Chinese Journal of Theoretical and Applied Mechanics ›› 2018, Vol. 50 ›› Issue (4): 787-797.DOI: 10.6052/0459-1879-18-069

• Orginal Article • Previous Articles     Next Articles


Zheng Baojing1,*(), Liang Yu2, Gao Xiaowei2, Zhu Qianghua2, Wu Zeyan1   

  1. 1College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, Hubei, China
    2State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
  • Online:2018-07-18 Published:2018-08-17
  • Contact: Zheng Baojing

Abstract: In order to quickly analysis the response of heterogeneous materials under dynamic loads, a reduced order method was presented in this paper which only needed to compute dynamic characteristics of homogeneous material under sudden load and got the results for analysis complex non-homogeneous material. Firstly, we used the finite element method to compute the displacement field of homogeneous materials under sudden load, and then discretized data samples was obtained to establish a database which including every moment displacement information of all degrees of freedom (order of L) during a period of time. Secondly, dealing with database by specific way of time discretization, a snapshot matrix was formed. The matrix was decomposed into H orthogonal basis by proper orthogonal decomposition method and we picked up the major H<L?N basis from that. Till now we achieved the goal that reducing the model (H). Finally, the [4-5] basis were used to obtain order-reduced governing dynamic equation. Different dynamic loads of time dependent were applied to the model, and the dynamic response of non-homogeneous material would be achieved by solving order-reduced governing dynamic equations. The displacement fields of traditional FEM and proposed ROM were compared. 2D and 3D examples showed that the computing scales reduced one or two orders of magnitude.

Key words: proper orthogonal decomposition, reduced order method, dynamic response, functionally graded materials

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