共查询到20条相似文献,搜索用时 15 毫秒
1.
A meshfree formulation of local radial point interpolation method (LRPIM) for incompressible flow simulation 总被引:4,自引:0,他引:4
The LRPIM method is adopted to simulate the two-dimensional natural convection problems within enclosed domain of different
geometries. In this paper, the vorticity-stream function form of N-S equations is taken as the governing equations. It was
observed that the obtained results agreed very well with others available in the literatures, and with the same nodal density,
the accuracy achieved by the LRPIM method is much higher than that of the finite difference (FD) method. The numerical examples
show that the present LRPIM method can successfully deal with incompressible flow problems on randomly distributed nodes.
Received: 2 April 2002 / Accepted: 6 January 2003
The authors would like to thank Mr. Y. T. Gu for his contribution to this work. 相似文献
2.
A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions 总被引:4,自引:0,他引:4
A meshless method is developed for the stress analysis of two-dimensional solids, based on a local weighted residual method
with the Heaviside step function as the weighting function over a local subdomain. Trial functions are constructed using radial
basis functions (RBF). The present method is a truly meshless method based only on a number of randomly located nodes. No
domain integration is needed, no element matrix assembly is required and no special treatment is needed to impose the essential
boundary conditions. Effects of the sizes of local subdomain and interpolation domain on the performance of the present method
are investigated. The behaviour of shape parameters of multiquadrics (MQ) has been systematically studied. Example problems
in elastostatics are presented and compared with closed-form solutions and show that the proposed method is highly accurate
and possesses no numerical difficulties.
Received: 10 November 2002 / Accepted: 5 March 2003 相似文献
3.
A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures 总被引:3,自引:0,他引:3
A mesh free method called point interpolation method (PIM) is presented for static and mode-frequency analysis of two-dimensional
piezoelectric structures. In the present method, the problem domain and its boundaries are represented by a set of properly
scattered nodes. The displacements and the electric potential of a point are interpolated by the values of nodes in its local
support domain using shape functions derived based on a point interpolation scheme. Techniques are discussed to surmount the
singularity of the moment matrix. Variational principle together with linear constitutive piezoelectric equations is used
to establish a set of system equations for arbitrary-shaped piezoelectric structures. These equations are assembled for all
quadrature points and solved for displacements and electric potentials. A polynomial PIM program has been developed in MATLAB
with matrix triangularization algorithm (MTA), which automatically performs a proper node enclosure and a proper basis selection.
Examples are also presented to demonstrate the accuracy and stability of the present method and their results are compared
with the conventional FEM results from ABAQUS as well as the analytical or experimental ones.
Received: 6 February 2002 / Accepted: 5 August 2002 相似文献
4.
This paper presents a truly meshless approximation strategy for solving partial differential equations based on the local
multiquadric (LMQ) and the local inverse multiquadric (LIMQ) approximations. It is different from the traditional global multiquadric
(GMQ) approximation in such a way that it is a pure local procedure. In constructing the approximation function, the only
geometrical data needed is the local configuration of nodes fallen within its influence domain. Besides this distinct characteristic
of localization, in the context of meshless-typed approximation strategies, other major advantages of the present strategy
include: (i) the existence of the shape functions is guaranteed provided that all the nodal points within an influence domain
are distinct; (ii) the constructed shape functions strictly satisfy the Kronecker delta condition; (iii) the approximation
is stable and insensitive to the free parameter embedded in the formulation and; (iv) the computational cost is modest and
the matrix operations require only inversion of matrices of small size which is equal to the number of nodes inside the influence
domain. Based on the present LMQ and LIMQ approximations, a collocation procedure is developed for solutions of 1D and 2D
boundary value problems. Numerical results indicate that the present LMQ and LIMQ approximations are more stable than their
global counterparts. In addition, it demonstrates that both approximation strategies are highly efficient and able to yield
accurate solutions regardless of the chosen value for the free parameter.
Received: 10 October 2002 / Accepted: 15 January 2003 相似文献
5.
Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure 总被引:1,自引:0,他引:1
Simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively
controlled plate structure is investigated in this paper. The system consists of a clamped-free plate, a H
2 controller and four surface-bonded piezoelectric actuators utilized for suppressing the bending and torsional vibrations
induced by external disturbances. The plate is represented by a rectangular design domain which is discretized by a regular
finite element mesh and for each element the parameter indicating the presence or absence of material is used as a topology
design variable. Due to the unavailability of large-scale 0–1 optimization algorithms, the binary variables of the original
topology design problem are relaxed so that they can take all values between 0 and 1. The popular techniques in the topology
optimization area including penalization, filtering and perimeter restriction are also used to suppress numerical problems
such as intermediate thickness, checkerboards, and mesh dependence. Moreover, since it is not efficient to treat the structural
and control design variables equally within the same framework, a nested solving approach is adopted in which the controller
syntheses are considered as sub processes included in the main optimization process dealing with the structural topology and
actuator locations. The structural and actuator variables are solved in the main optimization by the method of moving asymptotes,
while the control parameters are designed in the sub optimization processes by solving the Ricatti equations. Numerical examples
show that the approach used in this paper can produce systems with clear structural topology and high control performance.
Received 16 November 2001 / Accepted 26 February 2002 相似文献
6.
A meshfree method based on the first-order least-squares formulation for linear elasticity is presented. In the authors'
previous work, the least-squares meshfree method has been shown to be highly robust to integration errors with the numerical
examples of Poisson equation. In the present work, conventional formulation and compatibility-imposed formulation for linear
elastic problems are studied on the convergence behavior of the solution and the robustness to the inaccurate integration
using simply constructed background cells. In the least-squares formulation, both primal and dual variables can be approximated
by the same function space. This can lead to higher rate of convergence for dual variables than Galerkin formulation. In general,
the incompressible locking can be alleviated using mixed formulations. However, in meshfree framework these approaches involve
an additional use of background grids to implement lower approximation space for dual variables. This difficulty is avoided
in the present method and numerical examples show the uniform convergence performance in the incompressible limit. Therefore
the present method has little burden of the requirement of background cells for the purposes of integration and alleviating
the incompressible locking.
Received: 16 December 2001 / Accepted: 4 November 2002 相似文献
7.
A comparison between weak form meshless local Petrov-Galerkin method (MLPG) and strong form meshless diffuse approximate method (DAM) is performed for the diffusion equation in two dimensions. The shape functions are in both methods obtained by moving least squares (MLS) approximation with the polynomial weight function of the fourth order on the local support domain with 13 closest nodes. The weak form test functions are similar to the MLS weight functions but defined over the square quadrature domain. Implicit timestepping is used. The methods are tested in terms of average and maximum error norms on uniform and non-uniform node arrangements on a square without and with a hole for a Dirichlet jump problem and involvement of Dirichlet and Neumann boundary conditions. The results are compared also to the results of the finite difference and finite element method. It has been found that both meshless methods provide a similar accuracy and the same convergence rate. The advantage of DAM is in simpler numerical implementation and lower computational cost. 相似文献
8.
Z. Zong 《Computational Mechanics》2003,31(3-4):284-292
Lagrange interpolation is extended to the complex plane in this paper. It turns out to be composed of two parts: polynomial
and rational interpolations of an analytical function. Based on Lagrange interpolation in the complex plane, a complex variable
boundary collocation approach is constructed. The method is truly meshless and singularity free. It features high accuracy
obtained by use of a small number of nodes as well as dimensionality advantage, that is, a two-dimensional problem is reduced
to a one-dimensional one. The method is applied to two-dimensional problems in the theory of plane elasticity. Numerical examples
are in very good agreement with analytical ones. The method is easy to be implemented and capable to be able to give the stress
states at any point within the solution domain.
Received: 20 August 2002 / Accepted: 31 January 2003 相似文献
9.
Elyas Shivanian 《Engineering Analysis with Boundary Elements》2013,37(12):1693-1702
In this paper the meshless local radial point interpolation (MLRPI) method is applied to simulate a nonlinear partial integro-differential equation arising in population dynamics. This PDE is a competition model in which similar individuals are competing for the same resources. It is a kind of reaction–diffusion equation with integral term corresponding to nonlocal consumption of resources. In MLRPI method, it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes, such as circles or squares in two dimensions and spheres or cubes in three dimensions. The point interpolation method is proposed to construct shape functions using the radial basis functions. A one-step time discretization method is employed to approximate the time derivative. To treat the nonlinearity, a simple predictor–corrector scheme is performed. Also the integral term, which is a kind of convolution, is treated by the cubic spline interpolation. The numerical studies on sensitivity analysis and convergence analysis show that our approach is stable. Finally, two numerical examples are presented showing the behavior of the solution and the efficiency of the proposed method. 相似文献
10.
Underwater explosion arising from high explosive detonation consists of a complicated sequence of energetic processes. It
is generally very difficult to simulate underwater explosion phenomena by using traditional grid-based numerical methods due
to the inherent features such as large deformations, large inhomogeneities, moving interface and so on. In this paper, a meshless,
Lagrangian particle method, smoothed particle hydrodynamics (SPH) is applied to simulate underwater explosion problems. As
a free Lagrangian method, SPH can track the moving interface between the gas produced by the explosion and the surrounding
water effectively. The meshless nature of SPH overcomes the difficulty resulted from large deformations. Some modifications
are made in the SPH code to suit the needs of underwater explosion simulation in evolving the smoothing length, treating solid
boundary and material interface. The work is mainly focused on the detonation of the high explosive, the interaction of the
explosive gas with the surrounding water, and the propagation of the underwater shock. Comparisons of the numerical results
for three examples with those from other sources are quite good. Major features of underwater explosion such as the magnitude
and location of the underwater explosion shock can be well captured.
Received: 2 April 2002 / Accepted: 20 September 2002 相似文献
11.
A solution to the problem of radiation stability of metallic materials for nuclear power reactors is suggested. It is by
selecting and creating alloys with structural (unhealable) vacancies, whose concentration is determined precisely by the stoichiometry
of alloys, but being independent of temperature and any other external influences. The advantages as well as difficulties
arising from the technical application of radiation stable alloys proposed are considered.
Received: 8 April 1997/Accepted: 28 May 1997 相似文献
12.
Based on the mechanism of shear locking phenomenon and potential functional of Reissner plate bending problem, the generalized
mixed variational principle for Reissner plate analysis is presented by parameterized Lagrange multiplier method. The proposed
variational functional contains splitting factors which are able to adjust the shear potential energy and shear complementary
energy components in it. The generalized mixed finite element formulation of bilinear quardrilateral element for Reissner
plate bending analysis is established in terms of the new variational principle. The stiffness of the finite element model
can be changed by the alteration of the splitting factors. Thus both the free of shear locking and higher accuracy are obtained
by the choice of appropriate splitting factors. The most important is that this paper gives one self-adaptative way to choose
the splitting factors for thin and moderately thick plates. This results in the comparative order of magnitude between the
bending stiffness and shear stiffness for the arbitrary thickness. In the application of two-by-two exact Gaussian integration
scheme to the proposed mixed element model, numerical examples show that free of locking is obtained even in the thin plate
limit and high accuracy is given for moderately thick plate.
Received: 15 January 2002 / Accepted: 10 September 2002
This work is partially supported by the National Nature Science Fund in China under Award No. 53978376 相似文献
13.
This paper presents a rate-independent elastoplastic constitutive model for (nearly) incompressible biological fiber-reinforced
composite materials. The constitutive framework, based on multisurface plasticity, is suitable for describing the mechanical
behavior of biological fiber-reinforced composites in finite elastic and plastic strain domains. A key point of the constitutive
model is the use of slip systems, which determine the strongly anisotropic elastic and plastic behavior of biological fiber-reinforced
composites. The multiplicative decomposition of the deformation gradient into elastic and plastic parts allows the introduction
of an anisotropic Helmholtz free-energy function for determining the anisotropic response. We use the unconditionally stable
backward-Euler method to integrate the flow rule and employ the commonly used elastic predictor/plastic corrector concept
to update the plastic variables. This choice is expressed as an Eulerian vector update the Newton's type, which leads to a
numerically stable and efficient material model. By means of a representative numerical simulations the performance of the
proposed constitutive framework is investigated in detail.
Received: 12 December 2001 / Accepted: 14 June 2002
Financial support for this research was provided by the Austrian Science Foundation under START-Award Y74-TEC. This support
is gratefully acknowledged. 相似文献
14.
In this paper, a meshless local radial point collocation method based on multiquadric radial basis function is proposed to analyze the free vibration of laminated composite plates. This method approximates the governing equations based on first-order shear deformation theory using the nodes in the support domain of any data center. Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, and material properties are computed by present method. The choice of shape parameter, effect of dimensionless sizes of the support domain on accuracy, convergence characteristics are studied by several numerical examples. The results are compared with available published results which demonstrate the accuracy and efficiency of present method. 相似文献
15.
A. Sellier 《Computational Mechanics》2002,28(3-4):202-211
This work determines the electrophoretic motion of two colloidal particles embedded in a viscous and unbounded electrolyte.
Contrary to other works in the field, the advocated method does not calculate the perturbation electric potential and the
electrolyte Stokes flow in the whole fluid domain and its range of applications is not restricted to the case of uniformly
charged particles embedded in a uniform electric field E
∞. The idea consists in establishing and solving thirteen Fredholm boundary integral equations (one of the second kind plus
twelve of the first kind). The numerical implementation is briefly reported. Numerical benchmarks and new results are both
presented and discussed with a special attention to the interactions between the particles.
Received 26 February 2001 相似文献
16.
17.
A mixed formulation for Timoshenko beam element on Winkler foundation has been derived by defining the total curvature in
terms of the bending moment and its second order derivation. Displacement and moment have been chosen as primary variables,
while slope and first derivation of moment have been chosen as secondary variables. The behaviour matrix for Timoshenko beam
element has been obtained in mixed form by using weak formulation with equilibrium and compatibility equations. The presented
formulation makes the analysis of beams free of shear locking.
Received: 10 July 2002 / Accepted: 14 January 2003 相似文献
18.
Time Discontinuous Galerkin methods require the factorization of a matrix larger than that exploited in standard implicit
schemes. Therefore, they lend themselves to implementations based on predictor-multicorrector solution algorithms. In this
paper, various convergent and computationally efficient iterative methods implemented in the unknown displacements for determining
the solution of non linear systems are proposed. The iterative solutions presented here differ from those implemented in the
unknown velocities in that they are computationally superior. The results of numerical simulations relevant to Duffing oscillators
and to a stiff spring pendulum discretized with finite elements which are designed to evaluate the efficacy of these iterative
methods with non-linear systems, show a low-computational expense when compared to earlier iterative schemes.
Received: 27 May 2002 / Accepted: 28 January 2003
The financial support from the Italian Ministry for Education, Universities and Research (MIUR) is acknowledged. However,
opinions expressed in this paper are those of the writers, and do not necessarily reflect the views of the sponsoring agency. 相似文献
19.
On the method of finite spheres in applications: towards the use with ADINA and in a surgical simulator 总被引:2,自引:0,他引:2
In this paper we report some recent advances regarding applications using the method of finite spheres; a truly meshfree
numerical technique developed for the solution of boundary value problems on geometrically complex domains. First, we present
the development of a preprocessor for the generation of nodal points on two-dimensional computational domains. Then, the development
of a specialized version of the method of finite spheres using point collocation and moving least squares approximation functions
and singular weight functions is reported for rapid computations in virtual environments involving multi-sensory (visual and
touch) interactions.
Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many
years. 相似文献
20.
G. Y. Yu 《Computational Mechanics》2002,29(3):191-198
This paper presents a symmetric collocation BEM (SCBEM)/FEM coupling procedure applicable to 2-D time domain structural–acoustic
interaction problems. The use of symmetry for BEM not only saves memory storage but also enables the employment of efficient
symmetric equation solvers, especially for BEM/FEM coupling procedure. Compared with symmetric Galerkin BEM (SGBEM) where
double boundary integration should be carried out, SCBEM can reduce significantly the computing cost. Two numerical examples
are included to illustrate the effectiveness and accuracy of the proposed method.
Received: 2 November 2001 / Accepted: 27 May 2002 相似文献