Two-dimensional elastodynamics by the time-domain boundary element method: Lagrange interpolation strategy in time integration

Carrer, J. A. M.; Pereira, W.L.A.; Mansur, Webe João

doi:10.1016/j.enganabound.2012.01.004

Cited by 21 publications

(11 citation statements)

References 15 publications

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“…The time domain boundary integral equation (TD-BIE) can be written as follows (Carrer et al 2012;Lei et al 2015).…”

Section: Td-bem Formulationmentioning

confidence: 99%

“…Many investigations in which BEM techniques were employed to perform the dynamic analysis of structures can be found in the review paper (Hatzigeorgiou and Beskos 2011). Mansur and his colleges conducted extensive studies to improve the stability and accuracy of TD-BEM, most of which were focused on the time domain (Mansur and Delima-Silva 1992;Mansur et al 1998;Yu et al 1998a, b, Carrer and Mansur 2000 and wave equations (Mansur and Brebbia 1982;Carrer and Mansur 1996;Yu et al 2000;Abreu et al 2003;Carrer et al 2012). However, the aims of those efforts were to find optimal numerical solutions, so the above problems were still probed in the level of the numerical solution.…”

Section: Introductionmentioning

confidence: 99%

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Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis

Lei²,

Liu³

2020

Comp. Appl. Math.

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The coupling algorithm of the finite element method (FEM) and boundary element method (BEM) can make maximal use of both methods' advantages. However, such coupling will reduce the computational efficiency because the systems' degrees of freedom will increase sharply. Thus, a new coupling algorithm that achieves accuracy and computational efficiency is necessary. This study proposes the Newmark-based precise integration FEM (NBPI-FEM) and analytical-based time domain BEM (ABTD-BEM) coupling algorithm. In this coupling algorithm, the governing equation of the FEM is solved by Newmarkbased precise integration, and the governing equation of the BEM is solved by the analytical method. First, the procedures of NBPI-FEM and ABTD-BEM are given. The coupling strategy is then provided, and the relationship between the iteration numbers and the relaxation parameter is investigated. Finally, two illustrative examples-i.e., 1-D rod and a semi-infinite structure-are selected to verify the coupling algorithm proposed in the study. The results show that the numerical solutions agree well with the analytical solutions for the 1-D rod example and coincide with the numerical solutions calculated by FEM. Thus, NBPI-FEM and ABTD-BEM can be applied for solving elastodynamic problems with high accuracy and efficiency. Keywords Elastodynamic analysis • Finite element method • Time domain boundary element method • Newmark method • Analytical solution Mathematics Subject Classification 45Exx Communicated by Baisheng Yan.

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“…The time domain boundary integral equation (TD-BIE) can be written as follows (Carrer et al 2012;Lei et al 2015).…”

Section: Td-bem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis

Lei²,

Liu³

2020

Comp. Appl. Math.

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“…Note that, the numerical instability issue of TDBEM would eventually restrict the effective time length of the calculation. Owing to a variety of elaborate work that tries to solve the problem, the instability can be alleviated to some extent (Carrer, Pereira & Mansur 2012;Jang & Ih 2012). In the present model, the instability problem in TDBEM is simply alleviated by properly choosing the time step, t, and the length of boundary element, l e , for convenience.…”

Section: Sound Wave Propagation Within the Ductmentioning

confidence: 99%

“…It is recommended that the value of α should fall in the interval 0 < α < 1.0 and avoid too small or large values (Carrer, Pereira & Mansur 2012).…”

Section: Sound Wave Propagation Within the Ductmentioning

confidence: 99%

Frequency lock-in mechanism in flow-induced acoustic resonance of a cylinder in a flow duct

Hong

Wang

et al. 2019

J. Fluid Mech.

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“…Later, the TD-BEM was employed to solve the dynamic response of a semi-circular canyon by considering four types of incident waves [22]. Mansur and his colleagues conducted extensive studies to improve the stability and accuracy of the TD-BEM, most of which were focused on the time domain [23][24][25][26][27][28] and wave equations [17,[29][30][31][32]. Subsequently, Lei et al [33][34][35] adopted the analytical method to solve the singular integrals in the boundary integral equation (BIE), and the computation precision and accuracy of analytical-based TD-BEM were verified for several examples.…”

Section: Introductionmentioning

confidence: 99%

Time-domain boundary element method with von Mises model for solving 2-D elastoplastic dynamic problems

Lei

Zhu

2019

J Braz. Soc. Mech. Sci. Eng.

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The analytical-based time-domain boundary element method (TD-BEM) can make maximal use of its advantages with negligible computational errors and has been verified for elastodynamic problems. However, the application of the method is limited because structures subjected to the severe loading tend to exhibit inelastic behavior that is beyond the method's cope. Thus, an analytical-based TD-BEM that can deal with elastoplastic dynamic problems is necessary. This study first introduced time-dependent fundamental solutions for displacement and traction, as well as stress. The Mises model was selected as the constitutive model, and two different types of the model were considered. Second, the discretization of the constitutive equation was given in order to incorporate it into the TD-BEM. The analytical integration method, the Hadamard principle integral, was adopted for dealing with the singularities that exist in solving integral equations; we also give analytical solutions of singularities. Finally, two illustrative examples-that is, a cantilever plate and an infinite circular cavity-were selected to verify the analytical TD-BEM proposed in the study. The results showed that the numerical solutions agree well with the analytical solutions for the cantilever plate example and coincided with the numerical solutions calculated by the finite element method (FEM) for the infinite circular cavity example. Thus, the analytical TD-BEM can be applied for solving elastoplastic dynamic problems with high accuracy and efficiency.

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Two-dimensional elastodynamics by the time-domain boundary element method: Lagrange interpolation strategy in time integration

Cited by 21 publications

References 15 publications

Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis

Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis

Frequency lock-in mechanism in flow-induced acoustic resonance of a cylinder in a flow duct

Time-domain boundary element method with von Mises model for solving 2-D elastoplastic dynamic problems

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