Topic
Newmark-beta method
About: Newmark-beta method is a research topic. Over the lifetime, 1425 publications have been published within this topic receiving 28753 citations.
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TL;DR: In this paper, the method is capable of application to structures of any degree of complication, with any relationship between force and displacement, from linear elastic behavior through various degrees of inelastic behavior or plastic response, up to failure; any type of dynamic loading, due to shock or impact, vibration, earthquake, or nuclear blast can be considered.
Abstract: Method is capable of application to structures of any degree of complication, with any relationship between force and displacement, from linear elastic behavior through various degrees of inelastic behavior or plastic response, up to failure; any type of dynamic loading, due to shock or impact, vibration, earthquake, or nuclear blast can be considered; use of high-speed digital computers.
4,176 citations
TL;DR: In this article, a new family of unconditionally stable one-step methods for the direct integration of the equations of structural dynamics is introduced and is shown to possess improved algorithmic damping properties which can be continuously controlled.
Abstract: A new family of unconditionally stable one-step methods for the direct integration of the equations of structural dynamics is introduced and is shown to possess improved algorithmic damping properties which can be continuously controlled. The new methods are compared with members of the Newmark family, and the Houbolt and Wilson methods.
2,200 citations
TL;DR: The Bossak-Newmark algorithm as mentioned in this paper is an extension of the well-known Newmark algorithm for numerical integration of the equations of discretized structural dynamics problems, which enables the method (when used on the test equation i = -02x) to be simultaneously second order, unconditionally stable and with positive artificial damping.
Abstract: SUMMARY This paper discusses the Bossak-Newmark algorithm, which is an extension of the well-known Newmark algorithm’ for the numerical integration of the equations of discretized structural dynamics problems. The extra parameter introduced here enables the method (when used on the test equation i = -02x) to be simultaneously second order, unconditionally stable and with positive artificial damping. Com arisons are made with another modification of Newmark introduced by Hilber, Hughes and Taylor. P
499 citations
TL;DR: This article developed simple regression models to estimate Newmark displacement based on analysis of the small number of strong-motion records then available, but they have standard deviations of about 0.5 log units, such that the range defined by the mean±one standard deviation spans about an order of magnitude.
497 citations
TL;DR: This book surveys higher-order finite difference methods and develops various mass-lumped finite element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem.
Abstract: Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.
464 citations