GENERAL AXISYMMETRY PROBLEMS FOR SHELLS OF REVOLUTION AND ANALYSES OF INTEGRAL EQUATION

In this paper, a simplified equation in complex form for axisymmetry elastic thin shells of revolution under arbitrary distributed loads is given. The equation is equivalent to the exact equations within the error range of the thin shell theory, with the singularities at the points of meridional extreme values eliminated. A Volterra integral equation of the problem and the numerical solutions are given.

Stability of active trapdoors in axisymmetry

Trapdoor stability has been widely studied by many researchers in the field of tunneling engineering.A general question being fre-quently asked is that why most sinkholes have a near-perfect circular shape on the ground surface.This could be possibly explained by the current numerical study using finite element limit analysis under axisymmetric condition,where upper and lower bound solutions of active circular trapdoors are determined.The failure study of sinkholes and the associated failure mechanisms in this paper are for non-homogeneous clay with a linear increase of strength with depth under various cover depth ratios and dimensionless strength gra-dients.A design equation for predicting the stability solutions is also developed based on the novel three dimensional solutions using axisymmetry.

THE REGULARITY CRITERIA OF WEAK SOLUTIONS TO 3D AXISYMMETRIC INCOMPRESSIBLE BOUSSINESQ EQUATIONS

In this paper,we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations.To be more precise,under some conditions on the swirling component of vorticity,we can conclude that the weak solutions are regular.

AXISYMMETRIC CONTACT PROBLEM OF CUBIC QUASICRYSTALLINE MATERIALS

The axisymmetric elasticity theory of cubic quasicrystal was developed in Ref. [1]. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function, based on which, the exact analytic solutions for the elastic field of an axisymmetric contact problem of cubic quasicrystalline materials are obtained for universal contact stress or contact displacement. The result shows that if the contact stress has order - 1/2 singularity on the edge of the contact domain, die contact displacement is a constant in the contact domain. Conversely, if the contact displacement is a constant, the contact stress must have order - 1/2 singularity on the edge of die contact domain.

Undrained stability of a spherical cavity in cohesive soils using finite element limit analysis

A parametric study of undrained stability of a spherical cavity in clays is investigated by finite elementlimit analysis with an axisymmetric condition. Influences of cover depth ratio of cavity and dimensionlessoverburden factor on predicted failure mechanisms and dimensionless load factor are examined.It is found that a previously recommended and up-to-date lower bound solution to the problem wassignificantly inaccurate for practice use. Thus, an accurate approximate solution to the problem is proposedfrom nonlinear regression analysis of the computed average bound solutions. New cavity stabilityfactors for the soil cohesion and soil unit weight are proposed. New findings are revealed for the threedimensionaleffect of the cavity shape on these factors between the axisymmetric and plane strainconditions, and their applications to the undrained stability evaluation of cavity problems in practice aredescribed.

Free axisymmetric vibration of FGM circular plates

Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the Corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.

Detecting Intensity Evolution of the Western North Pacific Super Typhoons in 2016 Using the Deviation Angle Variance Technique with FY Data

This paper analyzes the complete lifecycle of super typhoons in 2016 in the western North Pacific(WNP) using the deviation angle variance technique(DAV-T). Based on the infrared images from Fengyun(FY) satellites, the DAV-T enables quantification of the axisymmetry of tropical cyclones(TCs) by using the DAV values; and thus, it helps improve the capability of TC intensity estimation. Case analyses of Super Typhoons Lionrock and Meranti were performed to explore the distribution characteristics of the DAV values at the various stages of TC evolution. The results show that the minimum DAV values(i.e., map minimum values: MMVs) gradually decreased and their locations constantly approached the circulation center with enhancement of the TC organization; however, when a ring or disk structure was formed around a TC, significant changes in MMV locations were no longer observed. Nonetheless,when large-scale non-closed deep convective cloud clusters appeared at the early stage or the dissipation stage of the typhoon, the axisymmetry of the TC was poor and the MMV locations tended to lie in the most convective region rather than in the TC circulation center. Overall, the MMVs and their locations, respectively, exhibited a strong correlation with the TC intensity and circulation center, and the correlation increased as the TCs became stronger. Combined with the China Meteorological Administration BestTrack dataset(CMA-BestTrack), statistical analysis of all research samples reveals that the correlation coefficient between the MMVs and maximum surface wind speeds(Vmax) was –0.80; the root mean square error(RMSE) of relative distance between the MMV locations and TC centers was 140.3 km; and especially, when the samples below the tropical depression(TD) intensity were removed, the RMSE of the relative distance decreased dramatically to 95.0 km. The value and location of the MMVs could be used as important indicators for estimating TC intensity and center.

Computing Viscous Flow in an Elastic Tube

We have developed a numerical method for simulating viscous flow through a compliant closed tube,driven by a pair of fluid source and sink.As is natural for tubular flow simulations,the problem is formulated in axisymmetric cylindrical coordinates,with fluid flow described by the Navier-Stokes equations.Because the tubular walls are assumed to be elastic,when stretched or compressed they exert forces on the fluid.Since these forces are singularly supported along the boundaries,the fluid velocity and pressure fields become unsmooth.To accurately compute the solution,we use the velocity decomposition approach,according to which pressure and velocity are decomposed into a singular part and a remainder part.The singular part satisfies the Stokes equations with singular boundary forces.Because the Stokes solution is unsmooth,it is computed to second-order accuracy using the immersed interface method,which incorporates known jump discontinuities in the solution and derivatives into the finite difference stencils.The remainder part,which satisfies the Navier-Stokes equations with a continuous body force,is regular.The equations describing the remainder part are discretized in time using the semi-Lagrangian approach,and then solved using a pressure-free projection method.Numerical results indicate that the computed overall solution is secondorder accurate in space,and the velocity is second-order accurate in time.

Nonlinear Axisymmetric Deformation Model for Structures of Revolution

An axisymmetric formulation for modeling three-dimensional deformation of structures of revolution is presented.The axisymmetric deformation model is described using the cylindrical coordinate system.Large displacement effects and material nonlinearities and anisotropy are accommodated by the formulation.Mathematical derivation of the formulation is given,and an example is presented to demonstrate the capabilities and efficiency of the technique compared to the full three-dimensional model.