“弹性力学”课程教学研究与实践

"弹性力学"课程的学习对于培养学生思维方法和独立工作能力有着重要意义。文章从立体化教材建设、教学内容、考核方式和科研促进教学等方面阐述了"弹性力学"课程的教学研究与实践。从多年的教学实践可以看出,"弹性力学"课程的教学充分发挥了学生学习的积极性和主动性,培养了学生严谨的力学思维、分析和解决问题的能力,提高了课程教学质量,达到了人才培养目的。

浅谈圣维南原理的启发式教学和课程思政方法

圣维南原理是“弹性力学”课程的一个十分重要的内容,在处理次要边界条件时具有重要的作用。文章根据作者多年的“弹性力学”教学体会,从圣维南原理的提出方法、圣维南原理概念中要注意的问题、圣维南原理的案例解析等三个方面探讨了圣维南原理的教学方法,同时对该知识点的课程思政进行了教学总结,以期对指导青年教师教学起到一定的帮助作用。

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.

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%.

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.

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.

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.

Science Letters:Analytical solution for fixed-end beam subjected to uniform load

A bi-harmonic stress function is constructed in this work. Ariy stress function methodology is used to obtain a set of analytical solutions for both ends fixed beams subjected to uniform load. The treatment for fixed-end boundary conditions is the same as that presented by Timoshenko and Goodier (1970). The solutions for propped cantilever beams and cantilever beams are also presented. All of the analytical plane-stress solutions can be obtained for a uniformly loaded isotropic beam with rectangular cross section under different types of classical boundary conditions.

A parametric study on the contact stress of half toroidal continuously variable transmission

The most general contact in mechanical transmission is the elliptical one. In particular, a toroidal continuously variable transmission (CVT) has an elliptical shape in the contact area under the elastohydrodynamic lubrication regime, where the shearing of the fluid subjects to high contact stress and transmits the power. Many parameters affect the contact service performance of the half toroidal CVT, which include the properties of the contacting material (Young抯 modulus), operating parameters (input torque and maximum traction coefficient) and geometrical parameters (aspect cavity ratio, curvature ratio and half cone angle of the power roller). In this paper, the contacts between the input disk, the power roller and the output disk are formulated using the classical Hertzian contact theory. Based on the formulated equations, different system parameters, which affect the maximum Hertzian stresses, are compared. The comparative results will provide some observations of the relations between the maximum Hertzian stresses and transmission ratios in the form of graphs. These graphs give useful information for designer to know the maximum Hertzian stress during operation in such systems.