Cheng Chang-jun

Boundary-integral equations and the boundary-element method for three-dimensional fracture mechanics

Abstract In this paper, the displacement-discontinuity fundamental solutions for three-dimensional fracture mechanics are obtained by an integral-transform method and the boundary-integral equations are established. By using finite-part integrals, the displacement-discontinuity boundary-element method is realized. Finally, two simple numerical exaamples are given.

Buckling and post-buckling of annular plates in shearing, part II: Post-buckling

Abstract Using the generalized and modified Von Karman theory for perforated thin plates having large deflections, the elastic buckling of annular plates under in-plane shear forces is studied in this paper. The mathematics problem is formulated rationally. The generalized eigenvalues of the linearized problem are discussed and the existence of bifurcation solutions near eigenvalues is analysed.

General mathematical theory of large deflections of thin plates with some holes

The theoretical analysis and the numerical computations for the problem of a thin plate with large deflection and some holes become much more difficult due to the multi-valued properties of the stress functionF and the single-valued demands on the displacements. The necessary and sufficient conditions which can assureF to be single-valued are obtained in this paper. At the same time, we prove that the single-valued demands on the displacements are equivalent to 3m functional constraint equationsDC(w,F)=0, wherem is the number of holes. From these conclusions, the single-valued governing-equations of the problem of plates with large deflection and some holes are derived. It is a system of fourth order partial differential equations with 3m unknown constants and constrained equations. A numerical method for solving this problem is presented. The problem of the critical load is considered and an iterative scheme for computing the buckled states is given when a critical load λ is ‘single’.

Non-axisymmetric instability of polar orthotropic annular plates

The non-axisymmetric instability of polar orthotropic annular plates under inplane uniform radial pressure is studied by use of the shooting method. The characteristic equations and eigenvalues under a variety of edge conditions are given. Under two appropriate hypotheses, we prove that all eigenvalues are bifurcation points. Hence, it is possible that non-axisymmetric buckled and post-buckled states branch from axisymmetric unbuckled states of an annular plate. Asymptotic formulae for buckled states are obtained and curves for the deflection and stress are shown.

Boundary integral equations and the boundary element method for buckling analysis of perforated plates

Abstract In this paper, a system of new boundary integral equations is established to solve the plane stress, critical loads and post-buckling problem for perforated thin plates, based on the general bifurcation theory and mathematical model for the stability analysis of perforated thin plates. As applications, we compute the critical loads and analyse the post-buckling behaviour of annular plates with simply supported and clamped edges under uniformly applied edge loads. The results agree well with those obtained by other methods. This shows that the boundary element method is efficiently applied to the post-buckling analyses of perforated thin plates and has the advantages of smaller-size matrices to process, less data to input and less time to use in computation compared with domain type solutions.

Boundary element method for solving dynamical response of viscoelastic thin plate (I)

In this paper, a boundary element method for solving dynamical response of viscoelastic thin plate is given. In Laplace domain, we propose two methods to approximate the fundamental solution and develop the corresponding boundary element method. Then using the improved Bellmans numerical inversion of the Laplace transform, the solution of the original problem is obtained. The numerical results show that this method has higher accuracy and faster convergence.

The growth of the void in a hyperelastic rectangular plate under a uniaxial extension

In the present paper, the finite deformation and stress analysis for a hyperelastic rectangular plate with a center void under a uniaxial extension is studied. In order to consider the effect of the existence of the void on the deformation and stress of the plate, the problem is reduced to the deformation and stress analysis for a hyperelastic annular plate and its approximate solution is obtained from the minimum potential energy principle. The growth of the cavitation is also numerically computed and analysed.

Thermal-buckling of thin annular plates under multiple loads

On the basis of Von Kármán equations, the thermal-buckling of thin annular plates subjected to a field of non-uniform axisymmetric temperature and a variety of boundary conditions is discussed. The linearized problem is analyzed and stability boundaries which characterize instability of a plate are obtained by means of numerical and analysis methods.

The buckled states of annular sandwich plates

In this paper, the axisymmetric buckled states of an annular sandwich plate (Reissner-type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled states in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.

A method of determining buckled states of thin plates at a double eigenvalue

A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.