基于PETSc的非线性逆向运动并行计算方法研究  

Study on parallel computation of nonlinear inverse motion method based on PETSc library

作　　者：范志瑞 阎军[1] 牛斌 隋倩倩 许琦 蒋存存 赵国忠[1] FAN Zhi-rui;YAN Jun;NIU Bin;SUI Qian-qian;XU Qi;JIANG Cun-cun;ZHAO Guo-zhong(State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China;School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,工程力学系,大连116024 [2]大连理工大学机械工程学院,大连116024

出　　处：《计算力学学报》2021年第6期695-703,共9页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(U1906233,11732004,51975087);国家重点研发计划(2017YFC0307203);山东省重点研发计划(2019JZZY010801);中央高校基本科研业务费专项资金(DUT20ZD213,DUT20LAB308)资助项目.

摘　　要：在考虑几何非线性的有限元分析中,初始构型和变形构型是严格区分的,并且变形后的构型对结构性能和功能的实现往往具有重要意义。传统的非线性有限元分析主要面向变形前的初始构型为导向的设计问题,而对于变形后构型为导向的设计问题则有较大局限性。针对此问题,引入非线性逆向运动分析方法,为了保证大变形非线性分析迭代的收敛性和计算效率,基于PETSc函数库建立了并行分析框架,并对并行框架中的模块划分、数据并行存储以及通信锁死和负载平衡等进行了详细阐述。在算例部分,首先通过正向运动和逆向运动分析结果对比,阐述了两种分析方法的不同以及逆向运动分析方法对变形前构型求解的准确性;其次,采用不同MPI进程数对并行分析程序的效率进行了测试。结果表明,合理地选择MPI进程数目可显著提高非线性逆向运动分析的效率。In the finite element analysis considering geometric nonlinearity,the initial configuration and deformed configuration are strictly distinguished.And the deformed configuration is of great significance to the realization of structural performances and functions.The traditional nonlinear finite element analysis is mainly employed to the design problem driven by the initial configuration,which is difficult for problems driven by the deformed configuration.Thus,nonlinear inverse motion analysis method is introduced in this study.To improve the efficiency of nonlinear inverse motion analysis,a parallel-analysis framework based on PETSc library is proposed.The corresponding sub-modulus of the framework,parallel data storage and interaction,as well the lock of communication and the remedy using load balance are presented in detail.In the numerical examples,through the comparison of the results of the forward and the inverse motion analysis,differences between the two analysis approaches and also the accuracy of form finding by inverse motion analysis are revealed.After that,the efficiency of the parallel-analysis is investigated by using different numbers of MPI processes.Numerical results show that a reasonable selection of the number of MPI processes can significantly improve the efficiency of the inverse motion analysis.

关 键 词：逆向运动分析 非线性分析 有限元方法 并行计算 PETSC 

分 类 号：O242.21[理学—计算数学]