Showing papers on "Newmark-beta method published in 1985"
TL;DR: A generalization of Newmark's time marching integration scheme, called the β-m method, which provides a gcneral single-step scheme applicable to any set of initial value problems and which unifies old and new methods.
Abstract: Introduced herein is a generalization of Newmark's time marching integration scheme, called the β-m method. Like the SSpj method (introduced in Parts 1 and 2 of this series), the β-m method provides a gcneral single-step scheme applicable to any set of initial value problems. The method is specialized by specifying the method order m along with rn integration parameters, β0, β1, …, βm−1. For a particular choice of m, the integration parameters provide a subfamily of methods which control accuracy and stability, as well as offering options for explicit or implicit algorithms. For the most part, attention is focused on the application to structural dynamic equations. Most well-known methods (e.g. Newmark, Wilson, Houbolt, etc.) are shown to be special cases within the β-m family. Hence, one computationally efficient and surprisingly simple algorithm unifies old and new methods. Stability and accuracy analyses are presented for method orders m = 2, 3 and 4 to determine optimal parameters for implicit and explicit schemes, along with numerical verification.
222 citations
TL;DR: In this article, the Hybrid method, which makes use of both the finite element method and the boundary element method in the same problem, is reviewed and examples for two dimensional and axisymmetric vector and scalar problems are given.
Abstract: The Hybrid method, which makes use of both the finite element method and the boundary element method in the same problem is reviewed. The relative advantages and disadvantages of the Hybrid method are explained. The basic formulation of the method is given and examples for two dimensional and axisymmetric vector and scalar problems are given. The extension of the Hybrid method to three dimensional problems is discussed.
49 citations
1 Jan 1985
TL;DR: In this paper, the spectral decomposition of the variance covariance matrix is used to obtain the response of the deterministic model corresponding to selected perturbations of these uncorrelated variables via a Newton-type iterative scheme.
Abstract: This paper investigates the use of Fast Probability Integration (FPI) algorithms in a Finite Element environment. A method allowing the representation of correlated fields in terms of a vector of uncorrelated transformed variables, based on the spectral decomposition of the variance-covariance matrix is developed. The response of the deterministic model corresponding to selected perturbations of these uncorrelated variables is then obtained via a Newton-type iterative scheme. The results of the perturbed problems are used to construct a local representation of the model's behavior in the neighborhood of the deterministic state, which the FPI algorithm will use to estimate the reliability of the system. Although the proposed strategy has thus far only been applied to linear elastostatics, the extension of the method to a broader class of problems appears to be feasible.
27 citations
TL;DR: In this article, a three-dimensional finite element analysis has been used to simulate the coupled static and dynamic behaviour of compliant ocean structures, which are assumed to be in the Morison regime.
18 citations
TL;DR: In this paper, a modified modal method for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented, which involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates.
Abstract: The procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures which exhibit a stiffening behavior and to those with a softening behavior is presented.
13 citations
TL;DR: In this paper, the amplitude and period error of a single mode of vibration was evaluated by using the Newmark's method for direct integration in structural dynamics, and the results of numerical experiments confirmed the anticipated error order and showed how the error formula varies with β.
Abstract: The usual assessment of performance of Newmark's method for direct integration in structural dynamics is by reference to amplitude and period error of a single mode of vibration. As an alternative the local and global truncation errors due to the time discretization are introduced. Methods of obtaining norms of the error sequences are presented. The results of numerical experiments confirm the anticipated error order and show how the error formula varies with β. The effect of the presence of physical damping on the error order and formula is also examined.
7 citations
1 Jan 1985
TL;DR: Research work on the finite element method continues, but new elements, which are economical, accurate and conform with existing elements for the other types of deformation and thus are worthy of inclusion in general programs, are of less frequent occurrence.
Abstract: In recent years the finite element method has been developed to the state where approximate mathematical models can be formulated for complex practical structures. These models have to represent the actual geometry and take into account the types of deformation which the structure will undergo in practice. Large versatile and efficient computer programs, which are based on the finite element method, exist for stress analysis; a general program will include the capability of determining response to dynamic loads. Research work on the finite element method continues, but new elements, which are economical, accurate and conform with existing elements for the other types of deformation and thus are worthy of inclusion in general programs, are of less frequent occurrence. Developments continue in elastic-plastic problems, which occur for large deformations, for example in earthquake engineering.
6 citations
TL;DR: In this paper, the Laplace transform was used to determine the transient flexural vibrations of a uniform cantilever beam, which is subjected to a transverse force at the free end, using the normal mode and Newmark average acceleration methods.
Abstract: When the finite element method is used to idealize a structure, its dynamic response can be determined from the governing matrix equation by the normal mode method or by one of the many approximate direct integration methods. In either method the approximate data of the finite element idealization are used, but further assumptions are introduced by the direct integration scheme. It is the purpose of this paper to study these errors for a simple structure. The transient flexural vibrations of a uniform cantilever beam, which is subjected to a transverse force at the free end, are determined by the Laplace transform method. Comparable responses are obtained for a finite element idealization of the beam, using the normal mode and Newmark average acceleration methods; the errors associated with the approximate methods are studied. If accuracy has priority and the quantity of data is small, the normal mode method is recommended; however, if the quantity of data is large, the Newmark method is useful.
1 citations
TL;DR: In this paper, a numerical method is proposed to solve a hyperbolic system of nonlinear partial differential equations of conservation laws, where the finite elements and the nodes move with arbitrary velocity.
Abstract: A numerical method is proposed to solve a hyperbolic system of nonlinear partial differential equations of conservation laws. The method is formulated as a finite element method (FEM), but the finite elements and the nodes move with arbitrary velocity (ALE). This method is called FEMALE. It is shown that the velocity of nodes should be identified with the local velocity of the nonlinear waves such as the shock wave, the contact discontinuity and the rarefaction wave, then numerical accuracy is much improved. A numerical method is also presented to obtain the local velocity of the nonlinear waves.
1 citations
TL;DR: In this paper, a new numerical calculation method, the time-periodic finite element method, for the nonlinear diffusion equation is proposed, where the equation is closed by the periodic-time of electrical characteristics and is solved by the numerical procedure which is used not for the initial value problem but for the boundary value one.
Abstract: A new numerical calculation method, the time-periodic finite element method, for the nonlinear diffusion equation is proposed. In the method, the equation is closed by the periodic-time of electrical characteristics and is solved by the numerical procedure which is used not for the initial value problem but for the boundary value one. The method is applied to the calculations of the voltage across the nonlinear corona shield region of a rotating machine. The results demonstrate that the method extensively reduces the computing time without losing the accuracy compared to the conventionally used methods.
Book•
1 Jan 1985
TL;DR: The Finite Element Method (FE) is the most widely used method for numerical approximation for partial differential equations defining engineering and scientific problems as mentioned in this paper, and it has been widely used in the field of structural engineering.
Abstract: THE FINITE ELEMENT METHOD : Basic Concepts and ApplicationsDarrell Pepper, Advanced Projects Research, Inc. California, and Dr . JuanHeinrich, University of Arizona, TucsonTh i s introductory textbook is designed for use in undergraduate, graduate, andshort courses in structural engineering and courses devoted specifically to thefinite element method. This method is rapidly becoming the most widely usedstandard for numerical approximation for partial differential equations definingengineering and scientific problems.The authors present a simplified approach to introducing the method and a coherentand easily digestible explanation of detailed mathematical derivations andtheory Example problems are included and can be worked out manually Anaccompanying floppy disk compiling computer codes is included and required forsome of the multi-dimensional homework problems.