基于PETSc的非线性逆向运动并行计算方法研究

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.

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

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.