RATIONAL FINITE ELEMENT METHOD FOR ELASTIC BENDING OF REISSNER PLATES

In this paper; some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements. And therefore the rational FEM, which is perfect combination of the analytic methods and numeric methods, has been presented. This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures. What's more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.

Pseudo-break imaging of carbon nanotubes for determining elastic bending energies

One-dimensional(1D)nanomaterials easily bend due to perturbations from their surroundings or their own behaviors.This phenomenon not only impacts the performances of various devices but has also been employed to develop a variety of new functional devices,in which the bending energies of the nanomaterials determine the device performances.However,measuring the energies of such nanomaterials is extremely difficult.Herein,pseudo-break imaging of 1D nanomaterials has been proposed and realized on individual carbon nanotubes(CNTs),in which a CNT appears to break and has a fracture but is actually intact.This imaging approach provides the values of the bending energies of the CNTs with an accuracy of 1–50 eV.Furthermore,this imaging approach can manipulate the bending shapes and energies of CNTs.This work presents a protocol for bending analysis and manipulation,which are vital to fundamental and applied studies of 1D nanomaterials.

BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT－IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD

In this paper, using of the superposition principle. the bending solution ofrectangular plate with one edge built-in and one corner point supported subjected touniform load is derived. The results indicate the method has the advantages of rabidconvergence and high precision.

ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR A PHASE FIELD BENDING ELASTICITY MODEL OF VESICLE MEMBRANE DEFORMATION

In this paper, we study numerical approximations of a recently proposed phase field model for the vesicle membrane deformation governed by the variation of the elastic bending energy. To overcome the challenges of high order nonlinear differential systems and the nonlinear constraints associated with the problem, we present the phase field bending elasticity model in a nested saddle point formulation. A mixed finite element method is then employed to compute the equilibrium configuration of a vesicle membrane with prescribed volume and surface area. Coupling the approximation results for a related linearized problem and the general theory of Brezzi-Rappaz-Raviart, optimal order error estimates for the finite element approximations of the phase field model are obtained. Numerical results are provided to substantiate the derived estimates.

Flexural rigidity of honeycomb consisting of hexagonal cells

In this study,the flexural rigidity of a honeycomb consisting of regular hexagonal cells is investigated.It is found that the honeycomb bending can not be evaluated by using the equivalent elastic moduli obtained from the in-plane deformation because the moments acting on the inclined cell wall are different for in-plane deformation and bending deformation.Based on the fact that the inclined wall is twisted under the condition of the rotation angle in both connection edges being zero,a theoretical technique for calculating the flexural rigidity of honeycombs is proposed,and the validity of the present analysis is demonstrated by numerical results obtained by BFM.

Positive Solution for a Singular Fourth-Order Differential System

In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system u(4) = φu + f (t, u, u”, φ), 0 < t < 1, -φ” = μg (t, u, u”), 0 < t < 1, u (0) = u (1) = u”(0) = u”(1) = 0, φ (0) = φ (1) = 0;where μ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.

Locating Malleable Bulk Metallic Glasses in Zr-Ti-Cu-Al Alloys with Calorimetric Glass Transition Temperature as an Indicator

We defined the plastic deformability under constrained loading conditions as malleability for bulk metallic glass （BMG） materials. Quaternary Zr-Ti-Cu-Al alloys in the Zr-rich composition range are selected to investigate the compositional dependence of malleability assessed by bending testing and glass transition temperature （Tg ）. As indicated, increasing the Al or Cu concentration in the alloys leads to the rise of T g . The Zr（61）Ti2Cu（25）Al（12） （ZT1） and Zr（61.6）Ti（4.4）Cu（24）Al（10） （ZT3） alloys exhibit an optimal combination of lower T g and higher glass-forming ability. The malleable BMGs such as ZT1 manifests two characters during deformation, the stable propagation of a single shear band indicated by large shear offsets and easy proliferation of shear bands. With increasing the T g of BMG, the yield strength σy,Young＇s modulus and shear modulus simultaneously increase as well, while the Poisson s ratio decreases. The σy of ZT1 BMG is about 1680 MPa in compression and 1600 MPa in tension. In tensile loading, no any visible plasticity appears even when the strain rate increases up to the order of magnitude of 10（-1）s（-1）. In consistent with the T g , malleability of Zr-Ti-Cu-Al BMGs manifests significant compositional dependence. The malleable BMG is associated with lower Tg , as well as lower shear modulus or higher Poisson s ratio, which can be understood on the basis of the correlation of Tg with shear energy barrier in metallic glass. Thus, the calorimetric Tg can be used as an indicator to screen malleable BMG-forming composition, with advantage of experimental accessibility.

Application of finite element analysis in properties test of finger-jointed lumber

Finger-jointed lumber production has now become the most extensively used method for spliced lumbers jointing together endwise.The properties of finger-jointed lumber are affected by many different factors such as the end-pressure.The main mechanical properties to be tested for struc-tural use finger-jointed lumber include the modulus of elasticity in static bending and the bending strength.The most commonly used method for testing these properties at present is the experi-mental test.In this study,we used finite element method to investigate the end-pressure range,the modulus of elasticity in static bending and the bending strength for Pinus sylvistriv var.finger-jointed lumber under three different fitness ratios(0 mm,0.1 mm,0.3 mm).With finite element analysis(FEA)modelling results compared with the experimental test results,it is possible to find the relationship between these two kinds of results and use the FEA to predict the properties of finger-jointed lumber.The FEA applied in the end pressure tests showed a narrower range com-pared with the modelling results.It indicated that the FEA could be used in the prediction of the end pressure for finger-jointed lumber.The modelling results for modulus of elasticity(MOE)test and bending strength(MOR)test showed about 20%discrepancies compared with the experimen-tal results.Moreover,the MOE modelling results showed the same trend as experimental results under three different fitness levels while the MOR modelling results showed the different trend.It can be concluded that the FEA is a feasible way in analysing the properties of finger-jointed lumber if the errors could be eliminated properly.Some modifications should be made in order to realize the prediction of the properties of finger-jointed lumber more accurately.