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高精度近场动力学方法:一维键型研究
High-precision peridynamics: one dimensional bond-based model
投稿时间:2020-04-17  修订日期:2020-07-16
DOI:
中文关键词:  近场动力学  微模量  边界效应  计算精度  数值方法
英文关键词:peridynamics, micro-modulus, surface effect, computational accuracy, numerical methods
基金项目:科学挑战专题(TZ2018002),中央高校基本科研业务费专项(DUT18LK04),国家自然科学基金面上项目(11672062)资助
作者单位E-mail
吴凡 大连理工大学 f251386704@qq.com 
段庆林 大连理工大学 qinglinduan@dlut.edu.cn 
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中文摘要:
      近些年发展起来的近场动力学方法对于模拟复杂的断裂破坏问题具有显著优势。然而,计算精度不高一直是困扰该方法进一步发展的瓶颈问题之一。区域积分不精确和键缺失导致的边界效应是降低该方法计算精度的两个主要原因。针对一维键型近场动力学模型,本文通过修正微模量提高区域积分的精度,通过理性构建固定边界和力边界虚拟键改善边界效应,建立了高精度近场动力学方法。数值结果表明,与经典的近场动力学方法相比,本文方法显著提高了计算精度,准静态常应变问题甚至能够达到机器精度。
英文摘要:
      Peridynamics (PD) developed in recent years possesses remarkable superiorities in modelling complicated fracture problems. However, its computational accuracy is unsatisfactory. This is one of the bottleneck issues which limit the further development of this method. Inaccurate domain integration and surface effect induced by the lack of bonds are the two main reasons which lead to low accuracy. Aiming at one-dimensional bond-based PD model, this paper presents a high-precision PD (hp-PD) method in which the accuracy of domain integration is improved by correcting the micro-modulus and the surface effect is improved by rationally establishing the virtual boundary bonds of fixed and traction boundaries. Numerical results show that, in comparison with the traditional PD method, the proposed method remarkably improves the computational accuracy and for quasi-static constant strain problems the accuracy even reaches the machine precision.
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