Interaction Between Line Soliton and Algebraic Soliton for Asymmetric Nizhnik-Novikov-Veselov Equation

Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.

THE INTERACTION OF PLANE SH－WAVES AND CIRCULAR CAVITY SURFACED WITH LINING IN ANISOTBOPIC MEDIA

In this paper. we use the complex function method for solving the problem ofinteraction of plane SH -waves and circular cavity surfaced with lining in anisotropicmedia.Anisotropic media can be used to simulate the conditions of the geology Thisproblem can be handled by using the method similar to that incorporated in Ref [5] todefine the scattering waves in media . added with the given boundary condition of the circular cavity. In this paper. as illustrated in the examples the results and discussions ofnumerical studies have been done for the interaction of plane SH-waves and two kinds of circular cavities surfaced with lining made up of different materials in anisotropicmedia.

Effect of rock joints on lined rock caverns subjected to high internal gaspressure

The storage of hydrogen gas in lined rock caverns(LRCs)may enable the implementation of the firstlarge-scale fossil-free steelmaking process in Sweden,but filling such storage causes joints in the rockmass to open,concentrating strains in the lining.The structural interaction between the LRC componentsmust be able to reduce the strain concentration in the sealing steel lining;however,this interaction iscomplex and difficult to predict with analytical methods.In this paper,the strain concentration in LRCsfrom the opening of rock joints is studied using finite element(FE)analyses,where the large-and small-scale deformation behaviors of the LRC are coupled.The model also includes concrete crack initiation anddevelopment with increasing gas pressure and rock joint width.The interaction between the jointed rockmass and the reinforced concrete,the sliding layer,and the steel lining is demonstrated.The results showthat the rock mass quality and the spacing of the rock joints have the greatest influence on the straindistributions in the steel lining.The largest effect of rock joints on the maximum strains in the steellining was observed for geological conditions of“good”quality rock masses.

Closed-form solution of beam on Pasternak foundation under inclined dynamic load

The dynamic response of an infinite Euler–Bernoulli beam resting on Pasternak foundation under inclined harmonic line loads is developed in this study in a closed-form solution.The conventional Pasternak foundation is modeled by two parameters wherein the second parameter can account for the actual shearing effect of soils in the vertical direction.Thus,it is more realistic than the Winkler model,which only represents compressive soil resistance.However,the Pasternak model does not consider the tangential interaction between the bottom of the beam and the foundation;hence,the beam under inclined loads cannot be considered in the model.In this study,a series of horizontal springs is diverted to the face between the bottom of the beam and the foundation to address the limitation of the Pasternak model,which tends to disregard the tangential interaction between the beam and the foundation.The horizontal spring reaction is assumed to be proportional to the relative tangential displacement.The governing equation can be deduced by theory of elasticity and Newton’s laws,combined with the linearly elastic constitutive relation and the geometric equation of the beam body under small deformation condition.Double Fourier transformation is used to simplify the geometric equation into an algebraic equation,thereby conveniently obtaining the analytical solution in the frequency domain for the dynamic response of the beam.Double Fourier inverse transform and residue theorem are also adopted to derive the closed-form solution.The proposed solution is verified by comparing the degraded solution with the known results and comparing the analytical results with numerical results using ANSYS.Numerical computations of distinct cases are provided to investigate the effects of the angle of incidence and shear stiffness on the dynamic response of the beam.Results are realistic and can be used as reference for future engineering designs.