Applications of wavelet galerkin fem to bending of beam and plate structures

I.IntroductionItilasbeenl'oundthatthewavelettheoryisapowerfLllmathematicaltooldevelopedillrecentyears.Asanewmathematicaltool,ithasbeenextensivelyappliedintheanalysisofsignalprocess,parttenrecognition,functionapproximation,andsolvingdifferentialequation(s),etc..Sinceasmallsignalinasighalprocesscanbecapturedbythewavelettheory,itsapplicationshavebeenpaidmuchattentionbothintheoryandinengneeringf'~'].Recently,thewavelettheory11asbeengeneralizedtofindanumericalsolutionofadifferentialequation.Forex…     

A meshless method of a thin plate

A meshless approach to analysis of arbitrary Kirchhoff plates by the local boundary integral equation(LBIE) method is presented. The method combines the advantageous features of, all the three methods: the Galerkin finite element method (GFEM), the boundary element method (BEM) and the element-free Galerkin method (EFGM). It is a truly meshless method, which means that the discretization is independent of geometric subdivision into elements or cells, but is only based on a set of nodes (ordered or scattered) over a domain in question. It involves only boundary integration, however, over a local boundary centered at the node in question; It poses no difficulties in satisfying the essential boundary conditions while leading to banded and sparse system matrices using the moving least square (MLS) approximations. It is shown that high accuracy can be achieved for arbitrary geometries for clamped and simply-supported edge conditions. The method is found to be simple, efficient, and attractive. Project supported by the National Science Foundation of China (No. 19972019).     

Galerkin meshless methods based on partition of unity quadrature

Introduction Meshlessmethodsarenewmethodsofnumericalcomputationwhichhavebeendeveloped rapidlyinrecentyears.Inthesemethods,onlynodesareneeded,meshinformationistotally unnecessary.Thiscanavoidorpartlyavoidthedifficultyofmeshgeneration.Duetohigh accuracyandstability,Galerkinmeshlessmethodsareappliedbroadly,butitisunavoidable tocomputetheintegrationoverthewholephysicaldomaininGalerkinweakform,whichisa greatchallengeforGalerkinmeshlessmethodsbecauseoftheabsenceofmesh.TocarryouttheintegrationinGal…     

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.     

The application of wavelet transform to wave breaking

Wavelet transform is a particularly useful tool to characterize transient phenomena such as wave breaking. In this paper, we apply wavelet transform to the detection and quantification of the breaking waves. We use a new method that uses the local properties of wavelet transform to detect and quantify the breaking waves and give some new breaking criteria. By comparing this method with the classic method, we find that wavelet transform is very effective in the detection of breaking waves. With wavelet transform, a set of measured wind wave data is investigated. The results have revealed some previously unknown phenomena about wave breaking. The project supported by the National Natural Science Foundation of China (49476254, 49606070) & the National High Technology Research and Development Program of China (863 Program)     

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).     

A simple postrocess procedure for Galerkin method

A kind simple postprocess procedure for classical Galerkin method for steady Navier-Stokes equations with stream function form was presented in this paper. The main ideal was to construct an approximate interactive rule between lower frequency components and higher frequency components by using the conception of Approximate Inertial Manifold (AIM) and a kind of new decomposition of the true solution. It is demonstrated in this paper that this kind of postprocess Galerkin method could derive a higher accuracy solution with lower computing efforts. Communicated by Zhang Hongqing Foundation item: the National Natural Science Foundation of China (19671067) Biography: Hou Yanren(1970-)     

Analysis of piezoelectric ceramic multilayer actuators based on an electro-mechanical coupled meshless method

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. In this method, an element free Galerkin (EFG) formulation, an enriched basic function and some special shape functions that contain discontinuous derivatives are employed. Based on the moving least squares (MLS) interpolation approach, the EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method can yield an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. In another example studying a ceramic multilayer actuator, the proposed model was found to be accurate in the simulation of stress and electric field concentrations arround the abrupt end of an internal electrode. The project supported by the National Natural Science Foundation of China (10025209, 10132010, and 90208002), and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7203/03E). The English text was polished by Yunming Chen.     

Orthogonal polynomials and determinant formulas of function-valued Padé-type approximation using for solution of integral equations

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given. Project supported by the National Natural Science Foundation of China (No.10271074)     

FINITE DEFORMATION ELASTO-PLASTIC THEORY AND CONSISTENT ALGORITHM

By using the logarithmic strain, the finite deformation plastic theory, corresponding to the infinitestimal plastic theory, is established successively. The plastic consistent algorithm with first order accuracy for the finite element method (FEM) is developed. Numerical examples are presented to illustrate the validity of the theory and effectiveness of the algorithm. Project supported by the National Natural Science Foundation of China (No. 19772973).     

Application of MLPG in Large Deformation Analysis

Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov–Galerkin method (MLPG) is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rotation. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O(N) algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.The project supported by the National Natural Science Foundation of China (10472051). The English text was polished by Keren Wang.     

DYNAMIC BUCKLING OF STATICALLY PRELOADED RING-STIFFENED CYLINDRICAL SHELLS UNDER AXIAL FLUID-SOLID IMPACT LOADING

The Initial Imperfection Amplified Criterion is applied to investigate the geometric nonlinear dynamic buckling of statically preloaded ring-stiffened cylindrical shells under axial fluid-solid impact. Taking account of the effects of large deformation and initial geometric imperfection, the governing equations are obtained by the Galerkin method and solved by the Runge-Kutta method. The effects of static preloading (uniform external radial pressure) on the buckling features and the load-carrying ability of ring-stiffened cylindrical shells against axial impact are discussed. The project is supported by the National Natural Sciences Foundation of China (No. 19802017).     

A numerical method for Cauchy principal value of singular integral under parametric transformation in BEM

A numerical method for the Cauchy principal value of the singular integral in BEM is developed using the concept of finite part integration under integral variable transformation. It is applied to the numerical integration on isoparametric element successfully, as shown in the examples in this paper.The project supported by National Natural Foundation of China.     

ANTIPLANE CIRCULAR INCLUSION WITH A CURVED CRACK CROSSING THE BOUNDARY

The weakly singular integral equation used to solve the problem of the curved crack crossing the boundary of the antiplane circular inclusion is presented. Using the principal part analysis method of the Cauchy type integral equation, the singular stress index at the intersection and the singular stress of angular regions near the intersection are obtained. By using the singular stress obtained, the stress intensity factor at the intersection is, defined. After the numerical solution of the integral equation, the stress intensity factors at the end points of the crack and intersection are obtainable. The research is supported by National Natural Science Foundation of China (No. 59879012) and is the project of Chinese Foundation of State Education Commission (No. 98024832).     

The hybrid control of vibration of thin plate with active constrained damping layer

This paper concerns in the active and passive hybrid control of vibration of the thin plate with Local Active Constrained damping Layer (LACL). The governing equations of system are formulated based on the constitutive equations of elastic, viscoelastic, piezoelectric materials. Galerkin method and GHM method are employed to transform partial differential equations into ordinary ones with a lower dimension. LQR method of classical control theory is used in simulating calculation. Numeral results show that the active and passive hybrid control manner obtained in this paper is a better one for vibration control of the plate. Project supported by the National Science Foundation of China (19632001) and the Research Foundation of Xian Jiaotong University     

INSTABILITY AND CHAOS IN A PIPE CONVEYING FLUID WITH ADDED MASS AT FREE END

This paper shows the mechanism of instability and chaos in a cantilevered pipe conveying steady fluid. The pipe under consideration has added mass or a nozzle at the free end. The Galerkin method is used to transform the original system into a set of ordinary differential equations and the standard methods of analysis of the discrete system are introduced to deal with the instability. With either the nozzle parameter or the flow velocity increasing, a route to chaos can be observed very clearly: the pipe undergoing buckling (pitchfork bifurcation), flutter (Hopf bifurcation), doubling periodic motion (pitchfork bifurcation) and chaotic motion occurring finally. The project supported by the National Key Projects of China under grant No. PD9521907 and Science Foundation of Tongji University under grant No. 1300104010.     

METHOD OF GREEN＇S FUNCTION OF CORRUGATED SHELLS

By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.     

Nonlinear vibration analysis of viscoelastic cable with small sag

Both the inplane and out-of-plane transverse vibrations of a viscoelastic cable subjected to an initial stress distributing uniform on the cross section are studied. The constitution of the cable material is assumed to be of the hereditary integral type. The partial differential-integral equations of motion are derived first. Then by applying Galerkin's method, the governing equations are reduced to a set of second-order nonlinear differential-integral equations which are solved by finite difference numerical integration procedures. Finally, the effects of the viscosity parameter and the elastic parameter on the transient amplitudes of the first mode are investigated by numerical simulation. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation of China.     

Analytical thermo-elastodynamic solutions for a nonhomogeneous transversely isotropic hollow sphere

Summary  The spherically symmetric dynamic thermoelastic problem for a special nonhomogeneous transversely isotropic elastic hollow sphere is formulated by introduction of a dependent variable and separation of variables technique. The derived solution can be degenerated into that for a homogeneous transversely isotropic hollow sphere, a nonhomogeneous isotropic hollow sphere or a solid sphere. The present method, allow to avoid integral transforms, is suited for a hollow sphere of arbitrary thickness subjected to arbitrary spherical symmetric thermal and mechanical loads, and is convenient in dealing with different boundary conditions of dynamic thermoelasticity . The numerical calculation involved is easy to be performed and its results are also presented. Received 30 October 2001; accepted for publication 21 February 2002 The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016)     

Time discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed. As compared with the existing discontinuous Galerkin finite element methods, the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured, whereas the discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously reduced, particularly, for material non-linear problems. Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed. Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain. The project supported by the National Natural Science Foundation of China (19832010, 50278012, 10272027) and the National Key Basic Research and Development Program (973 Program, 2002CB412709)