摘要:

AbstractThe conjugate gradient method holds great appeal for the solution of the stiffness equation set up with finite elements. Inexpensive, low‐order finite‐element discretization solutions are suggested as initial guesses for higher‐order, more accurate, discretiza

ISSN:0748-8025    

DOI:10.1002/cnm.1630080802

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA four‐node quadrilateral plate element with a set of incompatible modes is presented in this work. In an analysis of thin plates, the element exhibits a similar performance as the well known discrete Kirchhoff plate element. The computational effort associated with the element is also comparable to that associated with the discrete Kirchhoff element. However, as opposed to the discrete Kirchhoff plate element, the presented plate element is based on the Reissner–Mindlin plate theory and can be used in a thick plate analysis as w

ISSN:0748-8025    

DOI:10.1002/cnm.1630080803

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper describes an approach for implementing quadrilateral finite elements which usesBmatrices of average strain when assembling element stiffness matrices. The approach avoids isoparametric transformations, thereby making stiffness matrix assembly and stress calculations more efficient. An example is presented which compares the proposed approach and those based on Gauss quadrature integration.

ISSN:0748-8025    

DOI:10.1002/cnm.1630080804

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA second‐order explicit method is developed for the numerical solution of the Ricatti (logistic) initial‐value problemu′ ≡ du/dt= αu(1 ‐u),t>0,u(0) =U0, in which α ≠ 0 is a real parameter. The method is based on two first‐order methods which appeared in an earlier paper by the authors (Twizellet al.1). In addition to being chaos‐free and of higher order, the novel method is seen to converge to the correct, stable, steady‐state solution for any value of the parameter α, provided the denominator of the method does not vanish. Convergence is monotonic or oscillatory depending on the magnitude of the product αl, wherelis the parameter in the discretization of the independent variablet.This dependence of the type of convergence on αlis likened to the behaviour of the well known Crank–Nicolson method for solving the simple heat equation. Conversion of the numerical method to a reliable, empirical model for predicting the limited growth of successive generations of a population is given. When extended to the numerical solution of Fisher's equation, in which the quadratic polynomial αu(1 –u) appears as the reaction term, the numerical solution is found by solving a linear algebraic system at each time step, as opposed to solving a non‐linear system, which often happens when solving non‐linear

ISSN:0748-8025    

DOI:10.1002/cnm.1630080805

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractNumerical solutions of a non‐linear oscillator have been produced by various methods. Some unexpected discrepancies have been found in the solutions obtained. This behaviour is reported herein, and the implications to the application of numerical methods to non‐linear dynamical systems are discus

ISSN:0748-8025    

DOI:10.1002/cnm.1630080806

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe stochastic boundary‐element method (SBEM) is developed in this paper for the reliability analysis of a structural component. The integral equations of BEM are derived partially by a random variable, and the integral equations of SBEM are established. Considering the applied loads and the limitation of material strength to be a Gauss distribution, the numerical results of two examples are given for the problems of stochastic stress‐strain and reliability. The results show good agreement with those obtained from Monte Carlo simulation and theoretical soluti

ISSN:0748-8025    

DOI:10.1002/cnm.1630080807

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper presents the vibrations of annular sectorial plates with two opposite radial edges simply supported using the spline strip method. To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by the analytical method and by other numerical methods. Stable convergence and excellent accuracy are obtained using the high‐order spline strip models. Accurate frequencies of annular sector plates with different sector angles, radii ratios and tapered thickness in the angular direction are shown in tabular for

ISSN:0748-8025    

DOI:10.1002/cnm.1630080808

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA finite‐element approach for computing cable structure fully non‐linear response is presented in this work. Both the problems of statics and of dynamics are considered. The formulation encompasses arbitrary large strains and displacements. A very general constitutive equation for non‐linear elastic cables can be posed by an adequate choice for the strain energy function. In this work we consider two model problems, posed by St. Venant's and Ogden's material models. The proposed formulation is set in a fixed reference frame which yields a very efficient finite‐element implementation. The additional advantage of setting the formulation in a fixed reference frame is a bilinear form of the kinetic energy and a simplified solution procedure for dynamic equilibrium equations. Consistent linearization is used at each step of the Newton algorithm to obtain the tangent operators, which provide the quadratic rate of the solution convergence. This is demonstrated in the numerical examples presented

ISSN:0748-8025    

DOI:10.1002/cnm.1630080809

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630080810

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630080801

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY