Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications

Review, Article English OPEN
Cao, Changyong ; Qin, Qing-Hua (2015)
  • Publisher: Hindawi Publishing Corporation
  • Journal: Advances in Mathematical Physics (issn: 1687-9120, eissn: 1687-9139)
  • Related identifiers: doi: 10.1155/2015/916029
  • Subject: Physics | QC1-999 | Article Subject

An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM) and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field) are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.
  • References (90)
    90 references, page 1 of 9

    Wang, H., Qin, Q. H.. FE approach with Green's function as internal trial function for simulating bioheat transfer in the human eye. Archives of Mechanics. 2010; 62 (6): 493-510

    Cao, C., Yu, A., Qin, Q. H.. Evaluation of effective thermal conductivity of fiber-reinforced composites. International Journal of Architecture, Engineering and Construction. 2012; 1 (1): 14-29

    Santos, W. J., Santiago, J. A. F., Telles, J. C. F.. Optimal positioning of anodes and virtual sources in the design of cathodic protection systems using the method of fundamental solutions. Engineering Analysis with Boundary Elements. 2014; 46: 67-74

    Karageorghis, A., Lesnic, D., Marin, L.. The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity. Computers and Structures. 2014; 135: 32-39

    Cao, C. Y., Qin, Q. H., Yu, A. B.. Micromechanical analysis of heterogeneous composites using hybrid trefftz FEM and hybrid fundamental solution based FEM. Journal of Mechanics. 2013; 29 (4): 661-674

    Wang, K. Y., Qin, Q. H., Kang, Y. L., Wang, J. S., Qu, C. Y.. A direct constraint-Trefftz FEM for analysing elastic contact problems. International Journal for Numerical Methods in Engineering. 2005; 63 (12): 1694-1718

    Bussamra, F. L. S., Lucena Neto, E., Ponciano, W. M.. Simulation of stress concentration problems by Hexahedral Hybrid-Trefftz finite element models. Computer Modeling in Engineering & Sciences. 2014; 99 (3): 255-272

    Pearce, C. J., Edwards, G., Kaczmarczyk, L., Bicanic, N., Mang, H., Meschke, G., de Borst, R.. 3D cohesive crack propagation using hybrid-Trefftz finite elements. Computational Modelling of Concrete Structures. 2014; 1

    Wang, H., Qin, Q. H.. Special fiber elements for thermal analysis of fiber-reinforced composites. Engineering Computations. 2011; 28 (8): 1079-1097

    Qin, Q. H.. Nonlinear analysis of reissner plates on an elastic foundation by the BEM. International Journal of Solids and Structures. 1993; 30 (22): 3101-3111

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