摘要:

AbstractA direct boundary element method is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions. The formulation employs the static fundamental solution of the problem and this creates not only boundary integrals but surface integrals as well owing to the presence of the inertia force. Thus the discretization consists of boundary as well as interior elements. Quadratic isoparametric elements and quadratic isoparametric or constant elements are employed for the boundary and interior discretization, respectively. Both free and forced vibrations are considered. The free vibration problem is reduced to a matrix eigenvalue problem with matrix coefficients independent of frequency. The forced vibration problem is solved with the aid of the Laplace transform with respect to time and this requires a numerical inversion of the transformed solution to obtain the plate dynamic response to arbitrary transient loading. The effect of external viscous or internal viscoelastic damping on the response is also studied. The proposed method is compared against the direct boundary element method in conjunction with the dynamic fundamental solution as well as the finite element method primarily by means of a number of numerical examples. These examples also serve to illustrate the use of the proposed method.

ISSN:0029-5981    

DOI:10.1002/nme.1620280902

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper describes the stability conditions for difference diagrams applied to the approximation of one‐ and two‐dimensional non‐linear field equations. The one‐dimensional electromagnetic field is described by vectorBand vectorE, and the two‐dimensional field by magnetic vector potentialA.It has been proved that the presence of a lower order of derivatives has a decisive influence on the stability condition of the considered

ISSN:0029-5981    

DOI:10.1002/nme.1620280903

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA combination of the characteristics method and finite elements techniques is applied to solve a coupled heat transfer–chemical reaction system in the stationary case. The solution of the non‐linear discretized system is obtained by using Newton's algorithm. Finally, numerical results for several problems are presented to test the accuracy and stability of the met

ISSN:0029-5981    

DOI:10.1002/nme.1620280904

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems. The basic idea is to generate such an information at the expense of only one more ‘virtual load case’ in the sensitivity analysis part of the finite element code. To achieve this goal a primal–dual approach is employed, that can also be interpreted as a sequential quadratic programming method.Another objective is to relate the proposed method to the well known family of approximation concepts techniques, where the primary optimization problem is transformed into a sequence of non‐linear explicit subproblems. When restricted to diagonal second derivatives, the new approach can be viewed as a recursive convex programming method, similar to the ‘Convex Linearization’ method (CONLIN), and to its recent generalization, the ‘Method of Moving Asymptotes’ (MMA).This new method has been successfully tested on simple problems that can be solved in closed form, as well as on sizing optimization of trusses. In all cases the method converges faster than CONLIN, MMA or other approximation techniques based on recip

ISSN:0029-5981    

DOI:10.1002/nme.1620280905

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA general and efficient technique is developed for the evaluation of the integrals with various orders of singularity, such as occur in the three‐dimensional boundary element method (BEM). Generalized (extended) triangle, tetrahedron polar co‐ordinate mappings together with two conditions are used to remove the singularity of the integrals, and to evaluate the corresponding non‐singular ones in a new numerical space. Triangle and tetrahedron polar co‐ordinates in Reference 1 are proved to be a special case of the generalized ones in this paper. With the developed idea, boundary element results converge rapidly towards the analytical solutions for the strongly singular integrals evaluated directly, and the analytical solutions can be gained in principle, even when employing higher order, triangular boundary elements and tetrahedral cells. The generality and practicability of the method are demonstrated in the case of higher order elements, discontinuous elements and large engineering p

ISSN:0029-5981    

DOI:10.1002/nme.1620280906

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIt is well known that there are many benefits in solving axisymmetric solids subjected to non‐axisymmetric loading by using Fourier series expansion of field variables. Although many researchers have utilized this technique to solve problems of cooling towers and rocket nozzles, etc. by the Finite Element Method, the BEM formulation and implementation of such a method have been available only recently, mainly due to the efforts of Rizzo and Shippy3and Mayret al.4In this paper these early developments have been generalized further by including more expansion terms, an efficient decomposition of kernels into symmetric and antisymmetric forms, improved evaluation of matrix coefficients and developing more general computer implementation to include surface stress calculations, effects of body forces and extensive substructuring facilities to analyse multi‐zone probl

ISSN:0029-5981    

DOI:10.1002/nme.1620280907

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe stability of time‐stepping methods for parabolic differential equations is mostly a critical issue. Furthermore, solving such equations with a classical time‐stepping approach can be very expensive because many small time‐steps have to be taken if steep gradients occur in the solution, even if these occur only in a narrow part of the space domain. In this paper we present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a ‘time‐slab’. This technique may be repeatedly applied to obtain further parts of the solution in subsequent time‐intervals. It will be shown that, with the proposed method, the solution can be computed cheaply even if it has steep gradients and that stability is automatically guaranteed. For the solution of the non‐linear algebraic equations on each time‐slab fast iterative me

ISSN:0029-5981    

DOI:10.1002/nme.1620280908

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractFinite element partitioning (or substructuring) is employed to estimate the eigenproperties of large‐scale structural systems. A homotopy equation is constructed and its solutions are characterized by a number of curves which connect the eigensolutions of the partitions with those of the complete system. A step‐by‐step tracing procedure is developed to follow these curves. At each step, prediction and correction are performed. The Rayleigh–Ritz procedure and the conjugate gradient method are used as predictor and corrector, respectively. Compared with the sole use of either the Rayleigh–Ritz or gradient methods, the proposed method is more reliable and more efficient for large‐scale problems. Numerical implementation is well suited for sup

ISSN:0029-5981    

DOI:10.1002/nme.1620280909

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractConsiderable progress has been made in recent years toward advancing the state‐of‐the‐art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general‐purpose boundary element method (BEM) for steady‐state heat conduction. In particular, the BEM implementation involves the use of higher‐order conforming elements, self‐adaptive integration and multi‐region capability. Two‐ and three‐dimensional, as well as axisymmetric analyses, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three‐dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady

ISSN:0029-5981    

DOI:10.1002/nme.1620280910

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA finite element formulation has been developed to take into account the warping effect of composite beams undergoing large deflection or finite rotation. This formulation is to be used to model combined bending, torsional and extensional behaviour of composite helicopter rotor blades. The new approach can model thin to moderately thick walled composite beams with complicated cross‐sections, tapers and arbitrary planforms. The warping effects are incorporated by assuming warping displacements superimposed over cross‐sections normal to the beam axis in the deformed configuration of a shear flexible beam. The strain is assumed to vary linearly through the wall thickness. The fixed or total Lagrangian description is adopted in the present formulation and the Newton–Raphson method is used to solve the non‐linear equilibrium equation resulting from the finite element approximation. Numerical tests of example problems demonstrate the validity and effectiveness of the present a

ISSN:0029-5981    

DOI:10.1002/nme.1620280911

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY