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Advanced Development of Smoothed Finite Element Method (S-FEM) and Its Applications

Zeng, Wei
http://orcid.org/0000-0001-8473-9299
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439309306

Abstract Details

2015, PhD, University of Cincinnati, Engineering and Applied Science: Engineering Mechanics.
The smoothed finite element method (S-FEM) was recently proposed to bring softening effects into and improve the accuracy of the standard FEM. In the S-FEM, the system stiffness matrix is obtained using strain smoothing technique over the smoothing domains associated with cells, nodes, edges or faces to establish models of desired properties. In this dissertation, it will introduce several aspects of advanced development and applications of S-FEM in solid mechanics. The idea, main work and contribution are included in four aspects as following: (1) A Generalized Stochastic Cell-based S-FEM (GS_CS-FEM): The cell-based S-FEM is extended for stochastic analysis based on the generalized stochastic perturbation technique. Numerical examples are presented and the obtained results are compared with the solution of Monte Carlo simulations. It is found that the present GS_CS-FEM method can improve the solution accuracy with high-efficiency for stochastic problems with large uncertainties. (2) An effective fracture analysis method based on the VCCT implemented in CS-FEM: The VCCT is formulated in the framework of CS-FEM for evaluating SIF’s and for modeling the crack propagation in solids. The one-step-analysis approach of the VCCT is utilized based on the assumption of stress field equivalence under infinitesimal perturbations. The significant feature of the present approach is that it requires no domain integration but attains same level of accuracy compared to the standard FEM using the interaction integral method. Numerical examples are provided to validate the effectiveness of fracture parameter evaluation as well as to predict the crack growth trajectories. (3) Smoothing techniques based crystal plasticity finite element modeling of crystalline materials: A framework and numerical implementation for modeling anisotropic crystalline plasticity using strain smoothing techniques is presented to model anisotropic crystalline plasticity with rate-independence. The edge-based strain smoothing technique is extended to deal with finite strains in a nonlinear incremental integration procedure based on the Newton-Raphson scheme. Several representative examples are studied to demonstrate the capability of proposed method as well as the integration algorithm for capturing the strain localization and dealing with plastic incompressibility. The proposed method is also implemented to explore the mesoscopic and macroscopic elaso-plastic behavior of polycrystalline aggregates. (4) A novel beta finite element method (βFEM) of coupled edge/face and node based smoothing techniques: Smoothing domains generated upon both edges (faces for 3D) and nodes are employed to construct a smoothed model. In this work, a novel S-FEM is proposed, in which an adjustable parameter β is introduced to control the ratio of the area of edge-based/face-based and node-based smoothing domains. It is found that the nearly exact solution in strain energy can be obtained by tuning the parameter, making use of the important property that the exact solution is bonded by the solutions of NS-FEM and ES/FS-FEM. A number of examples have shown that the developed βFEM method is found to be ultra-accurate, insensitive to mesh quality, temporal stable and capable for modeling complex geometry and offers alleviation of volumetric locking. The βFEM is also applied in modeling crystal plasticity with monocrystalline, bi-crystalline and polycrystalline materials.
Guirong Liu, Ph.D. (Committee Chair)
Shaaban Abdallah, Ph.D. (Committee Member)
Yijun Liu, Ph.D. (Committee Member)
Francesco Simonetti, Ph.D. (Committee Member)
225 p.
Engineering
Smoothed Finite Element Method; Solid Mechanics; Stochastic Analysis; Fracture Mechanics; Crystal Plasticity; Beta FEM

Recommended Citations

Citations

  • Zeng, W. (2015). Advanced Development of Smoothed Finite Element Method (S-FEM) and Its Applications [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439309306

    APA Style (7th edition)

  • Zeng, Wei. Advanced Development of Smoothed Finite Element Method (S-FEM) and Its Applications. 2015. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439309306.

    MLA Style (8th edition)

  • Zeng, Wei. "Advanced Development of Smoothed Finite Element Method (S-FEM) and Its Applications." Doctoral dissertation, University of Cincinnati, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439309306

    Chicago Manual of Style (17th edition)

ucin1439309306
558
© 2015, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.