摘要:

AbstractBased on the Hellinger‐Reissner principle and the deformation energy due to assumed stresses and displacements, the problem of the kinematic deformation modes in assumed stress hybrid/mixed finite elements has been examined. Basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes. Quadrilateral membrane and axisymmetric elements, and three‐dimensional hexahedral elements, are used to illustrate the suggested proced

ISSN:0029-5981    

DOI:10.1002/nme.1620191202

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractThe smoothing effects of upstream collocation in convective problems are attributable to a dissipative error term analogous to that in upstream‐weighted finite difference

ISSN:0029-5981    

DOI:10.1002/nme.1620191203

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620191204

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractIn transient analysis it is generally thought that small time steps can only improve the accuracy, because standard stability theorems limit the maximum time step for a given mesh size. In finite element approximations, however, small time steps may cause stability problems which lead to physically unreasonable results. It is shown that this is due to the violation of a discrete maximum principle. The influence of lumped and consistent mass matrices on a stable discretization of time and space is presented.

ISSN:0029-5981    

DOI:10.1002/nme.1620191205

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractA multiple‐parameter reduced basis technique and a problem‐adaptive computational algorithm are presented for the bifurcation and post‐buckling analyses of composite plates subjected to combined loadings. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the stability boundary. The plate is discretized by using displacement finite element models and the analysis region is reduced by exploiting the special symmetries exhibited by the response of the plate. The vector of unknown nodal displacements is expressed as a linear combination of a small number of path derivatives (derivatives of the nodal displacements with respect to path parameters), and a Rayleigh‐Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the stability boundary of the plate.In the second stage, a nonllnear solution in the vicinity of the stability boundary is obtained by using a bifurcation buckling mode as a predictor, and a set of reduced equations is generated. In the third stage, the reduced equations are used to trace post‐buckling paths corresponding to various combinations of the load parameters.The potential of the proposed approach is discussed and its effectiveness is demonstrated by means of a numerical example of laminated composite plate subjected to combined compressive and shear

ISSN:0029-5981    

DOI:10.1002/nme.1620191206

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractA triangular cylindrical shell element based on discrete Kirchhoff theory is developed. It is a three‐node, 27‐degrees‐of‐freedom element using cubic polynomials for the tangential and normal displacement interpolations. The normal rotations are independently interpolated by quadratic polynomials. The formulation is capable of modelling general anisotropy representative of multi‐layered, multi‐directionally oriented composite construction. The numerical results indicate that the solution for displacements and stresses of cylindrical shells converge monotonically and rapidly to those based on deep s

ISSN:0029-5981    

DOI:10.1002/nme.1620191207

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractBoundary integral equation methods are presented for the solution of some two‐dimensional phase change problems. Convection may enter through boundary conditions, but cannot be considered within phase boundaries. A general formulation based on space‐time Green's functions is developed using the complete heat equation, followed by a simpler formulation using the Laplace equation. The latter is pursued and applied in detail. An elementary, noniterative system is constructed, featuring linear interpolation over elements on a polygonal boundary. Nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution. The system performs well against basic analytical solutions, using these values in the interphase jump condition, with the simplest formulation of the surface normal at boundary vertices. Because the discretized surface changes automatically to fit the scale of the problem, the method appears to offer many of the advantages of moving mesh finite element methods. However, it only requires the manipulation of a surface mesh and solution for surface variables. In some applications, coarse meshes and very large time steps may be used, relative to those which would be required by fixed grid domain methods. Computations are also compared to original lab data, describing two‐dimensional soil freezing with a time‐dependent boundary condition. Agreement between simulated and measured histories

ISSN:0029-5981    

DOI:10.1002/nme.1620191208

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractThe existence of locala posteriorierror indicators for thep‐version of the finite element method is demonstrated through numerical examples. The optimal sequence ofp‐distributions can be closely followed on the basis of the indicat

ISSN:0029-5981    

DOI:10.1002/nme.1620191209

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractThe heating (or cooling) of the rock adjacent to water flowing through a crevice is of interest in certain geothermal studies. For many purposes, only the rock temperature at the rock‐water interface is needed. The fact that the convective heat transfer coefficient is a function of time in the case of unsteady flow takes this problem out of the strictly classical domain.Several methods of solution are described. An approach in which the heat equation is solved, under appropriate side conditions, by standard finite difference techniques is shown to be satisfactory but rather wasteful because much unneeded information concerning internal rock temperatures must be obtained. Several integral equations of Volterra type are derived that provide the temperature only at the interface. Two numerical approaches to their solution are described: one quite classical and only partially effective; the other an apparently new algorithm that is fast and efficient. Analytical upper and lower bounds on the temperature are obtained and serve to demonstrate that this numerical device is also very accurate.The algorithm is applicable to a wide class of Volterra integral equations of the second kind. A brief discussion of the possible future uses of this scheme and the need for additional research is give

ISSN:0029-5981    

DOI:10.1002/nme.1620191210

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620191212

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY