An improved explicit integration algorithm with controllable numerical dissipation for structural dynamics
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O R I G I NA L
Chao Yang
· Xi Wang · Qiang Li · Shoune Xiao
An improved explicit integration algorithm with controllable numerical dissipation for structural dynamics
Received: 18 January 2020 / Accepted: 30 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In order to acquire efficient algorithms for complicated problems in structural dynamics, an improved integration algorithm with controllable numerical dissipation is developed based on a two-step explicit acceleration integration method. The improved method is a step-by-step integration scheme which is conditionally stable and robust in strongly nonlinear systems. The consistency, accuracy and the stability are analyzed for the improved method. Linear and nonlinear examples are employed to confirm the properties of the improved method. The results manifest that the improved method can be of second-order accuracy. It can be marginally stable in dynamic systems. The improved method possesses the property of energy conservation in conservative systems. Moreover, it is controllable for the numerical dissipation or algorithm damping which can be zero. The high-frequency oscillation can be effectively inhibited in a stiff problem. The spurious oscillation caused by the spatial discretization can be almost completely suppressed by the controllable numerical dissipation in a rod or a cantilever beam. It is applicable in transient and wave propagation problems. Keywords Explicit · Time integration · Nonlinear systems · Stability · Spurious oscillation
1 Introduction The numerical methods of structural dynamics can be divided into the mode superposition method and step-bystep integration methods, and the latter one can be further classified into explicit methods and implicit methods. Implicit methods have to be solved in terms of a set of coupled equations in each time step. In contrast, the unknown quantities of explicit methods are determined by previous solutions in a computation loop [1]. The implicit methods, which contain the Newmark method and the Wilson-θ method, are generally employed in stiff problems and linear problems [2]. A variation of the traditional central difference method (CDM) is one of the representatives in explicit methods [3]. Explicit methods are widely used in nonlinear dynamic problems. C. Yang (B) · X. Wang · Q. Li School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, People’s Republic of China E-mail: [email protected] X. Wang E-mail: [email protected] Q. Li E-mail: [email protected] S. Xiao State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China E-mail: [email protected]
C. Yang et al.
Since the computational efforts and costs are increasing significantly for large-scale and nonlinear structures, an effective step-by-step integration algorithm is desired while it also possesses higher accuracy. The Taylor’s theorem and the weighted residual method are usually applied to develop new algorith
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