摘要:

AbstractThe paper develops the theory of reparametrization within the context of computer‐aided geometric design. It is established that the parametrization plays a positive role in the numerical description of curves and surfaces and it is proposed that the parametrization should be controlled, independently from the shape, via reparametrization. A general approach to reparametrization is adopted in which a function to change the parametrization is modelled in addition to the basic parametric equation. Examples are given for parametric polynomial curves, probably the most commonly used curve segments in computer‐aided geometric design. Finally it is shown how reparametrization might be applied to enhance existing surface definition procedures. A surface equation is developed based on the parametric cubic segment that can define shapes virtually independent of the parametrizat

ISSN:0029-5981    

DOI:10.1002/nme.1620200202

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThis paper presents an efficient algorithm to solve phase change problems. The first part gives the definition of the problem and mentions some practical applications. The second part analyses how to deal with phase changes by means of concentrated fictitious heat flows. The principles of the method are described and compared to those of other methods. The concept of ‘the area associated with a node’ is developed and some practical values for the weight coefficients are recommended. Conclusions are given about the convergence and the stability of the algorithm, and about the improvements obtained by prescribing the temperatures and using relaxation techniques. Theoretical and practical examples illustrate the validity and efficiency of the proposed met

ISSN:0029-5981    

DOI:10.1002/nme.1620200203

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractFor the two most common rotor types–the cylindrical rotor with an arbitrarily shaped cross‐section and the axially symmetrical rotor with an arbitrary contour of the longitudinal section–algorithms for the computation of the moments of inertia with respect to the major axes are developed, which are particularly suitable for digital computer programming. In both cases the volume integrals can be reduced to area integrals which in turn can be reduced to contour integrals along the boundary of the generating area. The boundary can be approximated as accurately as desired by a polygonal course. For the area moments of any order of the resulting polygonal bounded domain, an analytical solution is presented, for whose numerical calculation only the co‐ordinates of the corner points are required. Hence the preparations for data processing are reduced to the absolutely necessary

ISSN:0029-5981    

DOI:10.1002/nme.1620200204

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractRecently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.

ISSN:0029-5981    

DOI:10.1002/nme.1620200205

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractFor physical phenomena governed by the Biot model of porous‐elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two‐dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous‐elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever pos

ISSN:0029-5981    

DOI:10.1002/nme.1620200206

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractFor the semi‐infinite crack propagating quasi‐statically in a porous‐elastic medium, the boundary integral equation method (BIEM), based on a reciprocal principle, is formulated for the governing equations of the Biot model of linear porous‐elasticity. The resulting numerical scheme is efficient since the discretization of the solution unknowns is required only along the axis of symmetry of a fracture. Fracture propagation criteria based on both elastic and plastic constitutive relations are investigated. Practical applications of the model are expected in the failure of overconsolidated clay, earthquake prediction and underground hydraulic fracturing for energy expl

ISSN:0029-5981    

DOI:10.1002/nme.1620200207

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA non‐iterative method is presented for solving a system of algebraic equations forming a banded matrix with each diagonal submatrix being tridiagonal and all other submatrices being diagonal. A recursion relation is assumed between successive elements of the solution vector. This relation is determined by equating a linearly combined form of it with the original set of equations also being linearly combined. The solution vector is determined by back‐substitution of elements in the recursion relation. Since the method takes advantage of the banded structure of the matrix, it is more efficient than the conventional methods. A FORTRAN program that incorporates the present method is inclu

ISSN:0029-5981    

DOI:10.1002/nme.1620200208

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA finite element model that is suitable for the analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of shell elements: rotational, general and transitional. The rotational shell elements, which are most efficient, are used in the region where the shell is axisymmetric. The general shell elements, which can simulate almost any shell geometry, are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis.The form of the global stiffness matrix is somewhat unique in the new model. Non‐zero terms are not confined to a narrow band along the diagonal, but occur throughout the matrix. This is due to the following: (1) two different types of nodes, ring nodes and point nodes, are combined in a single analysis; and (2) a locally non‐axisymmetric geometry creates a coupling of the Fourier harmonic coefficients of the rotational elements. Yet, the matrix still contains many scattered zero terms that should be considered for numerical efficiency. In this paper an efficient solution procedure that is effective for this situation is developed. The steps include the use of a substructuring technique and separate partial harmonic analysis. A numerical example is presented and compared with existing solutions to demonstrate the capabilities and the efficiency of the new mo

ISSN:0029-5981    

DOI:10.1002/nme.1620200209

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractViscoplastic constitutive models typically lead to compliance (strain–stress) relationships, which must be inverted for use in the finite element displacement method. Computational requirements can be increased significantly for models of practical size due to the large number of matrix inversions which are necessary. This paper describes a method of obtaining the required stress–strain relations analytically, thus eliminating the need for numerous matrix inversions in the solution. The technique is applicable to a number of commonly‐used viscoplastic models, as demonstrated in the exa

ISSN:0029-5981    

DOI:10.1002/nme.1620200210

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA new adaptive finite element method is proposed for the advection–dispersion equation using an Eulerian–Lagrangian formulation. The method is based on a decomposition of the concentration field into two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single‐step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices. Preliminary tests against analytical solutions of one‐ and two‐dimensional dispersion in a uniform steady‐state velocity field suggest that the proposed adaptive method can handle the entire range of Péclet numbers from 0 to ∞, with Courant numbers well

ISSN:0029-5981    

DOI:10.1002/nme.1620200211

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY