K. H. Muci‐Küchler  J. C. Miranda‐Valenzuela  S. Soriano‐Soriano 《International journal for numerical methods in engineering》2002,53(4):797-824

In this work, a new global reanalysis technique for the efficient computation of stresses and error indicators in two‐dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post‐processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to differentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an efficient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

    

Erik Abenius  Ulf Andersson  Fredrik Edelvik  Lasse Eriksson  Gunnar Ledfelt 《International journal for numerical methods in engineering》2002,53(9):2185-2199

We present a new approach to time domain hybrid schemes for the Maxwell equations. By combining the classical FD‐TD scheme with two unstructured solvers, one explicit finite volume solver and one implicit finite element solver, we achieve a very efficient and flexible second‐order scheme. The second‐order accuracy of the hybrid scheme is verified through convergence studies on perfectly conducting as well as dielectric and diamagnetic circular cylinders. The numerical results also show its superiority to the FD‐TD scheme. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

    

C. L. Pettit  P. S. Beran 《International journal for numerical methods in engineering》2002,55(4):479-497

The response of a fluid moving above a panel to localized oscillation of the panel is predicted using reduced‐order modelling (ROM) with the proper orthogonal decomposition technique. The flow is assumed to be inviscid and is modelled with the Euler equations. These non‐linear equations are discretized with a total‐variation diminishing algorithm and are projected onto an energy‐optimal subspace defined by an energy‐threshold criterion applied to a modal representation of time series data. Results are obtained for a bump oscillating in a Mach 1.2 flow. ROM is found to reduce the degrees of freedom necessary to simulate the flowfield by three orders of magnitude while preserving solution accuracy. Other observed benefits of ROM include increased allowable time step and robustness to variation of oscillation amplitude. Published in 2002 by John Wiley & Sons, Ltd.  相似文献   

    

Z. S. Abo‐Hammour  M. Yusuf  N. M. Mirza  S. M. Mirza  M. Arif  J. Khurshid 《International journal for numerical methods in engineering》2004,61(8):1219-1242

Second‐order, two‐point boundary‐value problems are encountered in many engineering applications including the study of beam deflections, heat flow, and various dynamic systems. Two classical numerical techniques are widely used in the engineering community for the solution of such problems; the shooting method and finite difference method. These methods are suited for linear problems. However, when solving the non‐linear problems, these methods require some major modifications that include the use of some root‐finding technique. Furthermore, they require the use of other basic numerical techniques in order to obtain the solution. In this paper, the author introduces a novel method based on continuous genetic algorithms for numerically approximating a solution to this problem. The new method has the following characteristics; first, it does not require any modification while switching from the linear to the non‐linear case; as a result, it is of versatile nature. Second, this approach does not resort to more advanced mathematical tools and is thus easily accepted in the engineering application field. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. However, being a variant of the finite difference scheme with truncation error of the order O(h²), the method provides solutions with moderate accuracy. Numerical examples presented in the paper illustrate the applicability and generality of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

    

Jian Ding  Wenjing Ye 《International journal for numerical methods in engineering》2004,60(9):1535-1567

In this paper, we describe an efficient numerical method for modelling oscillatory incompressible slip Stokes flows in three dimensions. The efficiency is achieved by employing an integral approach combined with an accelerated boundary‐element‐method (BEM) solver. First the integral representations for slip flows with two different slip models are formulated. The resulting integral equations are then solved using the BEM combined with the precorrected‐FFT accelerated technique. 3D numerical codes have been developed based on the method described above. These codes are then used to calculate the drag forces on oscillating objects immersed in an unbounded slip flow. Three objects are considered, namely a sphere, a pair of plates and a comb structure. The simulated drag forces on these objects obtained from the two slip models are compared. In the sphere case, the simulated results are also compared with the analytical solutions for both the steady‐state case and the no‐slip oscillatory case and are found to be in good agreement. In addition, qualitative comparison of the simulation results with the experimental results in the plate problem is also presented in this paper. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

    

Seung Tai Yeo  Byung Chai Lee 《International journal for numerical methods in engineering》1997,40(16):2933-2952

A new stress assumption for hybrid stress elements is presented. Generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses. The physical meaning of the resulting constraint equations is discussed. The present stress assumption, which can consider the mesh distortion more rigorously, is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper. The stress assumption is adapted to the previous four-node hybrid stress element, 5β-I and the eight-node hybrid stress brick element, 18β, which results in a new four-node plane element, M5β and an new eight-node brick element, M18β. Numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high-accuracy of stresses. © 1997 John Wiley & Sons, Ltd.  相似文献   

    

Terje O. Espelid  Jarle Berntsen  Knut Barthel 《International journal for numerical methods in engineering》2000,49(12):1521-1545

The linear equations governing the propagation of inertia‐gravity waves in geophysical fluid flows are discretized on the Arakawa C‐grid using centered differences in space. In contrast to the constant depth case it is demonstrated that varying depth may give rise to increasing energy (and loss of stability) using the natural approximations for the Coriolis terms found in many well‐known codes. This is true no matter which numerical method is used to propagate the equations. By a simple trick based on a modified weighting that ensures that the propagation matrices for the spatially discretized equations become similar to skew‐symmetric matrices, this problem is removed and the energy is conserved in regions with varying depth too. We give a number of examples both of model problems and large‐scale problems in order to illustrate this behaviour. In real applications diffusion, explicit through frictional terms or implicit through numerical diffusion, is introduced both for physical reasons, but often also in order to stabilize the numerical experiments. The growing modes associated with varying depth, the C‐grid and equal weighting may force us to enhance the diffusion more than we would like from physical considerations. The modified weighting offers a simple solution to this problem. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

    

D. L. Young  J. T. Chang  T. I. Eldho 《International journal for numerical methods in engineering》2001,51(9):1053-1077

This paper describes a new computational model developed to solve two‐dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier–Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three‐step finite element method. The arbitrary Lagrangian–Eulerian method is incorporated into the model, to solve the moving boundary problems. The present model is applied to simulate various external flow problems like flow across circular cylinder, acceleration and deceleration of the circular cylinder moving in a still fluid and vibration of the circular cylinder induced by the vortex shedding. The simulation results are found to be very reasonable and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

    

K. Davey  L. D. Clark 《International journal for numerical methods in engineering》2003,56(4):553-587

This paper is concerned with the minimization of functionals of the form ∫_Γ(b) f( h ,T( b, h )) dΓ( b ) where variation of the vector b modifies the shape of the domain Ω on which the potential problem, ?²T=0, is defined. The vector h is dependent on non‐linear boundary conditions that are defined on the boundary Γ. The method proposed is founded on the material derivative adjoint variable method traditionally used for shape optimization. Attention is restricted to problems where the shape of Γ is described by a boundary element mesh, where nodal co‐ordinates are used in the definition of b . Propositions are presented to show how design sensitivities for the modified functional ∫_Γ(b) f( h ,T ( b, h )) dΓ( b ) +∫_Ω(b) λ( b, h ) ?²T( b, h ) dΩ( b ) can be derived more readily with knowledge of the form of the adjoint function λ determined via non‐shape variations. The methods developed in the paper are applied to a problem in pressure die casting, where the objective is the determination of cooling channel shapes for optimum cooling. The results of the method are shown to be highly convergent. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

    

T. C. Fung 《International journal for numerical methods in engineering》2003,56(3):405-432

One of the important issues in the implementation of the differential quadrature method is the imposition of the given boundary conditions. There may be multiple boundary conditions involving higher‐order derivatives at the boundary points. The boundary conditions can be imposed by modifying the weighting coefficient matrices directly. However, the existing method is not robust and is known to have many limitations. In this paper, a systematic procedure is proposed to construct the modified weighting coefficient matrices to overcome these limitations. The given boundary conditions are imposed exactly. Furthermore, it is found that the numerical results depend only on those sampling grid points where the differential quadrature analogous equations of the governing differential equations are established. The other sampling grid points with no associated boundary conditions are not essential. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献