Functional Dependence of IM and HV Angle in Hallux Valgus Deformity before and after Operative

Hallux valgus is a relatively common and multifaceted complex deformity of the front part of the foot. It is the result of multiple effects of innate (endogenous) and exogenous etiological factors with different degrees of influence. The degree of hallux valgus deformity is usually assessed by radiological values of hallux valgus (HV) and intermetatarsal (IM) angles. The aim of the paper is to justify the definition of hallux valgus deformity as a function of one angle, (HVA or IMA), and then to determine the functional connection and the most suitable function equalizing the values of the angles IMA and HVA. As hallux valgus is a double angulation deformity, the analytically determined connection between the HVA and IMA angles reduces the study of the deformity to the study of function with one argument, and makes the analysis of deformity changes before and after operative treatment simpler. For the determined connections between the angles, the values of linear proportionality coefficients and regression coefficients of corresponding linear functions of analytical equalization of the value of the IM angle and the degree of deformity for a given value of the HV angle were experimentally determined. The obtained results were checked on a sample of 396 operatively treated hallux valgus deformities. The presented analytical approach and the obtained functional links of IMA and HVA enable quantitative observation of the change in the degree of deformity based on the radiologically determined value of these angles, and the established nonlinear function will be useful for evaluating the expected value of the IM angle and the degree of deformity based only on the measured value of the HV angle. .

Thermoelastic Analysis of Non-uniform Pressurized Functionally Graded Cylinder with Variable Thickness Using First Order Shear Deformation Theory(FSDT) and Perturbation Method

Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

The research on relationship between wavelet transform on vertical deformation and moderate earthquakes in Hexi region,Gansu Province

n this paper, the possibility of wavelet transform applied to compute the vertical deformation is discussed. Both two dimension plane equation of wavelet transform and B-wavelet based on basic spline function are deduced. According to the equation and B-wavelet, multi-periods vertical deformation data which were measured from 1971 to 1995 in Hexi-Qilian Mountain region, Gansu Province are calculated. The results are: ① The multi-resolution analysis of wavelet transform can filter the different spatial wavelength in vertical deformation information on different scales effectively and let us to see the heterogeneous in distribution of vertical deformation clearly, therefore, it is an important tool in investigating the relationship between the vertical deformation and the seismicity; ② The main variation of both the first and second results in wavelet transform mainly takes place along the main faults which explains that the short wave variation of vertical deformation is caused by the faults activities; ③ The wavelet transform of vertical deformation in Hexi-Qilian Mountain area shows that the vertical deformation in southeast parts of Hexi region was larger than that in other parts and there were several moderate earthquakes such as Menyuan Ms=6.4 earthquake in 1986, Jingtai Ms=6.2 earthquake in 1990, Yongdeng Ms=5.8 earthquake in 1995. The vertical deformation in the northwest part of the region was not so large as that in southeast part where ware no strong earthquakes.

A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω)

In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.

RBFs-MSA Hybrid Method for Mesh Deformation

Simulating unsteady flow phenomena involving moving boundaries is a challenging task,one key requirement of which is a reliable and fast algorithm to deform the computational mesh.Radial basis functions（RBFs） interpolation is a very simple and robust method to deform the mesh.However,the number of operations and the requirement of memory storage will be increased rapidly as the number of grid nodes increases,which limits the application of RBFs to three-dimensional（3D） moving mesh.Moving submesh approach（MSA） is an efficient method,but its robustness depends on the method used to deform the background mesh.A hybrid method which combines the benefits of MSA and RBFs interpolation,which is called RBFs-MSA,has been presented.This hybrid method is proved to be robust and efficient via several numerical examples.From the aspect of the quality of deforming meshes,this hybrid method is comparable with the RBFs interpolation;from the aspect of computing efficiency,one test case shows that RBFs-MSA is about two orders of magnitude faster than RBFs interpolation.For these benefits of RBFs-MSA,the new method is suitable for unsteady flow simulation which refers to boundaries movement.

Numerical studies of static aeroelastic effects on grid fin aerodynamic performances

The grid fin is an unconventional control surface used on missiles and rockets. Although aerodynamics of grid fin has been studied by many researchers, few considers the aeroelastic effects.In this paper, the static aeroelastic simulations are performed by the coupled viscous computational fluid dynamics with structural flexibility method in transonic and supersonic regimes. The developed coupling strategy including fluid–structure interpolation and volume mesh motion schemes is based on radial basis functions. Results are presented for a vertical and a horizontal grid fin mounted on a body. Horizontal fin results show that the deformed fin is swept backward and the axial force is increased. The deformations also induce the movement of center of pressure, causing the reduction and reversal in hinge moment for the transonic flow and the supersonic flow,respectively. For the vertical fin, the local effective incidences are increased due to the deformations so that the deformed normal force is greater than the original one. At high angles of attack, both the deformed and original normal forces experience a sudden reduction due to the interference of leeward separated vortices on the fin. Additionally, the increment in axial force is shown to correlate strongly with the increment in the square of normal force.

Effects of uniaxial compressive strain on the electronic- transport properties of zigzag carbon nanotubes

Recently, substantial attention has been paid to the strain sensitivity of the carbon nanotubes＇ （CNTs＇） electronic properties. In this study, the relationships between the geometric structures and electronic states of zigzag CNTs under uniaxial compressive strain were investigated. We found that different factors dominate the electronic states of zigzag CNTs depending on the strain regions： the initial stage of the strain loading, which lasts until column-buckling deformation begins, and the strain regions corresponding to column- and shell-buckling deformations. Because shell-buckling deformation significantly increases the re-orbital angle, the angle between the π orbital axis vectors of adjacent atoms, strong localization of the density of states （LDOS） occurs in the buckled area. We also analyzed the current able to pass through deformed CNTs using a tight-binding-based Green＇s function approach and determined that the current can be significantly suppressed by applying uniaxial compressive strain. Our method of predicting the electronic state of a deformed CNT based on the π-orbital angle is expected to be useful for predicting the electronic properties of CNT-based electronic devices and sensors.