The probability stability of viscoelastic plates

The almost sure stability of homogeneous viscoelastic plates subjected to a random wide-band stationary in-plane load is investigated. The viscoelastic behavior of the plate is described in terms of the Boltzmann superposition principle, the relaxation kemels of which are represented by the sums of exponents. On the assumption that the in-plane load is random wide-band stationary process, sufficient conditions for almost sure stability of viscoelastic plates are obtained by the applications of Lyapunov's direct method. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation.     

A quasi-flow constitutive model with strain-rate dependence

In this paper, the proposed is a quasi-flow constitutive model with strain-rate sensitivity for elastic plastic large deformation. The model is based on the Quasi-flow Corner theory, and is suitable for the sheet metal forming process simulation with a variable punch machine velocity. Uniaxial tensile tests and deep-drawing tests of a circular blank with square punch are carried out and numerically simulated. The consistency between the experimental and the numerically simulated results shows the validity of the present new constitutive model. The project supported by the Scientific Foundation of National Outstanding Youth of China (10125208), the National Natural Science Foundation of China (19832020), and the National Education Committee of China     

Meshless method based on collocation with consistent compactly supported radial basis functions

Based on our previously study, the accuracy of derivatives of interpolating functions are usually very poor near the boundary of domain when Compactly Supported Radial Basis Functions (CSRBFs) are used, so that it could result in significant error in solving partial differential equations with Neumann boundary conditions. To overcome this drawback, the Consistent Compactly Supported Radial Basis Functions (CCSRBFs) are developed, which satisfy the predetermined consistency conditions. Meshless method based on point collocation with CCSRBFs is developed for solving partial differential equations. Numerical studies show that the proposed method improves the accuracy of approximation significantly. The project supported by the National Natural Science Foundation of China (10172052)     

Stability analysis of non-autonomous stochastic Cohen–Grossberg neural networks

This paper is concerned with pth moment exponential stability of stochastic Cohen–Grossberg neural networks (SCGNN) with time-varying connection matrix and delays. With the help of Lyapunov function, stochastic analysis technique and the generalized Halanay inequality, a set of novel sufficient conditions on pth moment exponential stability for SCGNN is given. These results are helpful to design exponentially stable non-autonomous Cohen–Grossberg neural networks when stochastic effects are taken into consideration in practice. This work was supported in part by the High-Tech Research and Development Program of China under Grant No. 2006AA04A104, the National Natural Science Foundation of China under Grant No. 50677014, China Postdoctoral Science Foundation under Grant No. 20070410300, the Hunan Provincial Natural Science Foundation of China under Grant No. 07JJ4001.     

Dynamic behavior of two parallel symmetric permeable cracks in a piezoelectric strip

The dynamic behavior of two parallel symmetric cracks in a piezoelectric strip under harmonic anti-plane shear waves is studied using the Schmidt method for permeable crack surface conditions. The cracks are parallel to the edge of the strip. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the schmidt method. The results show that the stress and the electric displacement intensity factors depend on the geometry of the cracks, the frequency of incident waves, the distance between cracks and the thickness of the strip. It is also found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. Project supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang Province, the National Science Foundation with the Excellent Young Investigator Award (No. 19725209) and the Scientific Research Foundation of Harbin Institute of Technology (HIT.2000.30).     

Micro/macromechanical plastic limit analyses of composite materials and structures

The load-bearing capacities of ductile composite materials and structures are studied by means of a combined micro/macromechanics approach. Firstly, on the microscopic scale, the aim is to get the macroscopic strength domains by means of the homogenization theory of micromechanics. A representative volume element (RVE) is selected to reflect the microstructures of the composite materials. By introducing the homogenization theory into the kinematic limit theorem of plastic limit analysis, an optimization format to directly calculate the limit loads of the RVE is obtained. And the macroscopic yield criterion can be determined according to the relation between macroscopic and microscopic fields. Secondly, on the macroscopic scale, by introducing the Hill's yield criterion into the kinematic limit theorem, the limit loads of orthotropic structures such as unidirectional fiber-reinforced composite structures are worked out. The finite element modeling of the kinematic limit analysis is deduced into a nonlinear mathematical programming with equality-constraint conditions that can be solved by means of a direct iterative algorithm. Finally, some examples are illustrated to show the application of the present approach. Project supported by the National Natural Science Foundation of China (No. 19902007), the National Foundation for Excellent Doctoral Dissertation of China (No. 200025), the Fund of the Ministry of Education of China for Returned Oversea Scholars and the Basic Research Foundation of Tsinghua University.     

Exact solutions for free vibration of transversely isotropic piezoelectric circular plates

By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented. The project supported by the National Natural Science Foundation of China (No. 19872060)     

A SOLUTION PROCEDURE FOR LOWER BOUND LIMIT AND SHAKEDOWN ANALYSIS BY SGBEM

The symmetric Galerkin boundary element method (SGBEM) instead of the finite element method is used to perform lower bound limit and shakedown analysis of structures. The self-equilibrium stress fields are constructed by a linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains and obtained through elastic-plastic incremental analysis. The complex method is used to solve nonlinear programming and determine the maximal load amplifier. The limit analysis is treated as a special case of shakedown analysis in which only the proportional loading is considered. The numerical results show that SGBEM is efficient and accurate for solving limit and shakedown analysis problems. Project supported by the National Natural Science Foundation of China (No. 19902007), the National Foundation for Excellent Doctorial Dissertation of China (No. 200025) and the Basic Research Foundation of Tsinghua University.     

Mixed energy method for solution of quadratic programming problems and elastic-plastic analysis of truss structures

A new algorithm for the solution of quadratic programming problems is put forward in terms of the mixed energy theory and is further used for the incremental solution of elastic-plastic truss structures. The method proposed is different from the traditional one, for which the unknown variables are selected just in one class such as displacements or stresses. The present method selects the variables in the mixed form with both displacement and stress. As the method is established in the hybrid space, the information found in the previous incremental step can be used for the solution of the present step, making the algorithm highly efficient in the numerical solution process of quadratic programming problems. The results obained in the examples of the elastic-plastic solution of the truss structures verify what has been predicted in the theoretical analysis. Project supported by the National Natural Science Foundation of China (No. 50178916, No. 19732020 and No. 19872016), the National Key Basic Research Special Foundation (No. G1999032805), the Special Funds for Major State Basic Research Projects and the Foundation for University Key Teachers by the Ministry of Education of China.     

EXACT SOLUTIONS FOR FREE VIBRATIONS OF TRANSVERSELY ISOTROPIC CIRCULAR PLATES

By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made. The project is supported by the National Natural Science Foundation of China (No. 19872060).     

Calculation for path-domain independentJ integral with elasto-viscoplastic consistent tangent operator concept-based boundary element methods

This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals. The project supported by National Natural Science Foundation of China (9713008) and Zhejiang Natural Science Foundation Special Funds No. RC.9601     

SPONTANEOUS POLARIZATION AND THE DISTRIBUTION OF INTERNAL STRESS ANDELECTRIC FIELDS AROUND A TRIPLE POINT

In this article, distributions of internal stress and internal electric fields around a triple point of ferroelectric polycrystals generated by the spontaneous deformation and spontaneous polarization were investigated. It was found that when all three grains consist of a single domain, the internal stresses and the internal electric fields do not vanish. Though it may be determined according to the principle of energy, the spontaneous configuration will not be unique without involving other conditions due to the symmetry of the crystal structure. Sponsored by National Natural Science Foundation of China(No. 19672053) and Special Funds for Doctoral Programs (No. 96061305).     

Effective elastic moduli of inhomogeneous solids by embedded cell model

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional two-phase composites. The project supported by the National Natural Science Foundation of China (No. 19704100) and the National Natural Science Foundation of Chinese Academy of Sciences (No. KJ951-1-201)     

Applications of wavelet Galerkin FEM to bending of plate structure

A kind of calculating method for high order differentials expanded by the wavelet scaling functions and the integral of their product used in Galerkin FEM is proposed, so that we can use the wavelet Galerkin FEM to solve boundary-value differential equations with orders higher than two. To combine this method with the Generalized Gaussian integral method in wavelet theory, we can find that this method has many merits in solving mechanical problems, such as the bending of plates and those with variable thickness. The numerical results show that this method is accurate. This project is supported by the National Natural Science Foundation of China (No. 19772014) and the National Outstanding Young Scientist Foundation of China (No. 19725207).     

Numerical solutions of incompressible Euler and Navier-Stokes equations by efficient discrete singular convolution method

An efficient discrete singular convolution (DSC) method is introduced to the numerical solutions of incompressible Euler and Navier-Stokes equations with periodic boundary conditions. Two numerical tests of two-dimensional Navier-Stokes equations with periodic boundary conditions and Euler equations for doubly periodic shear layer flows are carried out by using the DSC method for spatial derivatives and fourth-order Runge-Kutta method for time advancement, respectively. The computational results show that the DSC method is efficient and robust for solving the problems of incompressible flows, and has the potential of being extended to numerically solve much broader problems in fluid dynamics. The project supported by the National Natural Science Foundation of China (No.19902010).     

Analysis of transient wave scattering from an inclusion with an unilateral smoothly contact interface by BEM

Summary A 2D time-domain Boundary Element Method (BEM) is applied to solve the problem of transient scattering of plane waves by an inclusion with a unilateral smooth contact interface. The incident wave is assumed strong enough so that localized separations take place along the interface. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (separation and contact regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of plane waves by the cross section of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed. The financial support by the China National Natural Science Foundation under Grant No. 19872001 and No. 59878004 is gratefully acknowledged. The second author is also grateful to the support of the National Science Fund for Distinguished Young Scholars under Grant No. 10025211.     

EXPERIMENTAL INVESTIGATION AND COMPUTER SIMULATION ON DYNAMIC BUCKLING BEHAVIOR OF LIQUID-FILLED CYLINDRICAL SHELLS UNDER AXIAL IMPACT

This article reports an experimental investigation on the axial impact buckling of thin metallic cylindrical shells fully filled with water. Low velocity impact tests are carried out by DHR-9401 drop hammer rig. The whole process of dynamic buckling is simulated using LS-DYNA computer code. The consistency between experimental observation and numerical simulation is quite satisfactory. The investigation indicates that quite high internal hydrodynamic pressure occurs inside the shell during the impact process. Under the combined action of the high internal pressure and axial compression plastic buckling occurs easily in the thin-walled shells and buckling modes take on regular and axisymmetric wrinkles. This project is supported by the National Natural Science Foundation of China(19672039) and the Shanxi Foundation for Returned Scholars from Abroad.     

A note for analysis of thermo-mechanical contact problems

A discussion about the bifurcation and non-uniqueness of solutions in the analysis of thermo-mechanical contact problems with initial gap is given. Without loss of generality, a mechanical contact problem coupled with steady heat transfer is studied and an example of non-uniqueness of solutions caused by the thermo-mechanical mechanism is presented. The important work is that the non-uniqueness of solutions, which is different from that found in the analysis of the traditional frictional contact problems, is studied in detail. The possible oscillation and non-convergence problems in the iteraction process of the numerical computation are discussed, and an enhanced algorithm is put forward to overcome the difficulties. Project sypported by the National Natural Science Foundation of China (Nos. 50178016, 10225212 and 19872016), the National Key Basic Research Special Foundation (No. G1999032805) and the Foundation for University Key Teacher by the Ministry of Education.     

Nonlinear vibration of beamplates with a delamination

The problem of beam-plates with a delamination located at an arbitrary site undergoing non-linear free vibration without damp is investigated. For this problem, nonlinear governing equations as well as the continuity, equilibrium and compatibility conditions are established. The Galerkin method and harmonic balance method are employed to find solutions. Finally, in some examples amplitude-frequency curves of the delaminated structure are presented in order to reveal some special dynamic features. Supported by the National Natural Science Foundation of China (No. 19872024).     

DYNAMIC SIMULATION OF ROTATING SHELLS COUPLED WITH LIQUID

The dynamic behaviors of rotating shells coupled with liquid are shown. The shell under consideration has arbitrary boundary conditions and a complex shape. A modified boundary element method and finite strip technique are used to improve the computing efficiency and to guarantee the continuity conditions on the liquid-shell interaction plane. The effects of various parameters such as shell's thickness and liquid depth are investigated. Dynamic simulations are applied to several typical shell-liquid systems, and the natural frequencies, mode shapes and response of vibration are calculated numerically. Project supported by the National Natural Science Foundation of China (No. 19702004).