结合基降阶策略的高效安定分析数值算法

doi:10.3901/JME.2023.18.154

机械工程学报 ›› 2023, Vol. 59 ›› Issue (18): 154-164.doi: 10.3901/JME.2023.18.154

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结合基降阶策略的高效安定分析数值算法

王雨, 程耿东, 李凯

大连理工大学工业装备结构分析国家重点实验室大连 116024

收稿日期:2022-10-20 修回日期:2023-06-02 出版日期:2023-09-20 发布日期:2023-12-07
通讯作者: 程耿东(通信作者),男,1941年出生,中国科学院院士,教授,博士研究生导师。主要研究方向为计算力学,结构优化。E-mail:chenggd@dlut.edu.cn
作者简介:王雨,女,1988年出生,硕士研究生。主要研究方向为安定性分析。E-mail:wangyudlut@163.com
基金资助:
国家自然科学基金资助项目(52075070,U1906233)。

An Efficient Numerical Algorithm for Shakedown Analysis Combined with Basis Reduction

WANG Yu, CHENG Gengdong, LI Kai

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024

Received:2022-10-20 Revised:2023-06-02 Online:2023-09-20 Published:2023-12-07

摘要/Abstract

摘要： 结构安定分析是结构设计和完整性分析的一个重要问题。原对偶本征应力驱动算法(Primal-dual eigenstress-driven method,PEM)是一种有效的两水平嵌套的结构安定分析算法，可与商业有限元集成应用于实际工程问题，但计算效率仍存在进一步提升的空间。结合基降阶策略和原对偶本征应力驱动方法提出了高效安定性分析数值算法，利用PEM法每轮迭代形成的残余应力场作为基向量，与相应载荷顶点的弹性应力场叠加将安定分析问题简化为一维优化问题，降低优化变量的数量，利用一维搜索0.618法，结合PEM方法为安定乘子提供了更为准确的估计。该算法避免繁琐的塑性增量分析，仅进行有限次的弹性分析与迭代及高效的一维搜索，可以显著提高算法计算效率，并获得准确的残余应力场。结合ANSYS APDL二次开发实现算法，通过圆孔方板、Bree板、三维框架三个例题，进一步验证此算法的有效性。

关键词: 安定分析, 基降阶, 原对偶本征应力驱动方法, 弹塑性, 一维搜索0.618法

Abstract: Shakedown analysis is an important issue in structural design and integrity assessment. Primal-dual eigenstress-driven method (PEM) for shakedown analysis of structures is an efficient two-level nested algorithm which can be integrated with commercial finite element software for practical engineering problems, but the computational efficiency still needs to be further improved. An efficient numerical algorithm for shakedown analysis is proposed by combining basis reduction and the PEM method. The residual stress field generated by each iteration of the PEM method is used as the basis vector, and superimposed with the elastic stress field of corresponding load vertex, the shakedown analysis problem is simplified to a one-dimensional optimization problem in which the number of optimization variables is reduced. An accurate estimation of the shakedown multiplier is obtained by using the one-dimensional search 0.618 algorithm and the PEM method. This algorithm avoids the tedious incremental plastic analysis and only performs finite times iteration of elastic analysis and efficient one-dimensional search, which can significantly improve the computational efficiency of the algorithm and obtain accurate residual stress field. Combined with the commercial finite element software ANSYS APDL, the effectiveness of the algorithm is further verified by three examples of circular square plate, Bree plate and three-dimensional frame.

Key words: shakedown analysis, basis reduction, primal-dual eigenstress-driven method (PEM), elastoplastic, one-dimensional search 0.618 algorithm

中图分类号:

O302

王雨, 程耿东, 李凯. 结合基降阶策略的高效安定分析数值算法[J]. 机械工程学报, 2023, 59(18): 154-164.

WANG Yu, CHENG Gengdong, LI Kai. An Efficient Numerical Algorithm for Shakedown Analysis Combined with Basis Reduction[J]. Journal of Mechanical Engineering, 2023, 59(18): 154-164.

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结合基降阶策略的高效安定分析数值算法

An Efficient Numerical Algorithm for Shakedown Analysis Combined with Basis Reduction

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