Stress Field Analysis of Homogeneous Roof by Truss Support Based on Elasticity Mechanics Solution

This paper takes the solution of Boussinesq model, Cerrutl model and Mindlin model as basic solution of elasticity mechanics. on the basis of research conclusion of the accuracy property or rock bolt stress field studied in reference [7], satisfictory elaticity mechanics solution of homogeneous roof rock stress field is given and the rule of stress field change with various parameters is studied.

Eigen theory of elastic mechanics for anisotropic solids

Eigen characters of the fundamental equations, equilibrium equation of stress and harmony equation of deformation, of the traditional elastic mechanics under geometrical space were testified by means of the concept of standard space, and the modal equilibrium equation and the modal harmony equation under mechanical space were obtained. Based on them and the modal Hooke’s law, a new system of the fundamental equation of elastic mechanics is given. The advantages of the theory given here are as following: the form of the fundamental equation is in common for both isotropy and anisotropy, both force method and displacement method, both force boundary and displacement boundary; the number of stress functions is equal to that of the anisotropic subspaces, which avoids the man made mistakes; the solution of stress field or strain field is given in form of the modal superimposition, which makes calculation simplified greatly; no matter how complicated the anisotropy of solids may be, the complete solutions can be obtained.

Eigen elastic mechanics and its variation principle

The fundamental equations and the corresponding boundary condition of elastic mechanics under mechanical representation are given by using the conception of eigen space and elastic variation principle. It is proved theoretically that the solution of anisotropic elastic mechanics consists of modal ones, which are obtained respectively from the modal equation of the different subspaces. A simple application is also given.

A Wire-Driven Series Elastic Mechanism Based on Ultrasonic Motor for Walking Assistive System

In order to improve the elderly people's quality of life,supporting their walking behaviors is a promising technology.Therefore,based on one ultrasonic motor,a wire-driven series elastic mechanism for walking assistive system is proposed and investigated in this research.In contrast to tradition,it innovatively utilizes an ultrasonic motor and a wire-driven series elastic mechanism to achieve superior system performances in aspects of simple structure,high torque/weight ratio,quiet operation,quick response,favorable electromagnetic compatibility,strong shock resistance,better safety,and accurately stable force control.The proposed device is mainly composed of an ultrasonic motor,a linear spring,a steel wire,four pulleys and one rotating part.To overcome the ultrasonic motor's insufficient output torque,a steel wire and pulleys are smartly combined to directly magnify the torque instead of using a conventional gear reducer.Among the pulleys,there is one tailored pulley playing an important role to keep the reduction ratio as 4.5 constantly.Meanwhile,the prototype is manufactured and its actual performance is verified by experimental results.In a one-second operating cycle,it only takes 86 ms for this mechanism to output an assistive torque of 1.6 N·m.At this torque,the ultrasonic motor's speed is around 4.1 rad/s.Moreover,experiments with different operation periods have been conducted for different application scenarios.This study provides a useful idea for the application of ultrasonic motor in walking assistance system.

Modeling and analysis of nonlinear mechanics of a super-thin elastic rod

Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subject of dynamics and elasticity because elastic bodies are analyzed via the theory of dynamics. It is in frontiers of general mechanics （dynamics and control）. This dissertation is devoted to model a constrained super-thin elastic rod and analyze its stability in equilibrium. The existing research results are summarized. Analytical mechanics is systematically applied to model the elastic rod. The Schroedinger equation for complex curvatures or complex bending moments is, respectively, extended from the case of circular crosssections to that of non-circular ones. The equilibrium of a rod constrained on a surface is investigated.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space I: Newtonian Mechanics

We present the usefulness of the diagrammatic approach for analyzing two dimensional elastic collision in momentum space. In the mechanics course, we have two major purposes of studying the collision problems. One is that we have to obtain velocities of the two particles after the collision from initial velocities by using conservation laws of momentum and energy. The other is that we have to study two ways of looking collisions, i.e. laboratory system and center-of-mass system. For those two major purposes, we propose the diagrammatic technique. We draw two circles. One is for the center-of-mass system and the other is for the laboratory system. Drawing these two circles accomplish two major purposes. This diagrammatic technique can help us understand the collision problems quantitatively and qualitatively.

Operationalized principle of elastic mechanics

The fundamental mechanical equations were studied under the mechanical space. The differential stress operator and strain operator were obtained. There were strain energy operator and Hamilton operator for elastic body in same way, and the following results were testified. 1) The equilibrium equation of force is equivalent to the harmony equation of deformation under the mechanical space. They are all the basic mode of eigen equation of stress or strain operator. 2) The eigen value of stress or strain operator is corresponding to the order of kinetic energy of elastic body, and the elastic wave represents the non basic mode. 3) The eigen functions of stress operator or strain operator corresponding to some kinetic energy order are fields of modal stress or modal strain in same order. 4) The eigen equations of strain energy operator are the fundamental equations of elastic mechanics which are expressed with the potential functions. [

An elastic mechanics model and computation method for geotechnical material

Internal friction characteristic is one of the basic properties of geotechnical materials and it exists in mechanical elements all the time. However,until now internal friction is only considered in limit analysis and plastic mechanics but not included in elastic theory for rocks and soils. We consider that internal friction exists in both elastic state and plastic state of geotechnical materials,so the mechanical unit of friction material is constituted. Based on study results of soil tests,the paper also proposes that cohesion takes effect first and internal friction works gradually with the increment of deformation. By assuming that the friction coefficient is proportional to the strain,the internal friction is computed. At last,by imitating the linear elastic mechanics,the nonlinear elastic mechanics model of friction material is established,where the shear modulus G is not a constant. The new model and the traditional elastic model are used simultaneously to analyze an elastic foundation. The results indicate that the displacements computed by the new model are less than those from the traditional method,which agrees with the fact and shows that the mechanical units of friction material are suitable for geotechnical material.

THE MECHANICAL METHOD OF CONSTRUCTING THE DISPLACEMENT FUNCTIONS IN ELASTICITY

In this Paper we have proven the general solution to the equations of linear operatorsAu=f as u=Cv+e . where v satisfies the equation Dv=g and D is adiagonal matrix. Basing on the consstructive proof of Hilbert Nullstellensat=. we haregiven the mechanical method of constucting C. D and e.and some of the mechanicalalgorithm displacement functions in elasticity are given by this method also .

MATERIAL MULTIPOLE MECHANICS OF ELASTIC DIELECTRIC COMPOSITES

The overall mechanical and electrical behaviors of elastic dielectric composites are investigated with the aid of the concept of material multipoles. In particular, by introducing a statistical continuum material multipole theory, the effects of the electric-elastic interaction and the microstructure (size, shape, orientation,...) of inhomogeneous particles on the overall behaviors of the composites can be obtained. A basic solution for an ellipsoidal elastic inhomogeneity with electric polarization in an infinite elastic dielectric medium is first given, which shows that classical Eshelby 's elastic solution is modified by the presence of electric-elastic interaction. The overall macroscopic constitutive relations and their overall macroscopic material parameters accounting for electroelastic interaction effect are then derived for the elastic dielectric composites. Some quantitative calculations on the problems with statistical anisotropy, the shape effect and the electric-elastic interaction are finally given for dilute composites.

Elasticity Forces in Tourism Under Covid-19:The Model of the Imaginary Mechanical Tourist Spring

The forces of contraction and expansion about the seasons in tourism behave like an imaginary mechanical tourist spring.The article discusses tourist activities in Bulgaria from 2009 to 2020,predictions concerning Covid-19,and tendencies expected in the last quarter of 2021 till the end of 2022 on data published by the National Statistics Institute and Eurostat.The system’s dynamics observed before the pandemic crisis in tourism resembles the action of a mechanical spring that shrinks and extends,and we can empirically analyze the process of tourism activities.The study of this elasticity process of the system allows establishing a model with positive characteristics of the dynamics and further dealing with problems,better clarity in analysis and modeling of prognosis based on the potential of an imaginary mechanical spring concerning the possibility of the tourist destination.

Non-pneumatic mechanical elastic wheel natural dynamic characteristics and influencing factors

Non-pneumatic tire appears to have advantages over traditional pneumatic tire in terms of flat proof and maintenance free.A mechanical elastic wheel(MEW) with a non-pneumatic elastic outer ring which functions as air of pneumatic tire was presented.The structure of MEW was non-inflatable integrated configuration and the effect of hinges was accounted for only in tension. To establish finite element model of MEW, various nonlinear factors, such as geometrical nonlinearity, material nonlinearity and contact nonlinearity, were considered. Load characteristic test was conducted by tyre dynamic test-bed to obtain force-deflection curve. And the finite element model was validated through load characteristic test. Natural dynamic characteristics of the MEW and its influencing factors were investigated based on the finite element model. Simulation results show that the finite element model closely matched experimental wheel. The results also show that natural frequency is related to ground constraints, material properties, loads and torques. Influencing factors as above obviously affect the amplitude of mode of vibration, but have little effect on mode of vibration shape. The results can provide guidance for experiment research, structural optimization of MEW.

CALCULATION OF ELASTIC ERROR OF PLANAR MECHANISM—AN EQUIVALENT METHOD

Ｔｈｅａｃｕｒａｃｙｐｒｏｂｌｅｍｗａｓｏｎｅｏｆｔｈｅｐｒｉｎｃｉｐａｌｃｏｎｃｅｒｎｓｉｎｍａｃｈｉｎｅｄｅｓｉｇｎａｎｄｐｅｒｆｏｒｍａｎｃｅｃｏｎｓｉｄｅｒａｔｉｏｎ．Ｉｔｉｓｉｍｐｏｒｔａｎｔｔｏｕｎｄｅｒｓｔａｎｄｔｈｅｒｅｌａｔｉｏｎ...

Dynamic Modeling and Analysis of 5‑PSS/UPU Parallel Mechanism with Elastically Active Branched Chains

To study the characteristics of the 5-prismatic–spherical–spherical(PSS)/universal–prismatic–universal(UPU)parallel mechanism with elastically active branched chains,the dynamics modeling and solutions of the parallel mechanism were investigated.First,the active branched chains and screw sliders were considered as spatial beam elements and plane beam element models,respectively,and the dynamic equations of each element model were derived using the Lagrange method.Second,the equations of the 5-PSS/UPU parallel mechanism were obtained according to the kinematic coupling relationship between the active branched chains and moving platform.Finally,based on the parallel mechanism dynamic equations,the natural frequency distribution of the 5-PSS/UPU parallel mechanism in the working space and elastic displacement of the moving platform were obtained.The results show that the natural frequency of the 5-PSS/UPU parallel mechanism under a given motion situation is greater than its operating frequency.The maximum position error is -0.096 mm in direction Y,and the maximum orientation error is -0.29°around the X-axis.The study provides important information for analyzing the dynamic performance,dynamic optimization design,and dynamic control of the 5-PSS/UPU parallel mechanism with elastically active branched chains.

Influence Analysis of Machining and Installation Errors on the Radial Stiffness of a Non-Pneumatic Mechanical Elastic Wheel

Machining and installation errors are unavoidable in mechanical structures. However, the effect of errors on radial stiffness of the mechanical elastic wheel(ME-Wheel) is not considered in previous studies. To this end, the interval mathematical model and interval finite element model of the ME-Wheel were both established and compared with bench test results. The intercomparison of the influence of the machining and installation errors on the ME-Wheel radial stiffness revealed good consistency among the interval mathematical analysis, interval finite element simulation,and bench test results. Within the interval range of the ME-Wheel machining and installation errors, parametric analysis of the combined elastic rings was performed at different initial radial rigidity values. The results showed that the initial radial stiffness of the flexible tire body significantly influenced the ME-Wheel radial stiffness, and the inverse relationship between the hinge unit length or suspension hub and the radial stiffness was nonlinear. The radial stiffness of the ME-Wheel is predicted by using the interval algorithm for the first time, and the regularity of the radial stiffness between the error and the load on the ME-Wheel is studied, which will lay the foundation for the exact study of the ME-Wheel dynamic characteristics in the future.

Steady-State Cornering Properties of a Non-pneumatic Tire with Mechanical Elastic Structure

Mechanical elastic wheel(ME-wheel)is a new type of non-inflatable safety tyre,and the structure is significantly different from traditional pneumatic tyre.In order to investigate cornering properties of ME-wheel,experimental research on mechanics characteristics of ME-wheel under steady-state cornering conditions are carried out.The test of steady-state cornering properties of ME-wheel at different experimental parameter conditions is conducted by test bench for dynamic mechanical properties of tyre.Cornering property curves are used to analyze the steady-state cornering properties of ME-wheel,namely the variation tendency of lateral force or aligning torque with the increase of side-slip angle.Moreover,evaluation indexes for cornering properties of ME-wheel are extracted and the effect of different experimental parameters(including vertical load,friction coefficient,and speed)on cornering properties of ME-wheel is contrastively analyzed.The proposed research can provide certain reference to facilitate structure parameters and cornering properties optimizing process of ME-wheel.

Theoretical study of elastic, mechanical and thermodynamic properties of MgRh intermetallic compound

In the last years,Magnesium alloys are known to be of great technological importance and high scientific interest.In this work,density functional theory plane-wave pseudo potential method,with local density approximation(LDA)and generalized gradient approximation(GGA)are used to perform first-principles quantum mechanics calculations in order to investigate the structural,elastic and mechanical properties of the intermetallic compound MgRh with a CsCl-type structure.Comparison of the calculated equilibrium lattice constant and experimental data shows good agreement.The elastic constants were determined from a linear fit of the calculated stress-strain function according to Hooke's law.From the elastic constants,the bulk modulus B,shear modulus G,Young's modulus E,Poisson's ratioσ,anisotropy factor A and the ratio B/G for MgRh compound are obtained.The sound velocities and Debye temperature are also predicted from elastic constants.Finally,the linear response method has been used to calculate the thermodynamic properties.The temperature dependence of the enthalpy H,free energy F,entropy S,and heat capacity at constant volume C_(v)of MgRh crystal in a quasi-harmonic approximation have been obtained from phonon density of states and discussed for the first report.This is the first quantitative theoretical prediction of these properties.

EFFECT OF AGING ON INTERNAL FRICTION,ELASTIC MODULUS AND MECHANICAL PROPERTIES OF TERNARY Mn-Cu-Al ALLOYS

Internal friction and elastic modulus of ternary Mn-Cu-Al alloys containing 56—60 wt-% Mn,0-3.59 wt-% Al were measured with acoustic frequency,1 kHz,in the tempera- ture range of-150 to 150℃.It was found that when the specimen was aged in the temperature range under the spinodal curve within the miscibility gap(400—500℃),the internal fric- tion increases with an increase of the aging time and reaches a maximum value at a certain ag- ing time which is shorter with a higher aging temperature.Two internal friction peaks which did not appear before the aging were observed above room temperature after a definite aging time.These are respectively the martensitic tranformation peak and the relaxation peak orig- inating from the stress-induced movement of the twin boundaries.The former peak shifts to- ward higher temperatures with an increase of the aging time,whereas the relaxation peak ap- pearing at 15℃,is independent of the aging time and temperature.The activation energy as- sociated with the relaxation peak was found to be 0.56 eV which is about the same as that of the relaxation peak in binary alloy containing 90 wt-% Mn.It was also found that the hardness,strength and the brittleness of the specimen increase when aged below the spinodal curve within the miscibility gap.The addition or Al enhances the strength but reduces the in- ternal friction of the specimen.A choice of suitable aging time and temperature can give an optimum compromise of high strength and high internal friction.Analysis of experimental re- sults suggests that spinodal decomposition leads to Mn-rich zones in the specimen and thus causes the phase transformation and the change of mechanical properties of the specimen.

Complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application*

A new type of displacement pile, the X-section cast-in-place concrete （XCC） pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect （NUDE） of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index （CFI）, and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.

Compliant Mechanism Synthesis by Using Elastic Similitude

Compliant mechanisms have several advantages, especially smaller number of elements and therefore less movable joints. The flexural members furthermore allow an integration of special functions like balancing or locking. Especially fiber reinforced materials exhibit a wide range of function integration considering their compliance in passive as well active applications. To take advantage of compliant elements in applications a robust synthesis tool is needed. The synthesis based on topology optimization method or the pseudo rigid body approach leads to complex structures. Considering the use of fiber reinforced material a synthesis approach which leads to less complex structures is more suitable. For building up simple structures, with only one cantilever beam as compliant element（B） a graphical approach using the elastic similitude is the most efficient method. A step-by-step synthesis procedure is presented to synthesize compliant mechanisms with rotatory joints（R） and prismatic joints（P） to develop RRB/PRB- and RPB-linkages. Using the elastic similitude to implement these results into a graphical synthesis algorithm is the innovation part of this paper. It can be shown that this approach leads to a comfortable handling of beam elements during the synthesis, where the two free parameters can be directly coupled to scale and fix the orientation of the beam element. This advantage inherently shortens the development process. In giving an example the focus lies of the experimental approach, which also shows that the simple BERNOULLI beam model is valid and so the synthesis by using the elastic similitude. The method is presented and discussed by using an application for a cup holder mechanism made of fiber reinforced material.