Performance of the radial point interpolation method (RPIM) with implicit time integration scheme for transient wave propagation dynamics

The accuracy of the conventional finite element (FE) approximation for the analysis of acoustic propagation is always characterized by an intractable numerical dispersion error. With the aim of enhancing the performance of the FE approximation for acoustics, a coupled FE-Meshfree numerical method based on triangular elements is proposed in this work. In the proposed new triangular element, the required local numerical approximation is built using point interpolation mesh-free techniques with polynomial-radial basis functions, and the original linear shape functions from the classical FE approximation are employed to satisfy the condition of partition of unity. Consequently, this coupled FE-Meshfree numerical method possesses simultaneously the strengths of the conventional FE approximation and the meshfree numerical techniques. From a number of representative numerical experiments of acoustic propagation, it is shown that in acoustic analysis, better numerical performance can be achieved by suppressing the numerical dispersion error by the proposed FE-Meshfree approximation in comparison with the FE approximation. More importantly, it also shows better numerical features in terms of convergence rate and computational efficiency than the original FE approach; hence, it is a very good alternative numerical approach to the existing methods in computational acoustics fields.

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“…Following the formulation of the original RPIM approximation [54,71], the local numerical approximation is expressed by…”

Section: Construction Of the Coupled "Fe-meshfree" Numerical Approxim...mentioning

confidence: 99%

A Novel “Finite Element-Meshfree” Triangular Element Based on Partition of Unity for Acoustic Propagation Problems

2023

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“…In recent years, scholars have made notable progress in devising effective methods to derive exact solutions for NLPDEs. Successful approaches encompass the inverse scattering [6], Darboux transform [7], integral scheme [8], unified approach [9], Simplified Hirota's approach [10], Lie analysis [11], Painlevé test [12], sub-equation method [13], and F-expansion approach [14].…”

Section: Introductionmentioning

confidence: 99%

Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid

Riaz,

Kazmi,

Jhangeer

2024

Phys. Scr.

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In this study, an examination of the Yu-Toda-Sasa-Fukuyama equation is undertaken, a model that characterizes elastic waves in a lattice or interfacial waves in a two layer liquid. Our emphasis lies in conducting a comprehensive analysis of this equation through various viewpoints, including the examination of soliton dynamics, exploration of bifurcation patterns, investigation of chaotic phenomena, and a thorough evaluation of the model's sensitivity. Utilizing a simplified version of Hirota's approach, multi-soliton pattens, including 1-wave, 2-wave, and 3-wave solitons, are successfully derived. The identified solutions are depicted visually via 3D, 2D, and contour plots using Mathematica software. The dynamic behavior of the discussed equation is explored through the theory of bifurcation and chaos, with phase diagrams of bifurcation observed at the fixed points of a planar system. Introducing a perturbed force to the dynamical system, periodic, quasi-periodic and chaotic patterns are identified using the RK4 method. The chaotic nature of perturbed system is discussed through Lyapunov exponent analysis. Sensitivity and multistability analysis are conducted, considering various initial conditions. The results acquired emphasize the efficacy of the methodologies used in evaluating solitons and phase plots across a broader spectrum of nonlinear models.

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“…The numerical results demonstrate that the SFEM and SPIM are indeed effective numerical approaches for the analysis of MEE structures and the solution precision can be markedly improved compared to the conventional FEM. In addition to the SFEMs, the point interpolation method with radial basis functions (RPIM) [46][47][48][49], which has been developed by Liu et al using the meshless numerical technique [50][51][52][53], is also introduced to perform the numerical analysis of smart materials [54]. It is found from the numerical results that the RPIM is usually able to surpass the finite element approach in solving the smart structures.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

Chai,

Huang,

Wang

et al. 2024

Smart Mater. Struct.

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In this work, a carefully designed enriched finite element method (EFEM) is presented to improve the solution accuracy of the conventional FEM in analyzing the dynamic behaviors of the magnetic-electric-elastic (MEE) composite structures which are frequently used in designing various smart and intelligent devices. In formulating the proper EFEM with ideal numerical performance, different enrichment functions are considered and the corresponding solution quality of different versions of the EFEM are compared and examined in great detail. When the Lagrange polynomial basis functions together with the harmonic trigonometric functions are used as the enrichment functions, the obtained EFEM shows extremely powerful and ideal numerical performance, which are obviously better than the other versions of EFEM and the conventional FEM, in studying the free vibration and harmonic frequency responses of the MEE structures. The nearly exact numerical solutions for three-phase physical fields of MEE structures can be generated by the proposed EFEM even if very coarse mesh patterns are used. Intensive numerical studies are conducted to confirm and verify the excellent properties of the proposed EFEM in performing dynamic analysis of the MEE structures.

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Performance of the radial point interpolation method (RPIM) with implicit time integration scheme for transient wave propagation dynamics

Cited by 48 publications

References 53 publications

A Novel “Finite Element-Meshfree” Triangular Element Based on Partition of Unity for Acoustic Propagation Problems

A Novel “Finite Element-Meshfree” Triangular Element Based on Partition of Unity for Acoustic Propagation Problems

Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

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