Some Investigations of Fast Multipole BEM in Solid Mechanics

Yao, Zhenhan

doi:10.1007/978-1-4020-9710-2_28

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…The well-known numerical solution of integral equations is by the BEM and by its more effective form, FMBEM [4,[7][8][9][10][11]. However, no one formulation was used for composites reinforced by fibres with large aspect ratio and authors of this paper do not know any publications to problems like those shown below.…”

Section: Methods Of Continuous Source Functions For Simulation Of Fibresmentioning

confidence: 99%

“…The FMBEM is the only numerical method which enables solving representative volume element (RVE) of the matrix containing two to five thousand short fibres (three to eleven million degrees of freedom (d.o.f.)). The problems have been solved on a supercomputers, or on clusters of PCs [9][10][11]. If a matrix reinforced by carbon nanotubes (CNTs) having 1% volume of CNTs 1 mm long and 20 nm diameter will contain 3.2 × 10 7 tubes and the CNTs can have general form (curvature and orientation) and can be randomly distributed, then the control volume element (CVE) for homogenisation would contain several millions of CNTs for correct assessment of homogenized properties of the composite.…”

Section: Introductionmentioning

confidence: 99%

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Thermal Properties of Short Fibre Composites Modeled by Meshless Method

Kompiš

Murčínková

2014

Advances in Materials Science and Engineering

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Computational model using continuous source functions along the fibre axis is presented for simulation of temperature/heat flux in composites reinforced by short fibres with large aspect ratio. The aspect ratio of short fibres reinforcing composite material is often as large as 103 : 1–106 : 1, or even larger. 1D continuous source functions enable simulating the interaction of each fibre with the matrix and also with other fibres. The developed method of continuous source functions is a boundary meshless method reducing the problem considerably comparing to other methods like FEM, BEM, meshless methods, or fast multipole BEM formulation.

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Section: Methods Of Continuous Source Functions For Simulation Of Fibresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal Properties of Short Fibre Composites Modeled by Meshless Method

Kompiš

Murčínková

2014

Advances in Materials Science and Engineering

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“…Boundary governing equations of every plate element in the lateral and interior can be deduced based on DBEM. Considering the computational quantum is very large when using dynamic fundamental solutions to establish the governing equations [5,6], it is noticed that dynamic differential equations are distinguished from the equation of time variants. Moreover, the expressions of static fundamental solutions are very simple.…”

Section: Dynamic Simulation Equation Of Antenna Radomesmentioning

confidence: 99%

Study on One Kind of Antenna Radomes Materials Numerical Algorithm Simulation Based on DBEM

Fang

Wang

2008

MSF

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An approach of numerical modeling and simulation algorithm is presented to predict dynamic behaviors of one kind of antenna radomes materials efficiently. Considering the dynamic behaviors in the lateral and interior of the antenna radomes materials, the dynamic simulation equations of the antenna radomes materials is established based on a dynamic boundary element method (DBEM) by using the domain reducing to decrease computational scale and costs of the equations greatly, and the dynamic behaviors of the antenna radomes materials can be gotten effectively. Numerical simulation calculating and experiments show that the presented method not only saves computational efforts, raises analytical efficiency and simulation accuracy but also can provide the theoretical bases for avoiding the weak pose of the antenna radomes materials. It has very important reference value for improving theoretical calculation and design level of the antenna radomes materials.

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“…He has personally experienced many kinds of progress of BEM in depth and breadth (Du et al , 1984; Zheng et al , 1995; Yao et al , 1999; Yao and Du, 2001; Yao et al , 2001; Kong et al , 2002; Qian et al , 2004; Yao et al , 2004; Zhao and Yao, 2005; Huang et al , 2011; and many more introduced in Yao and Wang, 2010). Especially, the Fast Multipole BEM (FMBEM) and other Fast BEM has made great progress in this century (Nishimura, 2002; Lei et al , 2006; Lei, et al , 2007; Wang et al , 2007; Wang and Yao, 2004; Wang and Yao, 2013a, 2013b; Wang et al , 2005; Wang et al , 2007; Wang and Yao, 2006; Wang et al , 2005; Wang et al , 2006; Yao et al , 2008). However, from the point of view of engineering application, the BEM has been more and more marginalized.…”

Section: Introductionmentioning

confidence: 99%

Research progress of high-performance BEM and investigation on convergence of GMRES in local stress analysis of slender real thin-plate beams

Yao

Zheng

Yuan

et al. 2019

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Purpose Based on the error analysis, the authors proposed a new kind of high accuracy boundary element method (BEM) (HABEM), and for the large-scale problems, the fast algorithm, such as adaptive cross approximation (ACA) with generalized minimal residual (GMRES) is introduced to develop the high performance BEM (HPBEM). It is found that for slender beams, the stress analysis using iterative solver GMRES will difficult to converge. For the analysis of slender beams and thin structures, to enhance the efficiency of GMRES solver becomes a key problem in the development of the HPBEM. The purpose of this paper is study on the preconditioning method to solve this convergence problem, and it is started from the 2D BE analysis of slender beams. Design/methodology/approach The conventional sparse approximate inverse (SAI) based on adjacent nodes is modified to that based on adjacent nodes along the boundary line. In addition, the authors proposed a dual node variable merging (DNVM) preprocessing for slender thin-plate beams. As benchmark problems, the pure bending of thin-plate beam and the local stress analysis (LSA) of real thin-plate cantilever beam are applied to verify the effect of these two preconditioning method. Findings For the LSA of real thin-plate cantilever beams, as GMRES (m) without preconditioning applied, it is difficult to converge provided the length to height ratio greater than 50. Even with the preconditioner SAI or DNVM, it is also difficult to obtain the converged results. For the slender real beams, the iteration of GMRES (m) with SAI or DNVM stopped at wrong deformation state, and the computation failed. By changing zero initial solution to the analytical displacement solution of conventional beam theory, GMRES (m) with SAI or DNVM will not be stopped at wrong deformation state, but the stress error is still difficult to converge. However, by GMRES (m) combined with both SAI and DNVM preconditioning, the computation efficiency enhanced significantly. Originality/value This paper presents two preconditioners: DNVM and a modified SAI based on adjacent nodes along the boundary line of slender thin-plate beam. In the LSA, by using GMRES (m) combined with both DNVM and SAI, the computation efficiency enhanced significantly. It provides a reference for the further development of the 3D HPBEM in the LSA of real beam, plate and shell structures.

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Some Investigations of Fast Multipole BEM in Solid Mechanics

Cited by 5 publications

References 20 publications

Thermal Properties of Short Fibre Composites Modeled by Meshless Method

Thermal Properties of Short Fibre Composites Modeled by Meshless Method

Study on One Kind of Antenna Radomes Materials Numerical Algorithm Simulation Based on DBEM

Research progress of high-performance BEM and investigation on convergence of GMRES in local stress analysis of slender real thin-plate beams

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