摘要:

AbstractPreviously published literature shows widely different results for the free vibration frequencies of twisted cantilever plates. Inasmuch as it is important to know the vibration characteristics of turbomachinery blades, which may have considerable twist, it would be desirable to have a comprehensive, definitive set of results, and to establish which of the numerous theoretical methods available can adequately analyse such problems. For this purpose, a joint government/industry/university research study was organized. Numerical results were obtained for a set of 20 different twisted plates having various aspect ratios, thickness ratios and pretwist angles. Nineteen distinct theoretical methods were employed, 15 using finite elements, two using shell theory, and two using beam theory. Although some of the best‐known computational procedures (especially finite element codes) were used by analysts with great experience, the numerical results obtained showed considerable disagreement. The present paper describes the analytical methods used and exhibits samples of the type of results obtaine

ISSN:0029-5981    

DOI:10.1002/nme.1620210802

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA numerical scheme has been constructed to simulate the imposition of a step in heat transfer at the surface of a multi‐layered substrate. The numerical simulation of this process is carried out by applying an extended version of the Keller Box‐Scheme to multi‐layered diffusion problems. Numerical calculations show that accurate choice of length and time‐scales is critical in determining the behaviour of the heat flow through the substrate. Thus, the results from the numerical simulations are of value to the experimentalist, particularly in determining the accurate shape of the response curves which enable experimental apparatus to be designed effectively. The proposed scheme yields heat fluxes as accurately as temperatures, and can be easily adapted to other related appli

ISSN:0029-5981    

DOI:10.1002/nme.1620210803

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe best approach for the numerical determination of stress intensity factors at crack tips in plane and antiplane elasticity problems is frequently the numerical solution of the corresponding Cauchy‐type singular integral equation by the Gauss–Chebyshev method, followed by the application of the natural extrapolation formula for the numerical determination of the stress intensity factors. It is shown here that this approach converges for Hölder‐continuous and discontinuous (with jump discontinuities) loading distributions along the crack (or cracks) and that in all cases the rate of convergence is greater than that believed up to now. This superconvergence result is based on a theorem on the numerical equivalence of the Gauss–Chebyshev direct method to a relevant indirect method for the numerical solution of Cauchy‐type singular integral equations, also proved here. Numerical results in various crack problems corroborate the theore

ISSN:0029-5981    

DOI:10.1002/nme.1620210804

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThis paper describes a new algorithm to generate interior nodes within any arbitrary multi‐connected regions. The boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner. Owing to the generality of the central generation program, the global domain is allowed to be divided into as many irregular subdomains as desired, in order to model closely the actual physical situation. Moreover, the boundaries of the sub‐domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner, generating radiating mesh from a prescribed node, generating mesh between two circular arcs, etc. Despite its flexibility and capabilities, data for triangulation have been kept to a minimum by a logical input module;no connectivity information between subregions is needed, and common boundaries are defined once only. All these features have contributed to a powerful method to generate 3‐node or 6‐node triangular element meshes of great variety within the most irregular heterogeneous

ISSN:0029-5981    

DOI:10.1002/nme.1620210805

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractWhen the finite element method is applied to the analysis of tidal currents in an inland sea with many islands, a system of linear equations with large band and sparse coefficient matrix is solved at each time step, and therefore the finite element methods usually suffer a severe economic disadvantage for practical calculations. The method used in this paper for solving a system of linear equations with large band and sparse coefficient matrix is the incomplete Cholesky conjugate gradient (ICCG) method: The ICCG method was compared with other methods such as the Gaussian elimination method, the Gauss–Seidel method and the conjugate gradient method. This method showed significant improvement in computation time and it can overcome the disadvantage that the efficiency to solve the matrix equations which appear in the finite element analysis of tidal currents usually diminishes as the bandwidth grows. The simulation results of tidal currents in the Seto Inland Sea of Japan were compared with field data and good agreements were obtaine

ISSN:0029-5981    

DOI:10.1002/nme.1620210806

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA method of solving inverse problems of stationary electromagnetic fields is described. It can be applied to problems in non‐homogeneous, linear and isotropic environments. The method is based on application of integral equations of the first kind which require regularization because they are ill‐posed. Numerical calculations of some selected problems confirm the effectiveness of the proposed met

ISSN:0029-5981    

DOI:10.1002/nme.1620210807

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThis paper considers nine‐point difference schemes for a two‐dimensional boundary value singular perturbation problem without turning points and parabolic boundary layers. Necessary conditions are given for the uniform convergence (in the sense of the maximum norm) of a scheme. Using these conditions, several widely used schemes are analysed. It is shown that some common schemes are not uniformly convergent in ϵ. and that in some cases we are able to compute uniquely free parameters in the scheme. Some remarks on the treatment of a problem with a parabolic boundary layer are g

ISSN:0029-5981    

DOI:10.1002/nme.1620210808

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractFor the numerical treatment of stress concentration problems in plane elasticity, special finite elements with circular and elliptic holes and internal cracks have been developed. Two different variational formulations have been used to construct elements, which may be combined with conventional displacement elements. Using complex functions and conformal mapping techniques the systematic construction of trial functions is shown which not only satisfya priorithe governing differential equations but also the boundary conditions on such influential boundary portions as hole or crack surfaces. For the evaluation of the stiffness matrices of the special elements, only boundary integral computations arc necessary. The numerical results of various examples are very accurate for both functionals.

ISSN:0029-5981    

DOI:10.1002/nme.1620210809

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA method is presented for the calculation of weight functions used in fracture mechanics to determine stress intensity factors of cracks loaded by stress gradients. The reference solution for the stress intensity factor and for the reference crack opening displacement field is computed numerically by use of finite elements. The accuracy of the method is checked by comparison with well‐known solutions from the literatur

ISSN:0029-5981    

DOI:10.1002/nme.1620210810

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA simplified technique for the dynamic analysis of geometrically nonlinear plate structures is developed. The essence of this technique is the construction of a linear substitute of the nonlinear problem. The linear substitute problem is derived from an equivalence criterion which involves balancing the energies of the linear substitute model and the nonlinear model over one period of oscillation. The linearized equations are discretized by a finite element method, and solutions at different amplitudes are obtained numerically by an incremental‐iterative scheme. To verify the equivalent energy linearization approach, example problems consisting of the free and forced vibration of nonlinear circular plates with various boundary conditions are studied. All results are compared to theoretical and numerical solutions in the literature. In addition, the forced vibration results are compared to available experimental results. These comparisons tend to validate the assumptions made in the equivalent energy linearization procedure. The proposed method is found to be computationally more efficient than other available procedure

ISSN:0029-5981    

DOI:10.1002/nme.1620210811

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY