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An assessment of the newmark method for solving chaotic vibrations of impacting oscillators
Computers & Structures, 1993This paper presents the solution of the chaotic problem of impacting single-degree-of-freedom oscillators, using the Newmark method which is computationally efficient and unconditionally stable. The scheme incorporates an equilibrium iteration and variable time-stepping algorithm based on a convergence criteria which ensures that solution errors are ...
MOORTHY, RIK +3 more
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Explicit Newmark-FDTD Method Based on Maxwell’s Equation
2020 IEEE International Conference on Computational Electromagnetics (ICCEM), 2020In this paper, we employ Newmark method to discretize the time differential term of Maxwell equation, and apply the power series expansion method to solve the coefficient matrix explicitly. Eventually, a large time step can be used in the Newmark-FDTD method and we can find the solution explicitly without incurring any instability.
Xinbo He, Bing Wei, Kaihang Fan
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Assessment of errors in the newmark method in structural dynamics
Earthquake Engineering & Structural Dynamics, 1990AbstractIn the Newmark and other approximate step‐by‐step methods, having introduced assumptions in order to transform the differential equations, which are characteristic of response problems, into simultanéous equations, successive solutions lead to a response‐time history.
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International Journal for Numerical Methods in Engineering, 1999
Summary: We examine an incomplete iterative solver aimed at an approximate solution of equilibrium equations resulting from the finite element semidiscretization in space. Our approach is motivated by the fact that: (i) the effective stiffness matrix is well-conditioned because of the stabilizing effect of diagonally dominated mass matrix; (ii) the ...
Fish, Jacob, Chen, Wen
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Summary: We examine an incomplete iterative solver aimed at an approximate solution of equilibrium equations resulting from the finite element semidiscretization in space. Our approach is motivated by the fact that: (i) the effective stiffness matrix is well-conditioned because of the stabilizing effect of diagonally dominated mass matrix; (ii) the ...
Fish, Jacob, Chen, Wen
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Numerical vibration analysis of plate structures by Newmark's method
Journal of Sound and Vibration, 1985Abstract This paper deals with the free vibration of plate structures such as isotropic or orthotropic rectangular plates with several boundary conditions, a plate with stepped thickness and a thin-walled box beam, by using Newmark's numerical method. Simplicity and usability of the method for design use is demonstrated in several numerical examples.
N. Nakahira +3 more
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A Fast Time-Stepping Strategy for the Newmark-Beta Method
Volume 1A: 34th Computers and Information in Engineering Conference, 2014In this paper, we develop a fast time-stepping strategy for the Newmark-beta method; the latter is used extensively in structural dynamics. In particular, we speed up the repeated inversion of the linear systems in the Newmark-beta method by implementing and merging four distinct but complementary concepts: (1) voxelization, (2) assembly-free finite ...
Amir M. Mirzendehdel, Krishnan Suresh
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Blast response in concrete beam with nanoparticles utilising Newmark method
International Journal of Hydromechatronics, 2019The project focuses on the dynamic analysis of concrete beams reinforced with silica-nanoparticles under blast loading. The structure is located at two boundary conditions. The effective composite properties are obtained utilising Mori-Tanak theory. The structure is simulated with sinusoidal shear deformation theory.
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Accuracy Evaluation of Newmark Method Referring to Theoretical Solutions
Journal of Earthquake Engineering, 2008Current accuracy evaluation of a step-by-step integration method is generally based on the numerical solution itself and the exact solution is not referred to except for period distortion. Furthermore, the numerical accuracy associated with external force is generally not considered.
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Four-stage Newmark method for structural dynamics analysis
AIP Conference Proceedings, 2017This paper develops a four-stage direct integration scheme for structural dynamics analysis. Based on Newmark method, the new scheme is formulated by expanding displacement to the fourth derivative. The stability, accuracy and dissipation of the new scheme are discussed, which results in two optimal sets of control parameters δ and α.
Huimin Zhang, Yufeng Xing, Zhenyu Li
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A technique for overcoming load discontinuity in using Newmark method
Journal of Sound and Vibration, 2007Although a closed form solution can be obtained for the shock response to an impulse by using the Duhamel integral method for a single degree-of-freedom system, it is analytically verified herein that an extra amplitude distortion will be introduced at the end of the impulse by using the Newmark method.
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