Design and fabrication of compound varifocal lens driven by polydimethylsiloxane film elastic deformation

A compound varifocal lens based on electromagnetic drive technology is designed and fabricated, where the polydimethylsiloxane(PDMS) film acts as a driving component, while the PDMS biconvex lens and the plane-concave lens form a coaxial compound lens system. The plane-concave lens equipped with driving coils is installed directly above the PDMS lens surrounded by the annular magnet. When different currents are applied, the annular magnet moves up and down, driving the PDMS film to undergo elastic deformation, and then resulting in longitudinal movement of the PDMS lens. The position change of the PDMS lens changes the focal length of the compound lens system. To verify the feasibility and practicability of this design, a prototype of our compound lens system is fabricated in experiment. Our proposed compound lens shows that its zoom ability reaches 9.28 mm when the current ranges from -0.20 A to 0.21 A.

A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials

We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation rondel was based on the large deflection of the inclined members of the cells of celluar materials, The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensioned cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.

Nonlinear elastic deformation of magnesium and cobalt by Preisach-Mayergoyz model

A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively tested by uniaxial test machine to obtain their stress—strain curves with hysteretic loops. The hysteretic loops do have two properties of P-M hysteretic systems： wiping out and congruency. It is proved that P-M model is applicable for the analysis of these two metals’ hysteresis. This model was applied on Mg at room temperature and Co at 300 ℃. By the P-M model, Co and Mg nonlinear elastic deformation can be calculated based on the stress history. The simulated stress—strain curves agree well with the experimental results. Therefore, the mechanical hysteresis of these two metals can be easily predicted by the classic P-M hysteretic model.

Trajectory compensation for multi-robot coordinated lifting system considering elastic catenary of the rope

The multi-robot coordinated lifting system is an unconstrained system with a rigid and flexible coupling.The deformation of the flexible rope causes errors in the movement trajectory of the lifting system.Based on the kinematic and dynamic analysis of the lifting system,the elastic catenary mod-el considering the elasticity and mass of the flexible rope is established,and the effect of the deform-ation of the flexible rope on the position and posture of the suspended object is analyzed.According to the deformation of flexible rope,a real-time trajectory compensation method is proposed based on the compensation principle of position and posture.Under the lifting task of the low-speed move-ment,this is compared with that of the system which neglects the deformation of the flexible rope.The trajectoy of the lifting system considering the deformation of flexible rope.The results show that the mass and elasticity of the flexible rope can not be neglected.Meanwhile,the proposed trajectory compensation method can improve the movement accuracy of the lifting system,which verifies the ef-fectiveness of this compensation method.The research results provide the basis for trajectory plan-ning and coordinated control of the lifting system。

Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

Three kinds of nonlinear dispersive waves in elastic rods with finite deformation

On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.

Gauge-meter model building based on the effect of elastic deformation of rolls in a plate mill

The calculation error of the gauge-meter model will affect the gap setting precision and the self-learn precision of rolling force. The precision of the gauge-meter model is strongly influenced by plate width, working roll radius, backup roll radius, working roll crown, backup roll crown, and rolling force. The influence rules are hard to get by measuring. Taking a conventional 4-h plate mill as the research subject, these influences were transferred into the calculation of roll deflection and flattening deformation. To calculate these deformations, the theory of the influence function method was adopted. By modifying the traditional gauge-meter model, a novel model of the effect of roll elastic deformation on the gap setting was built by data fitting. By this model, it was convenient to analyze the variation caused by the rolling condition. Combining the elastic deformation model of rolls with the kiss-rolls method, a gauge-meter model was put forward for plate thickness prediction. The prediction precision of thickness was greatly improved by the new gauge- meter model.

Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional(2 D) decagonal quasicrystal(QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2 D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional(3 D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories.Numerical examples are provided to display the effects of the quasiperiodic direction,length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence,and medium elasticity on the vibration frequency and critical buckling load of the 2 D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate.This feature is useful since the frequency and critical buckling load of the 2 D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

BEM Simulation on Elastic Deformation of Oil Film Bearing in Low Speed and Heavy Load Rolling Mill

The particularity of low speed and heavy load rolling loadcase makes the elastic deformation of radial journal bearing in rolling mill far more than that of bearing under general loadcase. Instead of deformation matrix algorithm based on conventional Hertz contact theory,3D boundary element method (BEM) is used to exactly calculate elastic deformation between contact bodies,the sample is given to calculate the elastic deformation of radial journal bearing in rolling mill. The deformation field and stress field of contact surfaces between bearing and roll are analyzed,as well as the influence of elastic deformation on lubrication properties of bearing.

Large Deformation Analysis and Synthesis of Elastic Closed-loop Mechanism Made of a Certain Spring Wire Described by Free Curves

Recently novel mechanisms with compact size and without many mechanical elements such as bearing are strongly required for medical devices such as surgical operation devices. This paper describes analysis and synthesis of elastic link mechanisms of a single spring beam which can be manufactured by NC coiling machines. These mechanisms are expected as disposable micro forceps. Smooth Curvature Model（SCM） with 3rd order Legendre polynomial curvature functions is applied to calculate large deformation of a curved cantilever beam by taking account of the balance between external and internal elastic forces and moments. SCM is then extended to analyze large deformation of a closed-loop curved elastic beam which is composed of multiple free curved beams. A closed-loop elastic link is divided into two free curved cantilever beams each of which is assumed as serially connected free curved cantilever beams described with SCM. The sets of coefficients of Legendre polynomials of SCM in all free curved cantilever beams are determined by taking account of the force and moment balance at connecting point where external input force is applied. The sets of coefficients of Legendre polynomials of a nonleaded closed-loop elastic link are optimized to design a link mechanism which can generate specified output motion due to input force applied at the assumed dividing point. For example, two planar micro grippers with a single pulling input force are analyzed and designed. The elastic deformation analyzed with proposed method agrees very well with that calculated with FEM. The designed micro gripper can generate the desired pinching motion. The proposed method can contribute to design compact and simple elastic mechanisms without high calculation costs.

Buoyancy driven Flow of a Second-Grade Nanofluid flow Taking into Account the Arrhenius Activation Energy and Elastic Deformation:Models and Numerical Results

The buoyancy driven flow of a second-grade nanofluid in the presence of a binary chemical reaction is analyzed in the context of a model based on the balance equations for mass,species concentration,momentum and energy.The elastic properties of the considered fluid are taken into account.The two-dimensional slip flow of such non-Newtonian fluid over a porous flat material which is stretched vertically upwards is considered.The role played by the activation energy is accounted for through an exponent form modified Arrhenius function added to the Buongiorno model for the nanofluid concentration.The effects of thermal radiation are also examined.A similarity transformations is used to turn the problem based on partial differential equations into a system of ordinary differential equations.The resulting system is solved using a fourth order RK and shooting methods.The velocity profile,temperature profile,concentration profile,local skin friction,local Nusselt number and local Sherwood number are reported for several circumstances.The influence of the chemical reaction on the properties of the concentration and momentum boundary layers is critically discussed.

Electronic,Elastic and Piezoelectric Properties of Two-Dimensional Group-Ⅳ Buckled Monolayers

Electronic, elastic and piezoelectric properties of two-dimensional （2D） group-IV buckled monolayers （GeSi, SnSi and SnGe） are studied by first principle calculations. According to our calculations, SnSi and SnGe are good 2D piezoelectric materials with large piezoelectric coefficients. The values of d11d11 of SnSi and SnGe are 5.04pm/V and 5.42pm/V, respectively, which are much larger than 2D MoS2 （3.6pm/V） and are comparable with some frequently used bulk materials （e.g., wurtzite AlN 5.1pm/V）. Charge transfer is calculated by the L wdin analysis and we find that the piezoelectric coefficients （d11d11 and d31） are highly dependent on the polarizabilities of the anions and cations in group-IV monolayers.

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products,and are an active area of research.In this paper,according to the optimization of regular honeycomb structures,two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented.The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods,in which the axial deformation of the rods was considered.The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures.The elastic properties of the structure can be considered by the enclosed area of the unit structure,the shape of the unit structure,and the elastic properties of the original materials.The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.

TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS

Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteristic ware speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock wares. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation, the oblique reflection problem of a plane shock is not solvable in general.

Study on magneto-elastic-plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.

Influence of Roll Elastic Deformation on Gaugemeter Equation for Plate Rolling

The error of gaugemeter equation decreases the gap setting precision.The precision of gaugemeter equation is strongly influenced by plate width,work roll radius,backup roll radius,work roll crown,backup roll crown and rolling force.And these influences are hard to measure.All these factors are converted to roll deflection deformation and roll flattening deformation for calculation.In order to calculate the deformation,the theory of influence function method was adopted.By using simulation program,the influence of these factors on deformation was obtained.Then a simple model can be built.With this model,it is convenient to analyze the influence of different factors on gaugemeter equation.

LARGE DEFORMATION SYMMETRICAL ELASTICITY PROBLEMS SOLVED BY THE VARIATIONAL METHOD

In this paper, based on the mathematical theory of classical mechanics and Chen's theorem, the variational method was used in the study of large deformation symmetrical elasticity problems. The generalized variational principles of potential energy and complementary energy based on the instantaneous configuration were obtained, and the equivalence between the two principles was proved. Besides, the generalized variational principles of dynamical problems based on the instantaneous configuration were also given.

Elastic deformation of ellipsoidal shell of different axis ratio under inner pressure

Discusses the elastic deformation of ellipsoidal shell of different axis ratio under inner pressure during hydraulic bulging forming with theoretical results in good agreement with actual result, thereby providing theoretical basis for hydraulic bulging forming of ellipsoidal shell.

Elastic-plastic deformation of sandwich rod on elastic basis

Sandwich composite material possesses advantages of both light weight and high strength. Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied, little work has been done in the study of mechanical property, in view of the nonlinear behavior of sandwich composites in the complicated external environments. In this paper, the problem about the bending of the three-layer elastic-plastic rod located on the elastic base, with a compressibly physical nonlinear core, has been studied. The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined. The complicated problem about curving of the three-layer rod located on the elastic base has been solved. The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable. The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis.