幂强化弹塑性材料平面应变反问题

梅杰, 张博文, 张春云, 彭海峰, 崔苗

梅杰, 张博文, 张春云, 彭海峰, 崔苗. 幂强化弹塑性材料平面应变反问题[J]. 工程力学, 2020, 37(1): 248-256. DOI: 10.6052/j.issn.1000-4750.2019.01.0086
引用本文: 梅杰, 张博文, 张春云, 彭海峰, 崔苗. 幂强化弹塑性材料平面应变反问题[J]. 工程力学, 2020, 37(1): 248-256. DOI: 10.6052/j.issn.1000-4750.2019.01.0086
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MEI Jie, ZHANG Bo-wen, ZHANG Chun-yun, PENG Hai-feng, CUI Miao. THE INVERSE PROBLEM OF PLANE STRAIN IN POWER-HARDENING ELASTICOPLASTICITY MATERIALS[J]. Engineering Mechanics, 2020, 37(1): 248-256. DOI: 10.6052/j.issn.1000-4750.2019.01.0086
Citation: MEI Jie, ZHANG Bo-wen, ZHANG Chun-yun, PENG Hai-feng, CUI Miao. THE INVERSE PROBLEM OF PLANE STRAIN IN POWER-HARDENING ELASTICOPLASTICITY MATERIALS[J]. Engineering Mechanics, 2020, 37(1): 248-256. DOI: 10.6052/j.issn.1000-4750.2019.01.0086
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幂强化弹塑性材料平面应变反问题

  • 大连理工大学, 工业装备结构分析国家重点实验室, 辽宁省空天飞行器前沿技术重点实验室, 辽宁 大连 116024

基金项目: 国家自然科学基金资助项目（51576026）；中国博士后基金项目（2016M601305）；中央高校基本科研业务费项目（DUT17LK04）
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    作者简介:

    梅杰(1995-),男,江西人,硕士生,主要从事计算热/力学及其反问题的研究(E-mail:meijie2013@dlut.mail.edu.cn);张博文(1996-),男,河南人,硕士生,主要从事计算热/力学及其反问题的研究(E-mail:1193996167@qq.com);张春云(1995-),女,山东人,博士生,主要从事计算热/力学及其反问题的研究(E-mail:1969528001@qq.com);彭海峰(1986-),男,辽宁人,讲师,博士,硕导,主要从事计算热/力学的研究(E-mail:hfpeng@dlut.edu.cn).

    通讯作者:

    崔苗(1980-),女,辽宁人,教授,博士,博导,主要从事计算热/力学及其反问题的研究(E-mail:miaocui@dlut.edu.cn).

  • 中图分类号: O344.3

THE INVERSE PROBLEM OF PLANE STRAIN IN POWER-HARDENING ELASTICOPLASTICITY MATERIALS

  • State Key Laboratory of Structural Analysis for Industrial Equipment, Key Laboratory of Advanced Technology for Aerospace Vehicles, Dalian University of Technology, Dalian 116024, China

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    摘要
  • 摘要: 幂强化弹塑性材料在工程领域诸如金属管材制备、岩土工程分析中都具有广泛的应用。幂强化弹塑性材料的本构参数（例如弹性模量）和结构的边界条件（例如位移）往往不容易确定。在这种情况下，反问题为确定这些参数提供了一种新思路。将ABAQUS二次开发的子程序和复变量求导法结合，用于求解基于幂强化弹塑性材料的平面应变力学反问题：以传统的用户单元子程序为框架，将程序中实数变量转换为复数，建立了复数用户单元；采用复变量求导法确定测点位移对反演参数的灵敏度矩阵；结合最小二乘法和高斯消去法对反问题进行迭代求解。给出应用算例讨论了复变量求导法对正问题计算精度影响、算法在反问题求解过程中的精度，以及反演初值、测量误差对反演结果的影响。
    Abstract: Power-hardening elastoplastic materials have a wide range of engineering applications, such as metal pipe manufacturing and geotechnical analysis. The constitutive parameters of power-hardening elastoplastic materials (such as Young's modulus) and the boundary conditions of a structure (such as displacements) are often difficult to be determined. Under this circumstance, the inverse problem provides a new approach for determining these parameters. In the present work, ABAQUS UEL (user element subroutines) and the CVDM (complex variable-differentiation method) are combined to solve the inverse problem of plane strain mechanics based on power-hardening elastoplastic materials. Firstly, the traditional user element subroutine is used as the framework to convert a real variable in the subroutine into a complex variable, and the complex user element is established. Then the complex variable-differentiation method is used to determine the sensitivity matrix of the displacements at measurement point with respect to the inverse parameters. Finally, the inverse problem is solved iteratively by the Least-squares method and Gaussian elimination method. Numerical examples are given to discuss the influence of the CVDM on the accuracy of the direct problem calculation, and the accuracy of the present algorithm. The influence of initial value and measurement errors on inversion results are also investigated.
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出版历程
  • 收稿日期:  2019-03-04
  • 修回日期:  2019-06-16
  • 刊出日期:  2020-01-24

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