基于Peridynamics理论的材料可靠性分析数值方法的优化
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摘要
Peridynamics理论(近场动力学,PD理论)是研究材料破坏变形领域的一门新理论。该理论通过建立相应的数学模型,用积分的方式描述材料的断裂变形。对PD理论及其传统数值方法作了简要的介绍,基于前人针对PD理论提出的积分方法,引入了另一种全新的固定高斯点积分方法。通过对该方法的应用,PD理论数值计算中的效率和精度都有一定改善。
Peridynamics( PD) is an emerging new theory used in the research of material damage.This theory describes the fracture and deformation of material by establishing corresponding mathematical model and using integral method. This paper simply introduced the theory of peridynamics and traditional numerical method and a new integration method with fixed Gaussian points was introduced based on previous methods. The efficiency and accuracy of the numerical calculation of PD theory also have relative improvement through the application of the new method.
Peridynamics( PD) is an emerging new theory used in the research of material damage.This theory describes the fracture and deformation of material by establishing corresponding mathematical model and using integral method. This paper simply introduced the theory of peridynamics and traditional numerical method and a new integration method with fixed Gaussian points was introduced based on previous methods. The efficiency and accuracy of the numerical calculation of PD theory also have relative improvement through the application of the new method.
引文
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[11]陈明祥.弹塑性力学[M].武汉:科学出版社,2010.
[2]SILLING S A,ASKARI E.Peridynamic modeling of impact damage[C]//Proceeding of the ASME/JSME Pressure Vessels and Piping Conference.San Diego:[s.n.],2000:197-205.
[3]SILLING S A,ASKARI E.A meshfree method based on the peridynamic model of solid mechanics[J].Computers and Structures,2005,83:1526-1535.
[4]SILLING S A.Dynamic fracture modeling with a meshfree peridynamic code.Second MIT Conference on Computional Fluid and Solid Mechanics.Massachusettes:MIT,2003:641-644.
[5]MACEK R W,SILLING S A.Peridynamics via finite element analysis[J].Finite Elements in Analysis and Design,2007,43(15):1169-1178.
[6]YU K,XIN X J,LEASE K B.A new method of adaptive integration with error control for bond-based peridynamics[C]//Proceeding of the World Congress on Engineering and Computer Science.San Francisco:[s.n.],2010:1041-1046.
[7]YU K,XIN X J,LEASE K B.A new adaptive integration method for the peridynamic theory[J].Modeling and Simulation in Materials Science and Engineering,2011,19:45003.
[8]张民选,罗贤兵.数值分析[M].南京:南京大学出版社,2013.
[9]蔡大用.数值分析与实验学习指导[M].北京:清华大学出版社,2002.
[10]沈峰,章青,黄丹,等.基于近场动力学理论的混凝土轴拉破坏过程模拟[J].计算力学学报,.2013,30(6):79-83.
[11]陈明祥.弹塑性力学[M].武汉:科学出版社,2010.