A mesh refinement scheme for fourth order bi-harmonic equation of mixed boundary-value elastic problems

Aminul Islam Khan; Pranta Rahman Sarkar; Abdus Salam Akanda

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A mesh refinement scheme for fourth order bi-harmonic equation of mixed boundary-value elastic problems

机译：A mesh refinement scheme for fourth order bi-harmonic equation of mixed boundary-value elastic problems

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摘要

Fourth order bi-harmonic equation is extensively used for stress-strain analysis of mixed boundary-value elastic problems. However, currently existing uniform mesh scheme based on finite difference method (FDM) needs vast amount of computational resources and efforts for an acceptable solution. Therefore, in this study, a mesh refinement (MR) scheme based on FDM is developed to solve fourth order bi-harmonic equation effectively. The developed MR scheme allows high resolution computation in sub-domains of interest and relatively low resolution in other regions which overcomes the memory exhausting problems associating with the traditional uniform mesh based FDM. In this paper, sub-domain that needs high resolution (mesh refinement) are identified based on gradient of stress and displacement vectors. A very high gradient in any region signifies the need of fine mesh because coarse grained meshes are not adequate to capture the sharply changing stresses or displacements. Once the sub-domains of interest are identified, the mesh refinement is done by splitting course meshes into smaller meshes. Several new stencils are created to satisfy the fourth order by harmonic equation and associated boundary conditions over the various sizes of meshes. The developed MR scheme has been applied to solve several classical mixed boundary-value elastic problems to show its applicability. In addition, the validity, effectiveness, and superiority of the MR scheme have been established by comparing of obtained solutions with uniform mesh results, finite element method (FEM) results, and the well-known analytical results. Our results show that the developed MR scheme can provide a more reliable and accurate result than the conventional uniform mesh scheme with a reduced number of equations, thus, saves a huge amount of computational memory.

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来源
《The Journal of Strain Analysis for Engineering Design》 |2023年第3期|221-235|共15页
作者
Aminul Islam Khan; Pranta Rahman Sarkar; Abdus Salam Akanda;
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作者单位

Department of Mechanical Engineering, College of Engineering;

Department of Mechanical Engineering, Bangladesh University of Engineering and Technology;

Department of Mechanical Engineering, Bangladesh University of Engineering and Technology||School of Mechanical and Materials Engineering, Washington State University;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
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关键词
Structural mechanics; mesh refinement; finite difference method; displacement potential function; mixed boundary-value problems;

A mesh refinement scheme for fourth order bi-harmonic equation of mixed boundary-value elastic problems

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