Abstract
This chapter presents a summary of the contributions of the whole book, including seven new achievements in the finite element method, five new element series with 108 new element models, and new solution strategies for five challenging problems.
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Chien WZ (1980) Calculus of variations and finite elements (Vol. 1). Science Press, Beijing (in Chinese)
Long YQ, (1981) Piecewise generalized variational principles in elasticity. Shanghai Mechanics 2(2): 1–9. (in Chinese)
Long YQ, Zhi BC, Yuan S (1982) Sub-region, sub-item and sub-layer generalized variational principles in elasticity. In: He GQ et al (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 607–609
Long YQ (1986) Several patterns of functional transformation and generalized variational principles with several arbitrary parameters. International Journal of Solids and Structures 22(10): 1059–1069
Long YQ, Xin KG (1987) Generalized conforming element. Tumu Gongcheng Xuebao/China Civil Engineering Journal 20(1): 1–14 (in Chinese)
Long YQ, Xin KG (1989) Generalized conforming element for bending and buckling analysis of plates. Finite Elements in Analysis and Design 5: 15–30
Long YQ, Zhi BC, Kuang WQ, Shan J (1982) Sub-region mixed finite element method for the calculation of stress intensity factor. In: He GQ et al (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 738–740
Long YQ, Fu XR (2002) Generalized conforming elements based on analytical trial functions. In: Proceedings of the Eleventh National Conference on Structural Engineering (Vol. I), plenary lecture, China, Changsha, pp28–39 (in Chinese)
Long YQ, Li JX, Long ZF, Cen S (1997) Area-coordinate theory for quadrilateral elements. Gong Cheng Li Xue / Engineering Mechanics 14(3): 1–11 (in Chinese)
Long YQ, Li JX, Long ZF, Cen S (1999) Area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering 15(8): 533–545
Yuan S (1984) Spline elements in stress analysis [Doctoral Dissertation]. Tsinghua University, Beijing
Fan Z (1988) Applications of spline elements and sub-region mixed elements in structural engineering [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
Cen S, Long ZF (1998) A Mindlin triangular plate element with improved interpolation for the rotation and shear strain fields. Gong Cheng Li Xue/Engineering Mechanics 15(3): 1–14 (in Chinese)
Cen S, Long ZF Long YQ (1999) A Mindlin quadrilateral plate element with improved interpolation for the rotation and shear strain fields. Gong Cheng Li Xue/Engineering Mechanics 16(4): 1–15 (in Chinese)
Soh AK, Cen S, Long YQ, Long ZF (2001) A new twelve DOF quadrilateral element for analysis of thick and thin plates. European Journal of Mechanics A/Solids 20: 299–326
Cen S, Long ZF (1998) A new triangular generalized conforming element for thin-thick plates. Gong Cheng Li Xue/Engineering Mechanics 15(1): 10–22 (in Chinese)
Chen YL, Cen S, Yao ZH, Long YQ, Long ZF (2003) Development of triangular flat-shell element using a new thin-thick plate bending element based on SemiLoof constraints. Structural Engineering and Mechanics 15(1): 83–114
Long ZF (1992) Locking-free thick plate rectangular element. Gong Cheng Li Xue/Engineering Mechanics 9(1): 88–93 (in Chinese)
Long YQ, Xi F (1992) A universal method for including shear deformation in the thin plate elements. International Journal for Numerical Methods in Engineering 34: 171–177
Cen S, Long YQ, Yao ZH (2002) A new element based on the first-order shear deformation theory for the analysis of laminated composite plates. Gong Cheng Li Xue/Engineering Mechanics 19(1): 1–8 (in Chinese)
Cen S, Long YQ, Yao ZH (2002) A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates. Computers & Structures 80 (9–10): 819–833
Cen S, Soh AK, Long YQ, Yao ZH (2002) A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates. Composite Structures 58(4): 583–599
Long YQ, Huang MF (1988) A generalized conforming isoparametric element. Applied mathematics and Mechanics (English Edition) 9(10): 929–936
Xu Y, Long YQ (1993) Generalized conforming rectangular membrane elements with vertex rigid rotational freedom. In: Proceedings of the Second National Conference on Structural Engineering, pp199–206 (in Chinese)
Long YQ, Xu Y (1994) Generalized conforming quadrilateral membrane element with vertex rigid rotational freedom. Computers & Structures 52(4): 749–755
Long YQ, Xu Y (1994) Generalized conforming triangular membrane element with vertex rigid rotational freedom. Finite Elements in Analysis and Design 17: 259–271
Xu Y (1994) The generalized conforming approach and the development of the membrane elements with drilling degrees of freedom and thin plate and shell elements [Doctoral Dissertation] Tsinghua University, Beijing (in Chinese)
Long YQ, Xu Y (1994) Generalized conforming flat rectangular thin shell element. Computational Structural Mechanics and Applications 11(2): 154–160 (in Chinese)
Xu Y, Long YQ, Long ZF (1994) A triangular shell element with drilling freedoms based on generalized compatibility conditions. In: Proceeding of WCCM III. Japan pp1234–1235
Long YQ, Zhao JQ (1992) Generalized conforming curved rectangular element for shallow shells. Gong Cheng Li Xue/Engineering Mechanics 9(1): 3–10 (in Chinese)
Sun JH (1998) Research on generalized conforming shallow shell element and nonlinear analysis of plate and shell structures [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
Sun JH, Long ZF, Long YQ, Zhang CS (2001) Geometrically nonlinear stability analysis of shells using generalized conforming shallow shell element. International Journal of Structural Stability and Dynamics 1(3): 313–332
Long YQ, Zhao YQ (1985) Calculation of stress intensity factors in plane problems by the sub-region mixed finite element method. Enginering Software 7(1): 32–35
Huang MF, Long YQ (1988) Calculation of stress intensity factors of cracked Reissner plates by the sub-region mixed finite element method. Computers & Structures 30(4): 837–840
Long YQ, Qian J (1992) Calculation of stress intensity factors for surface cracks in a 3D body by the subregion mixed FEM. Computers & Structures 44(1/2): 75–78
Fan Z, Long YQ (1992) Sub-region mixed finite element analysis of V-notched plates. International Journal of Fracture 56: 333–344
Long YQ, Qian J (1992) Sub-region mixed finite element analysis of V-notches in a bimaterial. In: Zhu DC (ed) Advances in Engineering Mechanics. Peking University Press; Beijing. pp54–59
Qian J, Long YQ (1991) Sub region mixed FEM for calculating stress intensity factor of antiplane notch in bi-material. Computational Structural Mechanics and Applications 8(3): 325–330 (in Chinese)
Qian J, Long YQ (1992) The expression of stress and strain at the tip of notch in Reissner plate. Applied mathematics and Mechanics (English Edition) 13(4): 315–324
Qian J, Long YQ (1994) The expression of stress and strain at the tip of 3-D notch. Applied mathematics and Mechanics (English Edition) 15(3): 211–221
Fu XR, Long YQ (2002) Generalized conforming quadrilateral plane elements based on analytical trial functions. Gong Cheng Li Xue/Engineering mechanics 19(4): 12–16 (in Chinese)
Long YQ, Fu XR (2002) Two generalized conforming quadrilateral thick plate elements based on analytical trial functions. Gong Cheng Li Xue/Engineering Mechanics 19(3): 10–15 (in Chinese)
Fu XR, Long YQ (2001) Fracture analysis with the sub-region mixed element method. Gong Cheng Li Xue/Engineering Mechanics 18(6): 39–46 (in Chinese)
Fu XR (2002) Generalized conforming element method based on the analytical trial functions [Doctoral Dissertation]. Tsinghua University, Beijing (in Chinese)
Fan Z, Long YQ (1991) Linear analysis of tall buildings using spline element. Engineering Structure 13: 27–33
Fan Z, Long YQ (1989) Spline thick/thin shell element. In: Proceeding of 2nd East Asia-Pacific Conference on Structural Engineering & Construction. Chiang Mai, Thailand, pp1195–1200
Fan Z, Long YQ (1990) Large deflection and stability analysis by geometrically nonlinear spline element. In: Proceeding of International Conference on Numerical Methods in Engineering, Theory & Applications (Vol. 1). Swansea, UK, pp414–422
Soh AK, Long YQ, Cen S (2000) Development of eight-node quadrilateral membrane elements using the area coordinates method, Computational Mechanics 25(4): 376–384
Chen XM, Cen S, Long YQ, Yao ZH (2004) Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Computers & Structures 82(1): 35–54
Cen S, Chen XM, Fu XR (2007) Quadrilateral membrane element family formulated by the quadrilateral area coordinate method. Computer Methods in Applied Mechanics and Engineering 196(41–44): 4337–4353
Chen XM, Cen S, Fu XR, Long YQ (2008) A new quadrilateral area coordinate method (QACM-II) for developing quadrilateral finite element models. International Journal for Numerical Methods in Engineering 73(13): 1911–1941
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© 2009 Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg
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Cen, S., Long, YQ., Long, ZF. (2009). Concluding Remarks. In: Advanced Finite Element Method in Structural Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00316-5_20
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DOI: https://doi.org/10.1007/978-3-642-00316-5_20
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