基于Python的面向对象弹塑性有限元方法实现与数值模拟

doi:10.16182/j.issn1004731x.joss.23-0084

摘要/Abstract

摘要：

随着有限元应用领域的不断扩大，对有限元的可扩充性提出了更高的要求。为克服传统有限元的缺陷，基于Python提出了一种简单、易扩充的面向对象弹塑性有限元程序框架，结合Python的特性，设计了前处理类、后处理类、线性求解类、应力积分类、分析类等有限元类。通过将程序框架应用于几类典型弹塑性问题的有限元分析与模拟，并与ABAQUS计算结果进行了对比，验证了基于Python的面向对象弹塑性有限元程序的准确性和有效性。

关键词: 面向对象编程, 弹塑性有限元, 程序框架, 数值模拟, Python

Abstract:

With the continuous expansion of the application fields of finite element methods, higher requirements are put forward for the scalability of finite element methods. In order to overcome the defects of the traditional finite element methods, a simple and easily extensible object-oriented elastic-plastic finite element program framework is proposed based on Python. Combined with the characteristics of Python, we design some finite element classes such as the pre-processing class, the post-processing class, the linear solution class, the stress integration class and the analysis class. By applying the resulting framework to several typical elastic-plastic mechanical problems and comparing the results with those calculated by ABAQUS, the correctness and effectiveness of object-oriented elastic-plastic finite element program based on Python have been verified.

Key words: object-oriented programming, elastic-plastic finite element, program framework, numerical simulation, Python

中图分类号:

TP391.9

李恒辉,肖映雄 . 基于Python的面向对象弹塑性有限元方法实现与数值模拟[J]. 系统仿真学报, 2024, 36(5): 1107-1117.

Li Henghui,Xiao Yingxiong . Implementation and Numerical Simulation on Object-oriented Elastic-plastic Finite Element Method Based on Python[J]. Journal of System Simulation, 2024, 36(5): 1107-1117.

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单元数	坐标	理论解	本文解	ABAQUS解	本文解与理论解的相对误差/%	ABAQUS解与本文解的相对误差/%
100	(0.01, 0)	0.288 900	0.288 539	0.289 178	0.124 96	0.221 46
	(0.012 5, 0)	0.308 651	0.310 844	0.310 733	0.710 50	0.035 71
	(0.015, 0)	0.252 992	0.254 025	0.253 935	0.408 30	0.035 43
400	(0.01, 0)	0.288 900	0.287 863	0.288 462	0.358 95	0.208 01
	(0.012 5, 0)	0.308 651	0.309 647	0.309 455	0.322 69	0.062 01
	(0.015, 0)	0.252 992	0.253 803	0.253 646	0.320 56	0.061 86
1 600	(0.01, 0)	0.288 900	0.287 691	0.288 282	0.418 50	0.205 43
	(0.012 5, 0)	0.308 651	0.309 684	0.309 458	0.334 68	0.072 98
	(0.015, 0)	0.252 992	0.253 839	0.253 654	0.334 80	0.072 88

自由度数	纯Python	Cython加速
2 602	1.04	0.20
10 002	7.33	0.81
39 202	54.76	3.81
87 602	181.03	9.10
155 202	436.15	18.54

单元数	CS-FEM	nCS-FEM	FEM(Q4)
理论解	0.288 900
100	0.322 453	0.295 140	0.336 624
400	0.305 595	0.293 769	0.313 096
1 600	0.296 747	0.292 322	0.300 599

特征点	Mises		S22		U1		U2		PEEQ
特征点	①	②	①	②	①	②	①	②	①	②
A	136 536	136 580	-160 265	-160 275	0.014 48	0.014 19	-0.145 5	-0.146 0	0	0
B	170 984	169 983	-171 182	-169 860	-0.037 91	-0.037 86	-0.100 08	-0.100 69	0.003 21	0.003 33
C	133 589	134 058	-136 942	-136 407	-0.021 69	-0.021 75	-0.136 76	-0.138 22	0.017 39	0.018 07
D	133 480	133 487	-139 969	-140 358	0.003 89	0.004 23	-0.091 55	-0.091 27	0.001 61	0.001 56

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