First-order doubly-asymptotic formulation of the direct stiffness method for elastodynamic problems

Ceballos, Marcelo A.; Prato, Carlos A.

doi:10.1016/j.soildyn.2014.09.015

Soil Dynamics and Earthquake Engineering

2014

DOI: 10.1016/j.soildyn.2014.09.015

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First-order doubly-asymptotic formulation of the direct stiffness method for elastodynamic problems

Marcelo A. Ceballos

Carlos A. Prato

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Cited by 4 publications

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“…10-12 Other researchers only adopt the concept of "the doubly asymptotic", they derive the approximation models for the soil-structure interaction problems. [13][14][15] In this paper, a new stable third-order approximation model for an acoustic-structure interaction problem is introduced. It is found that the third-order DAA derived in 2000 has a convergence issue.…”

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Analysis of Acoustic-Structure Interaction Using a High-Order Doubly Asymptotic Approximation

Woo

Shin

2016

J. Comp. Acous.

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In this paper, a new third-order approximation model for an acoustic-structure interaction problem is introduced. The new approximation model is designed to be an accurate and a stable model for predicting the response of a submerged structure. The proposed model is obtained by combining two lower order approximation models instead of using an operator matching method. The stability of this model is checked by a modal analysis. Finally, the approximation model is coupled to the spherical shell structure, and its performance is checked by a shock analysis.commonly applied to the boundary surface of a structure to calculate the relationship between the pressure and particle velocity of the acoustic medium on the surface. This DAA was first developed to handle the fluid-structure interaction problem in the 1970s. 5 After its first development, DAAs were modified for accurate calculation by the operator matching process. 6-8 A third-order DAA was also introduced later. 9 DAA is still currently being used for underwater explosion problems. The secondorder DAA is usually used for the numerical simulations of underwater structures with a variety of shapes. 10-12 Other researchers only adopt the concept of "the doubly asymptotic", they derive the approximation models for the soil-structure interaction problems. [13][14][15] In this paper, a new stable third-order approximation model for an acoustic-structure interaction problem is introduced. It is found that the third-order DAA derived in 2000 has a convergence issue. To make a stable model, the proposed model did not use an operator matching method. Approximation models fully derived from Kirchhoff's Retarded Potential formula were used to derive the new model. [16][17][18] First-order and second-order approximation models were combined with a new weighting parameter. Performance of the proposed model was checked by an interaction problem. The approximation model was applied on the surface of a spherical shell structure excited by a cosine-type impulsive pressure. The response was compared with an exact solution. Proposed model showed a superb result in early time. This paper is organized as follows.Section 2 briefly introduces the first-and second-order DAAs obtained by the operator matching method. In Sec. 3, the third-order DAA is introduced. Both modal and shock analysis are performed using the third-order DAA. In Sec. 4, a new stable third-order approximation model is derived. And its performance is checked by the same analysis in Sec. 3. 1550021-2 J. Comp. Acous. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/24/15. For personal use only. 1550021-4 J. Comp. Acous. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/24/15. For personal use only. 1550021-7 J. Comp. Acous. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/24/15. For personal use only.

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confidence: 99%

Analysis of Acoustic-Structure Interaction Using a High-Order Doubly Asymptotic Approximation

Woo

Shin

2016

J. Comp. Acous.

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Numerical evaluation of integrals involving the product of two Bessel functions and a rational fraction arising in some elastodynamic problems

Ceballos

2017

Journal of Computational and Applied Mathematics

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Convergent and asymptotic expansions of the displacement elastodynamic integral in terms of known functions

Ferreira,

López,

Pérez Sinusía

2025

Journal of Computational and Applied Mathematics

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First-order doubly-asymptotic formulation of the direct stiffness method for elastodynamic problems

Cited by 4 publications

References 14 publications

Analysis of Acoustic-Structure Interaction Using a High-Order Doubly Asymptotic Approximation

Analysis of Acoustic-Structure Interaction Using a High-Order Doubly Asymptotic Approximation

Numerical evaluation of integrals involving the product of two Bessel functions and a rational fraction arising in some elastodynamic problems

Convergent and asymptotic expansions of the displacement elastodynamic integral in terms of known functions

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