摘要:

AbstractA modified version of the well known Euler method for numerical integration is presented, and its application in analyses of the dynamic response of structures is discussed. This modified method was first introduced in 1981, and it has been reported that it was discovered by accident. When first introduced, however, valuable information related to the accuracy, stability and merits of the method were not provided. It is shown that the modified Euler method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are made for the method by considering free‐vibrational responses of linear, undamped, single‐degree‐of‐freedom systems. The method is explicit and extremely easy to use. However, it is conditionally stable. Applications of the method are also made which illustrate its usefulness and inherent simplicity. Furthermore, comparisons of the modified Euler method and the Newmark beta method are reported which elucidate the relative merits of these

ISSN:0029-5981    

DOI:10.1002/nme.1620320502

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractBounds on eigenvalues of various finite element systems are analysed by using an element eigenvalue theorem together with the Global Eigenvalue Theorem. Both two dimensional continuum dynamics and heat conduction problems are considered. These bounds provide stable time steps for explict time integration schemes. A reduced eigenproblem at element quadrature point level, with all zero eigenvalues suppressed, is also presented in this paper. The simplified eigenproblem results in simple formulas for calculating the eigenvalues.

ISSN:0029-5981    

DOI:10.1002/nme.1620320503

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractNew temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems. To satisfy the spatial counterpart of the requirement on time step constraint, finite‐spectral elements and finite wave elements are developed. Finite‐spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate; whereas, finite wave elements are developed in parallel to the temporal shifting technique. Therefore, the spatial resolution is increased substantially. These methods are especially applicable to structural acoustics and linear space structures. Numerical examples are presented to illustrate the effectiveness of these meth

ISSN:0029-5981    

DOI:10.1002/nme.1620320504

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA computationally advantageous multi‐domain boundary element formulation is presented for uncoupled thermoelastic analysis of two‐ and three‐dimensional isotropic media. Particular integrals capable of representing exactly a quadratic temperature distribution in both two and three dimensions are employed. These particular integrals are derived using an orderly approach. When temperature data are provided at discrete points, the best fit quadratic distribution is generated in the least square error sense which, together with a multi‐domain approach, makes it possible to represent an arbitrary temperature distribution within acceptable bounds. Numerical examples are given to show the efficiency and effectiveness of the present formulation, which is now incorporated in a general purpose boundary element code named

ISSN:0029-5981    

DOI:10.1002/nme.1620320505

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractApplication of the two‐sided Lanczos recursion to the unsymmetric generalized eigenvalue problem is presented. The system matrices are real and unsymmetric. Therefore, the recursions are performed in real arithmetic and complex arithmetic is employed in the QR algorithm used to extract the eigenvalues of the transformed tridiagonal matrix. The biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in Appendices. Issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed. The example problems solved demonstrate the working of the algorithm in extracting the complex and/or real eignevalues of an unsymmetric system of matrices. Also, the algorithm is applied to extract a few of the eigenvalues of a large fluid‐structure interaction problem, and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literat

ISSN:0029-5981    

DOI:10.1002/nme.1620320506

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA variational higher‐order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented. The theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness. Additionally, independent expansions are introduced for the through‐thickness displacement gradients with the requirement of a least‐square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top/bottom beam surfaces. The theory is shown to be well suited for finite element development requiring simpleC0‐ andC−1‐ continuous displacement interpolation fields. To demonstrate the computational utility of the theory, a simple two‐node stretching‐bending finite element is formulated. The analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available. It is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement, strain and stress predictions, particularly, in the analysi

ISSN:0029-5981    

DOI:10.1002/nme.1620320507

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractBased on the assumed element strain fields and the interrelated displacement‐rotation interpolations, a four‐node (12 dof) quadrilateralC0finite element, designated as QCCP‐2, for the analysis of thick/thin plates is developed in this paper. The four‐nodeC0plate element presented here possesses a linear bending strain field, and the element stiffness matrices are given explicitly. Therefore, the present four‐nodeC0plate element is more efficient and accurate than the existing four‐nodeC0plate elements where the constant strain stiffness matrices are obtained by numerical integration. By the use of the interrelated displacement‐rotation interpolations, QCCP‐2 is capable of automatically satisfying the Kirchhoff assumption for the case of thin plates. Consequently, QCCP‐2 is not only free of shear locking, but also free from the numerical ill‐conditioning. Furthermore, QCCP‐2 passes the patch test of thin plates. The four‐node quadrilateralC0elements presented here can automatically reduce to the corresponding three‐node triangular elements. Several numerical examples are given to demonstrate the efficiency and accuracy of theC0pla

ISSN:0029-5981    

DOI:10.1002/nme.1620320508

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA self‐adaptive algorithm has been developed and implemented for the implicit time integration of non‐linear finite element analysis. In this algorithm, a proper time increment for the next time step is estimated based on the deformation pattern at the preceding step. The iteration process for the equalibrium employs expeditious methods such as quasi‐Newton updates and line searches as well as an adaptive stiffness matrix update strategy for efficiency. Convergence difficulties induced from inadequate prediction of step size or the change in non‐linearities are tackled by the bisection method. These procedures were also successfully applied to static problems by ignoring the damping and the inertia forces. The objective of this paper is to demonstrate the applicability and the effectiveness of the adaptive algorithm in a wide spectrum of non‐linear problems. Six example problems are illustrated, some of which are rather novel. As demonstrated in this paper, the self‐adaptive algorithm implemented in MSC/NASTRAN is proving to be versatile, accurate an

ISSN:0029-5981    

DOI:10.1002/nme.1620320509

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe source field superposition method for problems governed by Laplace's equation involves representing the potential field in a given solution domain as a superposition of fields generated by a number of sources. These sources are located outside the solution domain, and in the case of two‐dimensional singly‐connected finite domain problems can be uniformly distributed around the perimeter of a circle enclosing the physical domain. Some test problems are used to make detailed comparisons with the boundary element method. The results show that remarkable accuracy can be achieved, often to five or six significant figures, with very little computational effort relative to other numerical methods. In contrast to the boundary element method, however, geometric corners require no special treatment, and high aspect ratio of the solution domain is not a significant limitat

ISSN:0029-5981    

DOI:10.1002/nme.1620320510

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non‐linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step‐wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post‐bifurcation behaviour.For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and disc

ISSN:0029-5981    

DOI:10.1002/nme.1620320511

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY