摘要:

AbstractIn this paper we describe how wavelets may be used to solve partial differential equations. These problems are currently solved by techniques such as finite differences, finite elements and multi‐grid. The wavelet method, however, offers several advantages over traditional methods. Wavelets have the ability to represent functions at different levels of resolution, thereby providing a logical means of developing a hierarchy of solutions. Furthermore, compactly supported wavelets (such as those due to Daubechies1) are localized in space, which means that the solution can be refined in regions of high gradient, e.g. stress concentrations, without having to regenerate the mesh for the entire problem.In order to demonstrate the wavelet technique, we consider the one‐dimensional counterpart of Helmholtz's equation. By comparison with a simple finite difference solution to this problem with periodic boundary conditions, we show how a wavelet technique may be efficiently developed. Dirichlet boundary conditions are then imposed, using the capacitance matrix method described by Proskurowski and Widlund2and others. The convergence rates of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions. Preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method, at least for problems with simple geometr

ISSN:0029-5981    

DOI:10.1002/nme.1620371602

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper presents a Wave Equation Model (WEM) to solve advection dominant Advection–Diffusion (A–D) equation. It is known that the operator‐splitting approach is one of the effective methods to solve A–D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first‐order advection equation, the present wave equation model solves a second‐order equivalent wave equation whose solution is identical to that of the first‐order advection equation. Numerical examples of 1‐D and 2‐D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1‐D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for pra

ISSN:0029-5981    

DOI:10.1002/nme.1620371603

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractFully automatic three‐dimensional mesh generation is an essential and increasingly crucial requirement for finite element solution of partial derivative equations. The results of numerical simulation, more precisely the convergence and accuracy of numerical solutions, closely depends on the quality of the underlying mesh. This work introduces a fully automatic finite element mesh algorithm with simplexes (tetrahedra), adapted to complex geometries described by disctete data.This paper is divided in four sections: (a) brief introduction to discrete geometry is given, as well as the basic definition of the domain of interest; (b) description of the voxel approach to tetrahedronization. The tetrahedronization process uses a divide‐and‐conquer method, which provides small elements on the boundary of the domain of interest. Voxels of the domain are subdivided according to an automatic procedure, which preserves the topology. Specific rules were introduced which allow reducing the number of voxel configurations to be treated, and consequently the computation time; (c) presentation of results and performances of the mesh algorithms. The resulting algorithm demonstrates annlogngrowth rate with respect to the number of elements; (d) optimization of the mesh generation process at hand of a ‘finite‐octree’ type of explicit contro

ISSN:0029-5981    

DOI:10.1002/nme.1620371604

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper focuses on the numerical modelling of phase‐change processes with natural convection. In particular, two‐dimensional solidification and melting problems are studied for pure metals using an energy preserving deforming finite element model. The transient Navier–Stokes equations for incompressible fluid flow are solved simultaneously with the transient heat flow equations and the Stefan condition. A least‐squares variational finite element method formulation is implemented for both the heat flow and fluid flow equations. The Boussinesq approximation is used to generate the bulk fluid motion in the melt. The mesh motion and mesh generation schemes are performed dynamically using a transfinite mapping. The consistent penalty method is used for modelling incompressibility. The effect of natural convection on the solid/liquid interface motion, the solidification rate and the temperature gradients is found to be important. The proposed method does not possess some of the false diffusion problems associated with the standard Galerkin formulations and it is shown to produce accurate numerical solutions for convection dominated phase‐change

ISSN:0029-5981    

DOI:10.1002/nme.1620371605

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractSome optimal control problems arising from impressed cathodic protection systems are considered. Our objective is to find the location of anodes and the current density on the anodes that yield an optimal potential distribution on the cathode. We present a simple formula for the linear model and a gradient algorithm for the non‐linear model. Boundary element methods are employed for the numerical calculatio

ISSN:0029-5981    

DOI:10.1002/nme.1620371606

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper, a new one‐parameter hybrid functional is obtained as a special case of Felippa and Militello's parametrized variational principles. The functional contains stress, strain and compatible displacement as the primary fields. It will be proved that some of the existing variable stiffness formulations fall into the framework of the new functional. Novel applications of the functional are also suggested, mainly for removal of locking. Solid element, destabilized 8‐node and stabilized 9‐plate elements are designed. All of them can handle thin plate/shell analysis. In particular, a prominent method is devised for constructing stabilization vectors. The vectors are explicit linear functions of the nodal coordinates and can be implemented without resorting to Gram–Schmidt orthogonalization or numerical integration. Results of the new elements in popular benchmark tests are enco

ISSN:0029-5981    

DOI:10.1002/nme.1620371607

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractDelamination is a major damage mode in laminated composites since it can cause severe structural degradation. Based on an interlaminar shear stress continuity theory and a linear shear slip theory, a so‐called Interlayer Shear Slip Theory was presented in a previous study. This theory was verified to be feasible for shearing‐mode delamination analysis. However, in order to account for opening‐mode delamination in laminated composites, the continuity of interlaminar normal stress and the modelling of normal separation on the composite interface should also be considered. The present study gives a complete discussion on the Interlaminar Bonding Theory. The effects of interlaminar bonding condition on the laminate deformation and stress distribution are also presented. It is concluded from numerical results that the present theory is suitable for analysis of composite laminates with imperfect inter

ISSN:0029-5981    

DOI:10.1002/nme.1620371608

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe new method presented here is capable of building finite element meshes and managing their adaptation simultaneously to the object load case and geometry before any calculations, i.e. ana priorimesh adaptation is conducted. The principle relies on an analogy between a finite element mesh and the equilibrium position of a network of branches. Each branch is adequately sized by setting force–length ratios, calledforce densities. Starting from these data, the nodal co‐ordinates are obtained through the solution of a linear system which describes the equilibrium state of the net. This method seems very attractive since the only given data are: a connectivity table, the number of boundary and interior nodes and a geometrical description of the boundaries.It is also demonstrated how to obtain the equilibrium nodal positions when boundary nodes are allowed to slide and evolution laws of force densities cope with punctual forces and geometric singularities. A comparison of results is conducted between meshes issued by the new technique and those obtained with standard FE co

ISSN:0029-5981    

DOI:10.1002/nme.1620371609

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper, a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented. The method, which is based on the block Lanczos algorithm, is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs. Given the solution to the original systemAx= λx, procedures are developed for the modified standard eigenvalue Problem (A+ ΔA)x̄ =λx̄, where1ΔA= ΣjBSjBT, whereSj=S jT∈ ℛp×p,p≪nandB∈ ℛn×pis constant for all the perturbationsSj.2ΔA= ΣiΣjBiSjBiT, whereBi∈ ℛn×pmay vary with the pertubationsSj.The procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem. Numerical examples are given to demonstrate th

ISSN:0029-5981    

DOI:10.1002/nme.1620371610

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620371611

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY