Zhang Shan-yuan

The strain solitary waves in a nonlinear elastic rod

Solitary strain waves in a nonlinear elastic rod are analysed in this paper; influence of the physical and geometrical parameters of the rod on the waves are discussed; some main properties of the solitary waves are pointed out.

Geometrical nonlinear waves in finite deformation elastic rods

By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.

The dynamic buckling problem caused by propagation of stress wave in elastic cylindrical shells under impact torque

The buckling problem of cylindrical shells has been studied by many mechanic researchers from different points of view. In this paper, an elastic cylindrical shell with semi-infinite length is studied. Let its dynamic buckling under impact torque be reduced to a bifurcation problem caused by propagation of the torsional stress wave. The bifurcation problem is converted to a solution of nonlinear equations, the lateral inertia effect on the dynamic buckling is also discussed. Finally, numerical computation is carried out, from this, some beneficial conclusions are obtained.

Solitary waves in finite deformation elastic circular rod

A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.

Experimental studies on dynamic plastic buckling of circular cylindrical shells under axial impact

In the present paper, experimental studies on dynamic plasticbuckling of circular cylindrical shells under axial impact are carried out. Hopkinson bar and drop hammer apparatus are used for dynamic loading. Three groups of circular cylindrical shells made of copper are tested under axial impact. From the experiments, the first critical velocity corresponding to the axi-symmetric buckling mode and the second critical velocity corresponding to the non-axisymmetric buckling mode are determined. The present results come close to those of second critical velocity given by Wang Ren[4–6]. Two different kinds of non-axisymmetric buckling modes oval-shaped and triangle shaped are founded. The buckling modes under two loading cases, viz. with small mass but high velocity and with large mass and low velocity using Hopkinson bar and drop hammer, are different. Their critical energies are also discussed.

The impact torsional buckling of elastic cylindrical shells with arbitrary form imperfection

A perturbation analysis for the impact torsional buckling of imperfective elastic cylindrical shells subjected to a step torque is given. The imperfection is supposed to be small and has arbitrary form. It is shown that only the imperfection which has the shape of static torsional buckling mode could influence the critical step torque. Finally a formula is presented for the critical step torque.

The impact torsional buckling for the rigid plastic cylindrical shell

By using the energy criterion in[3], the impact torsional buckling for the rigid plastic cylindrical shell is studied. The linear dynamic torsional buckling equations for the rigid plastic shell is drived, and the critical impact velocity is given.

The asymptotic solution of a dynamic buckling problem in elastic columns

For the dynamic buckling of an elastic column, which is subjected to a longitudinal impact by a rigid body, the form of the axial load is very complicated. The problem may be reduced to discuss the solution of nonlinear partial differential equations. So far, a theoretical solution may not be obtained. In this paper, this dynamic buckling problem of an ideal elastic column with finite length is discussed. By the perturbation method with a small parameter and the variational method, a solution of this problem is given. Finally, numericall computation is carried out, from this, some beneficial conclusions are obtained.

A rate type method for large deformation problems of nonlinear elasticity

In this paper, we obtain the rate-type constitutive expressions of the nonlinear isotropic elasticity by using the Jaumann, Truesdell and Green-Naghdi stress rate respectively. Through analysing the simple shear deformation for Mooney-Rivlin material, three kinds of rate-type constitutive equations are verified to be equivalent to the original equation. Rate-type variational principles are also presented, and the Ritz method is used to obtain the numerical solution of a rectangular rubber membrane under uniaxial stretch.