摘要:

AbstractA new algorithm is presented for automatically grading meshes generated over planar triangular and quadrilateral regions using parametric mappings. Rational parametric bicubic Bézier polynomials are coupled with an element density function to concentrate elements around regions of high solution gradients

ISSN:0029-5981    

DOI:10.1002/nme.1620241202

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractIn this paper 8‐node traction singular boundary elements are employed to represent displacement and traction variations in the vicinity of the crack front in three‐dimensional geometries. The numerical procedure suggested for evaluating the singular integrals extending over these special elements is described. The efficiency and accuracy of the special elements and integration procedure are demonstrated by the results obtained in a simple test problem whose analytical solution is known. The interaction of two circular coplanar cracks embedded in an infinite medium under uniform tension loading is also analysed. Finally, the stress intensity factor variation computed for a semi‐circular inner surface crack in a pressurized cylinder is pres

ISSN:0029-5981    

DOI:10.1002/nme.1620241203

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractIn this paper we present a Legendre spectral element method for solution of multi‐dimensional unsteady change‐of‐phase Stefan problems. The spectral element method is a high‐order (p‐type) finite element technique, in which the computational domain is broken up into general (curved) quadrilateral macroelements, and the solution, data and geometry are expanded within each element in terms of tensor‐product Lagrangian interpolants. The discrete equations are generated by a Galerkin formulation followed by Gauss–Lobatto Legendre quadrature, for which it is shown that exponential convergence to smooth solutions is obtained as the polynomial order of fixed elements is increased. The spectral element equations are inverted by conjugate gradient iteration, in which the matrix‐vector products are calculated efficiently using tensor‐product sum‐factorization.To solve the Stefan problem numerically, the heat equations in the liquid and solid phases are transformed to fixed domains applying an interface‐local time‐dependent immobilization transformation technique. The modified heat equations are discretized using finite differences in time, resulting at each time step in a Helmholtz equation in space that is solved using Legendre spectral element elliptic discretizations. The new interface position is then computed using a variationally consistent flux treatment along the phase boundary, and the solution is projected upon the corresponding updated mesh. The rapid convergence rate and stability of the method are discussed, and numerical results are presented for a one‐dimensional Stefan problem using both a semi‐implicit and a fully implicit time‐stepping scheme. Finally, a two‐dimensional Stefan problem with a complex phase boundary is solved

ISSN:0029-5981    

DOI:10.1002/nme.1620241204

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractTransverse vibrations of an axially moving (travelling in its own plane) membrane submerged in ideal fluid are analysed using the FEM. The discrete equations differ from the equations of the common coupled problem in that there appear two additional inertia terms due to the convective acceleration. The effect of the density of the element mesh, the effect of the truncation distance and the effect of various lumping techniques on the accuracy of the results are studied. The FEM‐results are compared with available analytical and experimental results. The agreement seems to be rather goo

ISSN:0029-5981    

DOI:10.1002/nme.1620241205

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractIn this paper, we extend the concept of a grading function, as introduced by Carey and Dinh2in a one‐dimensional context, to curved contours. We then apply the idea to adaptive grid redistribution for a boundary element method to solve a model boundary value problem. Numerical results are included for a potential problem to demonstrate the effect of the redistribution scheme on the solution and the geometry of the domai

ISSN:0029-5981    

DOI:10.1002/nme.1620241206

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractAs a first step toward developing a finite element formulation that can model coupling among extensional, bending and torsional behaviour of beams, a new method is proposed to properly represent the warping of arbitrary cross‐sections. The basic approach is to introduce a small warping displacement superimposed over flat cross‐sections of a shear‐flexible beam in a deformed configuration. Numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach. The present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rot

ISSN:0029-5981    

DOI:10.1002/nme.1620241207

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractPlate and shell finite elements based upon Mindlin plate theory and evaluated by one‐point quadrature are attractive because of their effectiveness for both thick and thin shells, at minimal computing cost. However, these elements are rank‐deficient and must be stabilized to obtain reliable behaviour. Methods for achieving full rank of the stiffness and for stabilizing element behaviour in static analysis and in explicit dynamic calculations exist and are quite effective. This paper addresses the remaining issue of controlling spurious modes of response in vibration analysis and implicit dynamic solutions. Several alternatives for the element mass formulation are examined in detail. We show that non‐physical dynamic modes present a potential problem with most mass matrix formulations, and that spurious modes other than the familiar hourglassing motion are possible. A combination of projection methods and reduced quadrature is suggested which eliminates these deficiencies and produces accurate numerical results. The remaining techniques investigated give rise to anomalous behaviour which make them unsuitable for genera

ISSN:0029-5981    

DOI:10.1002/nme.1620241208

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractThis paper presents a method for determining the second order sensitivity matrix and logarithmic sensitivity functions in the frequency domain. The procedure described is applicable to any discrete and viscously damped mechanical system.A definition of the second order logarithmic sensitivity function has been proposed. The examples shown indicate that logarithmic sensitivity functions of the second order preserve the qualitative character of first order sensitivity functions and are more sensitive to changes of system parameters. The influence of large parameter changes on second order sensitivity functions has also been investigated.

ISSN:0029-5981    

DOI:10.1002/nme.1620241209

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractArch dams can be conveniently analysed by the finite element method. For dam–fluid interaction problems, the fluid domain may be more conveniently handled by the boundary element method as a substructure first before connecting to the dam substructure. The added‐mass matrix calculated from the fluid domain is symmetrized and lumped first so that the banded and symmetrical characteristics of the finite element method are retained. In the boundary element formulation, a mirror image method and quadratic elements are used for computational efficiency and accuracy. The strong singular terms are handled by using a solution which satisfies the governing equation and the free surface boundary condition. Infinite boundary conditions at the upstream of the reservoir can be reasonably approximated from the fundamental solution with accurate results, if the interior pressure distribution in the fluid domain is neglected. Numerical solutions on hydrodynamic pressure distribution and the natural frequencies of the dam–reservoir system with various water levels are obtained and compared with available analytical and experiment re

ISSN:0029-5981    

DOI:10.1002/nme.1620241210

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractA new shell element, which is free from serious locking problems and which does not possess hourglass modes, is proposed. Solutions obtained with this element exhibit good convergence and are satisfactorily insensitive to mesh distortion. The element also exhibits good convergence for plates with variable thickness. This element is based on the use of assumed covariant strains which are obtained from the covariant strain field defined with respect to the element natural co‐ordinate system. Only the linear version for thin shell cases is considered. The element performance is tested by application to several standard plate and shell problems. A problem involving variable thickness is also presente

ISSN:0029-5981    

DOI:10.1002/nme.1620241211

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY