Singular boundary elements for three-dimensional elasticity problems

Guzina, Bojan B.; Pak, Ronald Y. S.; Martínez-Castro, Alejandro E.

doi:10.1016/j.enganabound.2006.02.010

Cited by 21 publications

(11 citation statements)

References 38 publications

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“…Note that the comparison is in integrated values of the computed potential, and not in the potential itself. Both solutions includes representation errors; the analytic solution is given in series form, in which the singular behavior in corner is not included (Guzina et al, 2006). In contrast, the BEM solution is obtained with constant elements, and the radiation boundary condition is imposed in an approximate form.…”

Section: Added Mass Of a Floating Cylindermentioning

confidence: 99%

An Iterative Parallel Solver in GPU Applied to Frequency Domain Linear Water Wave Problems by the Boundary Element Method

Molina

Martínez-Castro

Ortiz

2018

Front. Built Environ.

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In this paper a parallel iterative solver based on the Generalized Minimum Residual Method (GMRES) with complex-valued coefficients is explored, with applications to the Boundary Element Method (BEM). The solver is designed to be executed in a GPU (Graphic Processing Unit) device, exploiting its massively parallel capabilities. The BEM is a competitive method in terms of reduction in the number of degrees of freedom. Nonetheless, the BEM shows disadvantages when the dimension of the system grows, due to the particular structure of the system matrix. With difference to other acceleration techniques, the main objective of the proposed solver is the direct acceleration of existing standard BEM codes, by transfering to the GPU the solver task. The CUDA programming language is used, exploiting the particular architecture of the GPU device for complex-valued systems. To explore the performances of the solver, two linear water wave problems have been tested: the frequency-dependent added mass and damping matrices of a 3D floating body, and the Helmholtz equation in a 2D domain. A NVidia GeForce GTX 1080 graphic card has been used. The parallelized GMRES solver shows reductions in computing times when compared with its CPU implementation.

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Section: Added Mass Of a Floating Cylindermentioning

confidence: 99%

An Iterative Parallel Solver in GPU Applied to Frequency Domain Linear Water Wave Problems by the Boundary Element Method

Molina

Martínez-Castro

Ortiz

2018

Front. Built Environ.

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“…For quadrilateral elements, the node shift is presented with a similar definition as triangular elements shown in Fig. 15, Mi and Aliabadi [1994] chose the node shift as 1/2 and the error less 4%, Subia et al [1995] considered that the node shift equals to 1/3 is the best but between 1/20 and 3/5 is relatively constant for the results, Guzina et al [2006] regarded the node shift in the range 1/20-1/4 is optimal. In view of the above node shift selection, we select node shift as 1/20, 1/10, 1/6, 1/4, 1/3, 1/2 and 3/5, and compare the stress results at Z-direction (traction adding direction) with analytical solution.…”

Section: Examplementioning

confidence: 99%

Boundary Condition Related Mixed Boundary Element and its Application in FMBEM for 3D Elastostatic Problem

Wang

Deng

Wang

et al. 2015

Int. J. Comput. Methods

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A boundary condition (BC) related mixed element method is presented to address the corner problem in boundary element method (BEM) for 3D elastostatic problems. In this method, noncontinuous elements (NCEs) are only used at the displacement-prescribed corners/edges and continuous elements (CEs) in other places, which can decrease the degrees of freedom (DOFs) compared to the approach using NCEs at all corners/edges. Moreover, an automatic generation algorithm of BC related mixed linear triangular elements is implemented with the help of 3D modeling engine ACIS, and the boundary element analysis (BEA) is integrated into CAD systems. In order to solve large scale problems, the fast multipole BEM (FMBEM) with mixed elements is proposed and utilized in the BEA. The examples show that the node shift scheme adopting 1/4 is optimal and the BEM/FMBEM using mixed elements can produce more accurate results by only increasing a small number of DOFs.

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“…For its versatility and rigor in treating threedimensional interior as well as exterior domain problems, the advanced computational BEM platform by Pak and Guzina [14] is employed in this treatment. It features a regularized boundary integral equation formulation, a library of fundamental solutions including a set of multi-layered elastic and visco-elastic dynamic half-space displacement and traction Green's functionsÛ andT [34,44] with a bi-material decomposition at layer interfaces [45], a set of singular and adaptivegradient (AG) elements for mixed boundary value problems [46,47], as well as a nested adaptive integration scheme for robustness and accuracy. To implement the proposed half-space decomposition, the homogenized finite zone I contiguous to the foundation is taken as an interior domain for which the use of the dynamic Kelvin solution is appropriate.…”

Section: Computational Implementationmentioning

confidence: 99%

A fundamental dual‐zone continuum theory for dynamic soil–structure interaction

Pak

Ashlock

2010

Earthq Engng Struct Dyn

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A continuum theory for an improved characterization of dynamic soil-structure interaction in the framework of three-dimensional elastodynamics is presented. Effective in demonstrating the importance of integrating free-field and near-field effects under general soil and foundation conditions, a compact twozone delineation of the soil medium is proposed as a quintessential mechanics perspective for this class of problems. Sufficient to deliver a practical resolution of some perennial analytical and experimental conflicts, a fundamental formulation commensurate to a gradated unification of the homogenization approach and any sole free-field inhomogeneous representation is developed and implemented computationally. Specialized to the problem of a rigid circular footing on sand, a nominal set of dynamic contact stress distributions and related impedance functions by the dual-zone theory is included for theoretical and engineering evaluation. Through its comparison with benchmark analytical solutions and relevant physical measurements, the usage of the underlying conceptual platform as an advanced yet practical foundation for general dynamic soil-structure interaction is illustrated.

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Singular boundary elements for three-dimensional elasticity problems

Cited by 21 publications

References 38 publications

An Iterative Parallel Solver in GPU Applied to Frequency Domain Linear Water Wave Problems by the Boundary Element Method

An Iterative Parallel Solver in GPU Applied to Frequency Domain Linear Water Wave Problems by the Boundary Element Method

Boundary Condition Related Mixed Boundary Element and its Application in FMBEM for 3D Elastostatic Problem

A fundamental dual‐zone continuum theory for dynamic soil–structure interaction

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