A complete orthogonal decomposition method for the comprehensive deformation energy of discrete elastomers

IF 3.8 2区工程技术 Q1 ENGINEERING, MECHANICAL

Acta Mechanica Sinica Pub Date : 2024-06-26 DOI:10.1007/s10409-024-23181-x

Kaixuan Liang (, ), Panxu Sun (, ), Dongwei Wang (, ), Yadan Yan (, )

{"title":"A complete orthogonal decomposition method for the comprehensive deformation energy of discrete elastomers","authors":"Kaixuan Liang \n (, ), Panxu Sun \n (, ), Dongwei Wang \n (, ), Yadan Yan \n (, )","doi":"10.1007/s10409-024-23181-x","DOIUrl":null,"url":null,"abstract":"<div><p>Based on mathematical orthogonality and mechanical equilibrium, a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials. By aid of this method, the comprehensive deformation energy of planar discrete elastomers can be decomposed into five basic deformation energies, and the comprehensive deformation energy of spatial discrete elastomers can be decomposed into eighteen basic deformation energies. The quantification and visualization of structural deformation performance can be realized. According to the magnitude of different deformation energy in the same element, the decomposition diagram is drawn, which can visually display the area dominated by each basic deformation energy. The cloud diagram is drawn based on the distribution of specific deformation energy in different elements, which can be used to analyze the gradient change of deformation energy in the structure. Finally, the deformation properties of cantilever beam and four-sided consolidation plate are analyzed by deformation energy decomposition method. The correctness and superiority of this method are verified by comparing with the results of strain energy decomposition.</p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"40 11","pages":""},"PeriodicalIF":3.8000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica Sinica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10409-024-23181-x","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}

引用次数: 0

Abstract

Based on mathematical orthogonality and mechanical equilibrium, a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials. By aid of this method, the comprehensive deformation energy of planar discrete elastomers can be decomposed into five basic deformation energies, and the comprehensive deformation energy of spatial discrete elastomers can be decomposed into eighteen basic deformation energies. The quantification and visualization of structural deformation performance can be realized. According to the magnitude of different deformation energy in the same element, the decomposition diagram is drawn, which can visually display the area dominated by each basic deformation energy. The cloud diagram is drawn based on the distribution of specific deformation energy in different elements, which can be used to analyze the gradient change of deformation energy in the structure. Finally, the deformation properties of cantilever beam and four-sided consolidation plate are analyzed by deformation energy decomposition method. The correctness and superiority of this method are verified by comparing with the results of strain energy decomposition.

查看原文本刊更多论文

离散弹性体综合变形能的完全正交分解法

基于数学正交性和力学平衡，考虑材料的物理参数，提出了经典各向同性正方体和立方体元素的变形能分解方法。借助该方法，平面离散弹性体的综合变形能可分解为五个基本变形能，空间离散弹性体的综合变形能可分解为十八个基本变形能。实现了结构变形性能的量化和可视化。根据同一构件中不同变形能的大小绘制分解图，可直观显示各基本变形能所占的面积。根据不同元素中特定变形能的分布情况绘制云图，可用于分析结构中变形能的梯度变化。最后，利用变形能分解法分析了悬臂梁和四面固结板的变形特性。通过与应变能分解法的结果对比，验证了该方法的正确性和优越性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Acta Mechanica Sinica 物理-工程：机械

CiteScore

5.60

自引率

20.00%

发文量

1807

审稿时长

4 months

期刊介绍： Acta Mechanica Sinica, sponsored by the Chinese Society of Theoretical and Applied Mechanics, promotes scientific exchanges and collaboration among Chinese scientists in China and abroad. It features high quality, original papers in all aspects of mechanics and mechanical sciences. Not only does the journal explore the classical subdivisions of theoretical and applied mechanics such as solid and fluid mechanics, it also explores recently emerging areas such as biomechanics and nanomechanics. In addition, the journal investigates analytical, computational, and experimental progresses in all areas of mechanics. Lastly, it encourages research in interdisciplinary subjects, serving as a bridge between mechanics and other branches of engineering and the sciences. In addition to research papers, Acta Mechanica Sinica publishes reviews, notes, experimental techniques, scientific events, and other special topics of interest. Related subjects » Classical Continuum Physics - Computational Intelligence and Complexity - Mechanics