摘要:

AbstractAn analysis, based on the use of Taylor series expansions, is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite‐element interpolant or approximation. The analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates (superconvergence). Moreover, it leads directly to a class of post‐processing strategies for the derivatives and offers a more direct constructive approach to the subj

ISSN:0029-5981    

DOI:10.1002/nme.1620280302

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper presents an efficient and numerically stable algorithm for computing accurately the eigenvalues of smallest moduli and the associated eigenvectors of the quadratic eigenproblem which arises in the analysis of spinning systems. Derived from the well‐known standard subspace iteration method, this solution procedure takes full advantage of the banded configuration of the structural matrices, and of the specific nature of gyroscopic systems. A numerical example is presented to show the efficiency and accuracy of the algorith

ISSN:0029-5981    

DOI:10.1002/nme.1620280303

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA new algorithm is presented for performing mesh rezoning on isoparametric elements used in simulations of non‐linear deformation processes. The method uses techniques from elimination theory to solve the parametric inversion problem for each node on the new, undistorted mesh. These parameter values are then used in the elemental shape functions to transfer the nodal state variables from the distorted mesh to each node in the new mesh by interpolation. The method has been implemented for bilinear and biquadiatic elements. The method is based on fundamental finite element approximations, since the interpolation functions which define the element are also used to perform rezonin

ISSN:0029-5981    

DOI:10.1002/nme.1620280304

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper deals with the formulation and the evaluation of a new three node, nine d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the DKT (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory.

ISSN:0029-5981    

DOI:10.1002/nme.1620280305

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe numerical technique of differential quadrature for the solution of linear and non‐linear partial differential equations, first introduced by Bellman and his associates, is applied to the equations governing the deflection and buckling behaviour of one‐ and two‐dimensional structural components. Separate transformations are used for higher‐order derivatives, as suggested by Mingle, thus extending the method to treat fourth‐order equations and to include multiple, boundary conditions in the respective co‐ordinate directions. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. The application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computati

ISSN:0029-5981    

DOI:10.1002/nme.1620280306

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper presents an optimality criterion method for the determination of the least weight design of a structural system which satisfies a specific frequency requirement plus upper and lower bounds on the design variables. The design algorithm is an iterative solution of the Kuhn–Tucker optimality criterion based on choosing a single value of the Lagrange multiplier which minimizes the sum of the squares of residuals.The method has been applied to a variety of structures. Results assert that the method is capable of locating the optimal design in a small number of redesign cycles. The method avoids the scaling of design variables. It can treat non‐structural masses and is applicable to. structural elements with a wide variety of size‐stiffness. The procedure has been completely automated in a computer program on an IBM‐PC microc

ISSN:0029-5981    

DOI:10.1002/nme.1620280307

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe introduction of composite materials is having a profound effect on the design process. Because these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require a more integrated multidisciplinary design process. Because of the complexity of the design process numerical optimization methods are required.The present paper is focused on a major difficulty associated with the multidisciplinary design optimization process—its enormous computational cost. We consider two approaches for reducing this computational burden: (i)development of efficient methods for cross‐sensitivity calculation using perturbation methods; and (ii) the use of approximate numerical optimization procedures. Our efforts are concentrated upon combined aerodynamic‐structural optimization. Results are presented for the integrated design of a sailplane wing. The impact of our computational procedures on the computational costs of integrated designs is disc

ISSN:0029-5981    

DOI:10.1002/nme.1620280308

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA unified approach to solving ill‐conditioned matrix problems is presented, concentrating on those problems arising in engineering where measurement inaccuracy is the major source of error. By applying the singular value decomposition, it is shown that regularization with a parameter can be used without squaring the condition number of the matrix. Numerical examples demonstrate that a smaller relative error is attainable using the unified approach over the more standard technique of discarding singular values. Lastly, a simple method is presented for locating the optimal solution using a computed residua

ISSN:0029-5981    

DOI:10.1002/nme.1620280309

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA collocation method is described which obtains an approximate solution to Poisson's equation, δu=f, on an L shaped region. The L shaped region is viewed as the union of two overlapping rectangles. The Schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle. The convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods. Several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the L shaped region

ISSN:0029-5981    

DOI:10.1002/nme.1620280310

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous, isotropic, linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face. The integral equation relates the unknown crack‐opening displacement, which depends on time and position, to the incident wave field. The integral equation has been solved numerically by a time‐stepping method in conjunction with a boundary element discretization of the crack surface. For normal incidence of a longitudinal step‐stress wave on a penny‐shaped crack, results as functions of time have been obtained for the crack‐opening displacement, the elastodynamic Mode‐I stress intensity factor and the scattere

ISSN:0029-5981    

DOI:10.1002/nme.1620280311

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY