摘要:

AbstractA new stiffness matrix for geometrically non‐linear analysis of three‐dimensional beam‐columns with bisymmetrical, thin‐walled, I‐type cross‐sections is presented. The displacement field is described in terms of natural and rigid‐body displacements and both Cartesian and natural matrices are derived. A novelty of the resulting method is the use of this dual description in all aspects of the analysis including the computer implementation. A companion paper1that introduces the plastic behaviour of the material also justifies the need for this dual approach as a means to separate nodal forces from stress resultants in the cross‐section of the 3D beam‐column element. The current development uses the updated Lagrangian formulation and corrections in the element matrix are made to properly consider the behaviour under finite rotation. It is shown that accuracy and convergence of the solution process can be improved if the natural matrices derived here are used in a new force recovery process that is insensitive to rigid

ISSN:0029-5981    

DOI:10.1002/nme.1620300202

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells. The formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields. To facilitate extension to materially non‐linear analysis, the variational principle is used in rate form and the plane stress assumption is not imposeda prioriin the formulation. When desired, the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions. The element geometry is based on a nine‐noded quadrilateral with biquadratic interpolation of the displacement field. The strain field is based on a bilinear interpolation with additional non‐linear terms, chosen on the basis of eigenvalue analysis. The element passes the required patch tests, does not display either membrane or shear locking effects, and is free of communicable spurious modes. Numerical results are presented for elastic analyses of several standard plate and shell test pro

ISSN:0029-5981    

DOI:10.1002/nme.1620300203

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractStiffness and consistent mass matrices for tapered bars and shafts are derived with the aid of static displacement functions. Moreover, the corresponding dynamic stiffness matrices are developed in the Laplace transform domain from the exact solutions of axial/torsional governing equations. Power series expansions of the Bessel functions comprising the dynamic stiffness influence coefficients show that the stiffness and consistent mass matrices can be mathematically derived from the dynamic stiffness matrices. A discussion on the convergence of the power series expansions is also presented. The developments provide further insight into the approximations present in conventional consistent mass formulations of frameworks with tapered members.

ISSN:0029-5981    

DOI:10.1002/nme.1620300204

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThe iterated θ‐methods employing residue smoothing for finding both steady state and time‐accurate solutions of semidiscrete hyperbolic differential equations are analysed. By the technique of residue smoothing the stability condition is considerably relaxed, so that larger time steps are allowed which improves the efficiency of the method. The additional computational effort involved by the explicit smoothing technique used here is rather low when compared with its stabilizing effect. However, in the case where time‐accurate solutions are desired, the overall accuracy may be decreased. This paper investigates the effect of residue smoothing on both the stability and accuracy, and presents a number of explicitly given methods based on the iterated implicit midpoint rule (θ = 1/2). Numerical examples confirm the theoretical

ISSN:0029-5981    

DOI:10.1002/nme.1620300205

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA combined spectral finite element method is devised for use in finding the thermal and thermoelastic dynamic response of truss structures to time‐periodic loading. The thermal problem is strongly non‐linear due to the presence of heat radiation. The problems considered are typical in the analysis of space structures. In the method proposed, the spatial domain is first discretized using a consistent finite element formulation. Then the resulting semi‐discrete equations in time are solved analytically by using a spectral method that is symbolically coded. Some numerical examples are presented which demonstrate the performance of the method and its ability to identify some key characteristics in space structure pro

ISSN:0029-5981    

DOI:10.1002/nme.1620300206

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractFor the linear diffusion–convection model problem, this paper develops the numerical analysis of two classes of three‐time‐level second order finite difference schemes: weighed schemes similar to two‐step schemes for differential equations and LF schemes based on the classical conservative approximation of the wave equation. As in our paper devoted to two‐level schemes, Fourier Analysis is an essential tool which yields several key properties (stability, dissipation, numerical diffusion and dispersion). It also permits the analysis of parasitic solutions characteristic of three‐level schemes and their control in terms of the starting scheme.The analysis is completed by giving results on the accuracy, positivity and parabolicity of the numerical schemes.The main conclusions are the expected superiority of these schemes over two‐level schemes when the diffusion phenomenon is not negligible (cell Reynolds number less than 1) and the very limited possibilities of obtaining satisfactory numerical results (even with upstream differencing) when convection is strongly

ISSN:0029-5981    

DOI:10.1002/nme.1620300207

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA new Petrov–Galerkin method to deal with convection–diffusion problems is presented. The formulation is derived from the concept of using a modifying function to make the differential operator self‐adjoint. The so‐called ‘optimal upwind’ parameter (α) arises naturally from the process of approximating the modifying function. Transient and steady‐state examples on uniform and non‐uniform

ISSN:0029-5981    

DOI:10.1002/nme.1620300208

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThe calculation of pressures when the penalty function approximation is used in finite element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from theC0velocity approximation using a least squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

ISSN:0029-5981    

DOI:10.1002/nme.1620300209

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper presents a new element based method through a treatment of a one dimensional model problem. The case solved in this work is of a rod with variable cross‐sectional area, supported along its length by variable stiffness elastic foundation, and loaded with variable axial load. The variations of all the quantities are taken as general polynomials. Using this method the exact terms in the stiffness matrix are found using the solution for the differential equation (up to any desired accuracy). The exact solution is obtained using one element for each segment with continuously varying properties, and the displacements and stresses are exact all along the ro

ISSN:0029-5981    

DOI:10.1002/nme.1620300210

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA finite element algorithm which can be used to model either linear or non‐linear viscoelastic material behaviour is described. The algorithm is verified for the linear case by comparing numerical and analytical solutions for (a) a uniaxial tensile specimen, and (b) an infinite plate with a hole subjected to a remote uniaxial stress. The algorithm is then used to determine the stress and strain fields near the tip of a moving crack in a linear viscoelastic medium. Numerical solutions for both growing and healing cracks are compared with results expected based upon the extended correspondence principle. Excellent agreement between theoretical and numerical solutions is obtained in all cases. Sources of numerical error in the FE solution procedure are identified and documented. The algorithm has not been verified for the non‐linear case, since (except for very simple geometries and loading configurations) no closed‐form solutions involving non‐linear viscoelastic material behaviour are available. A comparison between the measured and predicted response of a non‐linear viscoelastic material behaviour will be presented in a follow

ISSN:0029-5981    

DOI:10.1002/nme.1620300211

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY