Boundary element method for 2D solids with fluid-filled pores

Huang, Quanzhang; Zheng, Xiaoping; Yao, Zhenhan

doi:10.1016/j.enganabound.2010.08.004

Cited by 6 publications

(3 citation statements)

References 20 publications

(25 reference statements)

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“…For the boundary element method, Yang D. et al [13] used the fundamental solution of the Stokes equation to study incompressible viscous fluids. Qiang H. and Yao Z. et al [14] established a correlation matrix between interface force and displacement according to the constitutive relationship of the inclusion material. Zhu R. et al proposed a vertical integration method based on the multi-domain higher-order boundary element method [15] and a time-domain calculation method for wave propulsion [16].…”

Section: Introductionmentioning

confidence: 99%

Surface Pressure Calculation Method of Multi-Field Coupling Mechanism under the Action of Flow Field

et al. 2023

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At present, the majority of fluid mechanisms are multi-field coupling mechanisms, and their function is also achieved in the flow field. Therefore, calculating the aerodynamic characteristics of the multi-field coupling mechanism in a symmetric flow field is very important. However, at present, the strong coupling algorithm in the domain has the problems of low accuracy and computational efficiency, which make it more difficult to solve the coupling problem. This article obtains the vector potential of the law of conservation of momentum using the tensor analysis method in a Cartesian coordinate system. Meanwhile, the generalized operator of Navier–Stokes equations and the fundamental solution of the generalized operator are obtained on this basis. Then, this article proposes the boundary integral equation of the Navier–Stokes equations by combining the fundamental solution of the Laplace equation with generalized potential theory. Based on this boundary integral equation, this article has developed a new calculation method that can help achieve integral calculation without domains, greatly reducing the problem’s difficulty. Finally, by comparing the ellipsoid example solution with the experimental results, the algorithm’s reliability in solving the incompressible problem is verified.

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Section: Introductionmentioning

confidence: 99%

Surface Pressure Calculation Method of Multi-Field Coupling Mechanism under the Action of Flow Field

et al. 2023

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“…It is committed to making it an important supplement to the FEM. 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).…”

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

Self Cite

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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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“…Using the following two approaches, Zheng et al [11] studied a solid whose macrostructure comprised fluid-filled pores: the superposition method and a multi-subdomain method 2D BEM model using subregions. It was shown that the multi-subdomain method (with subregions) was more efficient and accurate for determining the effective properties.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Effective Elastic Modulus for Nodular Cast Iron Using the Boundary Element Method

Betancur

Anflor

Pereira

et al. 2018

Metals

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Abstract:In this work, a multiscale homogenization procedure using the boundary element method (BEM) for modeling a two-dimensional (2D) and three-dimensional (3D) multiphase microstructure is presented. A numerical routine is specially written for modeling nodular cast iron (NCI) considering the graphite nodules as cylindrical and real geometries. The BEM is used as a numerical approach for solving the elastic problem of a representative volume element from a mean field model. Numerical models for NCI have generally been developed considering the graphite nodules as voids due to their soft feature. In this sense, three numerical models are developed, and the homogenization procedure is carried out considering the graphite nodules as non-voids. Experimental tensile, hardness, and microhardness tests are performed to determine the mechanical properties of the overall material, matrix, and inclusion nodules, respectively. The nodule sizes, distributions, and chemical compositions are determined by laser scanning microscopy, an X-ray computerized microtomography system (micro-CT), and energy-dispersive X-ray (EDX) spectroscopy, respectively. For the numerical model with real inclusions, the boundary mesh is obtained from micro-CT data. The effective properties obtained by considering the real and synthetic nodules' geometries are compared with those obtained from the experimental work and the existing literature. The final results considering both approaches demonstrate a good agreement.

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Boundary element method for 2D solids with fluid-filled pores

Cited by 6 publications

References 20 publications

Surface Pressure Calculation Method of Multi-Field Coupling Mechanism under the Action of Flow Field

Surface Pressure Calculation Method of Multi-Field Coupling Mechanism under the Action of Flow Field

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

Determination of the Effective Elastic Modulus for Nodular Cast Iron Using the Boundary Element Method

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