastic module and elastic module is studied, and their ratio varies from 0.1 to 1.0. The non-linear motion equation with a lumped element model is put forward. Its increment equation and numerical solution are built. A dynamics simulation on a conveyor is carried out, mainly to calculate and compare belt speed, acceleration, tension, displacement of gravity take-up and wave period with linear and non-linear models. It shows that the simulation errors between two models vary from 6% to 50%.

Application of the generalized quasi-complementary energy principle to the fluid-solid coupling problem

The fluid-solid coupling theory, an interdisciplinary science between hydrodynamics and solid mechanics, is an important tool for response analysis and direct design of structures in naval architecture and ocean engineering. By applying the corresponding relations between generalized forces and generalized displacements, convolutions were performed between the basic equations of elasto-dynamics in the primary space and corresponding virtual quantities. The results were integrated and then added algebraically. In light of the fact that body forces and surface forces are both follower forces, the generalized quasi-complementary energy principle with two kinds of variables for an initial value problem is established in non-conservative systems. Using the generalized quasi-complementary energy principle to deal with the fluid-solid coupling problem and to analyze the dynamic response of structures, a method for using two kinds of variables simultaneously for calculation of force and displacement was derived.

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.

Elastic Tensor and Thermodynamic Property of Magnesium Silicate Perovskite from First-principles Calculations

The thermodynamic and elastic properties of magnesium silicate （MgSiO3） perovskite at high pressure are investigated with the quasi-harmonic Debye model and the first-principles method based on the density functional theory. The obtained equation of state is consistent with the available experimental data. The heat capacity and the thermal expansion coefficient agree with the observed values and other calculations at high pressures and temperatures. The elastic constants are calculated using the finite strain method. A complete elastic tensor of MgSiO3 perovskite is determined in the wide pressure range. The geologically important quantities： Young＇s modulus, Poisson＇s ratio, Debye temperature, and crystal anisotropy, are derived from the calculated data.

Representation Theory of Three-Dimensional Elliptical Crack Under Dynamic Loading

The relation between the normal displacement on the surface of a dynamical elliptical crack and the normal stress over the crack surface was studied. The three dimensional elastodynamic equations and Fourier Laplace transforms are used. Based on the influence function and the inversion of integral transforms, one can find that if the distribution of normal displacement on the surface of a dynamic elliptical crack is a polynomial of degree n in x 1 and x 2 , then the normal pressure acting over the ellipse is also a polynomial P n(x 1,x 2) of the same degree in x 1 and x 2 .

Modification of the linear viscoelastic deformation prediction model of asphalt mixture

A deformation prediction model for the dynamic creep test is deduced based on the linear viscoelastic（LVE）theory.Then,the defect of the LVE deformation prediction model is analyzed by comparing the prediction of the LVE deformation model with the experimental data.To improve accuracy,a modification of the LVE deformation prediction model is made to simulate the nonlinear property of the deformation of asphalt mixtures,and it is verified by comparing its simulation results with the experimental data.The comparison results show that the LVE deformation prediction model cannot simulate the nonlinear property of the permanent deformation of asphalt mixtures,while the modified deformation prediction model can provide more precise simulations of the whole process of the deformation and the permanent deformation in the dynamic creep test.Thus,the proposed modification greatly improves the accuracy of the LVE deformation prediction model.The modified model can provide a better understanding of the rutting behavior of asphalt pavement.

《弹性波动力学》教学内容与方法改革

《弹性波动力学》是一门理论性和实践性都很强的的综合性课程,该专业课程注重对学生的实践、探索、创新能力的培养。本次课题研究,以《弹性波动力学》为例,结合着我校教学管理工作实际,简要介绍《弹性波动力学》的课程基本情况,从课程体系、施教手段、课堂内容设置、知识考核等多个层面来切入,深入探讨分析新时期人本教育背景下的《弹性波动力学》课堂实践教学与体系创新变革。结合着实际教学案例展开论述,从中探寻出一些新颖的教学方法,从而更好的提高课堂教学质量,最大限度的激发出学生对该课程的积极学习与探索兴趣。

Mechanical mechanism analysis of tension type anchor based on shear displacement method

Based on the fact that the shear stress along anchorage segment is neither linearly nor uniformly distributed, the load transfer mechanism of the tension type anchor was studied and the mechanical characteristic of anchorage segment was analyzed. Shear stress?strain relationship of soil surrounding anchorage body was simplified into three-folding-lines model consisting of elastic phase, elasto-plastic phase and residual phase considering its softening characteristic. Meanwhile, shear displacement method that has been extensively used in the analysis of pile foundation was introduced. Based on elasto-plastic theory, the distributions of displacement, shear stress and axial force along the anchorage segment of tension type anchor were obtained, and the formula for calculating the elastic limit load was also developed accordingly. Finally, an example was given to discuss the variation of stress and displacement in the anchorage segment with the loads exerted on the anchor, and a program was worked out to calculate the anchor maximum bearing capacity. The influence of some parameters on the anchor bearing capacity was discussed, and effective anchorage length was obtained simultaneously. The results show that the shear stress first increases and then decreases and finally trends to the residual strength with increase of distance from bottom of the anchorage body, the displacement increases all the time with the increase of distance from bottom of the anchorage body, and the increase of velocity gradually becomes greater.

Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads

In this paper, the axisymmetric general solutions of transversely isotropic magnetoelectroelastic media are expressed with four harmonic displacement functions at first. Then, based on the solutions, the analytical three-dimensional solutions are provided for a simply supported magnetoelectroelastic circular plate subjected to uniform loads. Finally, the example of circular plate is presented.

Study on Dynamic Response of the “Dualistic” Structure Rock Slope with Seismic Wave Theory

Currently, scant attention has been paid to the theoretical analysis on dynamic response mechanism of the ＂Dualistic＂ structure roek slope. The analysis presented here provides insight into the dynamic response of the ＂Dualistie＂ structure rock slope. By investigating the principle of energy distribution, it is shown that the effect of a joint plays a significant role in slope stability analysis. A dynamic reflection and transmission model （RTM） for the ＂Dualistic＂ structure rock slope and explicit dynamic equations are established to analyze the dynamic response of a slope, based on the theory of elastic mechanics and the principle of seismic wave propagation. The theoretical simulation solutions show that the dynamic response of the ＂Dualistic＂ structure rock slope （soft-hard） model is greater than that of the ＂Dualistic＂ strueture rock slope （hard-soft） model, especially in the slope crest. The magnifying effect of rigid foundation on the dynamic response is more obvious than that of soft foundation. With the amplitude increasing, the cracks could be found in the right slope （soft-hard） crest. The crest failure is firstly observed in the right slope （soft-hard） during the experimental process. The reliability of theoretical model is also investigated by experiment analysis. The conclusions derived in this paper could also be used in future evaluations of Multi-layer rock slopes.

Study on structural,mechanical and thermodynamic properties of TiAl alloy under high pressure based on first-principles

The effect of pressure on structural, mechanical properties as well as the temperature dependence of thermodynamic properties of TiAl alloy are investigated by implementing first-principles calculations. The results show that the volume decrea-ses with the pressure increasing. We calculated the CtJ at various pressures and all the results satisfy mechanical stability crite-ria, thus the TiAl alloy is mechanically stable. The elastic constants？ bulk modulus and shear modulus calculated are well in a-greement with the calculated values at zero the pressure. The bulk modulus and shear modulus increase with the pressure in-creasing, which reflects the deformation resistance, and accordingly, deformation resistance can be strengthened with the in-crease of pressure. The brittle nature of TiAl alloy turns to ductile nature in 10 - 20 GPa . The Debye temperature, linear ther-mal expansion and heat capacity are calculated using the quasi-harmonic Debye model under the pressure ranging from 0 to 50 GPa and the temperature ranging from 0 to 1 000 K, which are useful to investigate the effect of temperature and pressure on thermodynamic parameters. Finally, electronic structure is calculated at various pressures,and it can be found that the peak intensity decreases with increasing pressure and the the strength of d-d orbital of Ti is weakened but the ductility is enhanced.