An improved quartic B-spline based explicit time integration algorithm for structural dynamics

Wang, Wen; Deng, Shanyao; Liu, Tianhao; Duan, Shengyu; Huang, Fanglin

doi:10.1016/j.euromechsol.2021.104407

Cited by 8 publications

(2 citation statements)

References 33 publications

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“…6,8,34 It is noted an explicit time integration scheme is efficient to calculate the responses in a time step but requires a restricted time step size to achieve stable numerical results. 35 On the contrary, implicit integration schemes can be unconditionally stable so that a large time step size can be adopted to achieve stable numerical results. 36 This paper intends to develop an implicit partitioned loose coupling method.…”

Section: Introductionmentioning

confidence: 99%

“…Implicit or explicit direct integration schemes can be adopted to calculate the dynamic responses of hyperelastic solid and acoustic waves 6,8,34 . It is noted an explicit time integration scheme is efficient to calculate the responses in a time step but requires a restricted time step size to achieve stable numerical results 35 . On the contrary, implicit integration schemes can be unconditionally stable so that a large time step size can be adopted to achieve stable numerical results 36 …”

Section: Introductionmentioning

confidence: 99%

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Implicit coupling methods for nonlinear interactions between a large‐deformable hyperelastic solid and a viscous acoustic fluid of infinite extent

Li,

Qu,

Meng

2023

Numerical Methods in Fluids

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This paper addresses the challenges in studying the interaction between high‐intensity sound waves and large‐deformable hyperelastic solids, which are characterized by nonlinearities of the hyperelastic material, the finite‐amplitude acoustic wave, and the large‐deformable fluid–solid interface. An implicit coupling method is proposed for predicting nonlinear structural‐acoustic responses of the large‐deformable hyperelastic solid submerged in a compressible viscous fluid of infinite extent. An arbitrary Lagrangian–Eulerian (ALE) formulation based on an unsplit complex‐frequency‐shifted perfectly matched layer method is developed for long‐time simulation of the nonlinear acoustic wave propagation without exhibiting long‐time instabilities. The solid and acoustic fluid domains are discretized using the finite element method, and two different options of staggered implicit coupling procedures for nonlinear structural‐acoustic interactions are developed. Theoretical formulations for stability analysis of the implicit methods are provided. The accuracy, robustness, and convergence properties of the proposed methods are evaluated by a benchmark problem, that is, a hyperelastic rod interacting with finite‐amplitude acoustic waves. The numerical results substantiate that the present methods are able to provide long‐time steady‐state solutions for a nonlinear coupled hyperelastic solid and viscous acoustic fluid system without numerical constraints of small time step sizes and long‐time instabilities. The methods are applied to investigate nonlinear dynamic behaviors of coupled hyperelastic elliptical ring and acoustic fluid systems. Physical insights into 2:1 and 4:2:1 internal resonances of the hyperelastic elliptical ring and period‐doubling bifurcations of the structural and acoustic responses of the system are provided.

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