How to cite this paper
Arruda, M., Arruda, P & Lopes, B. (2019). Energetic Convergence of a New Hybrid Mixed Finite Element.Engineering Solid Mechanics, 7(4), 291-312.
Refrences
Arruda, M. R.(2011) "Static and Dynamic Analysis of Concrete Structures Using Damage Mechanics". Lisbon, Instituto Superior Técnico. Ph.D. Thesis
Arruda, M. R., & Castro, L. M. S. S.(2011a). Hybrid mixed formulation in continuum damage mechanics. CFRAC. Barcelona
Arruda, M. R., & Castro, L. M. S. S.(2011b). Structural dynamic analysis using hybrid and mixed finite element models. Finite Elements in Analysis and Design, 57, 43-57.
Arruda, M. R. T., & Castro, L. M. S. (2013a). A new hybrid-mixed stress model for the analysis of concrete structures using damage mechanics. Computers & Structures, 125, 23-44.
Arruda, M. R., & Castro, L. M. S. (2013). Static and dynamic physically non-linear analysis of concrete structures using a hybrid mixed finite element model. Advances in Engineering Software, 65, 112-131.
Babuška, I., & Narasimhan, R. (1997). The Babuška-Brezzi condition and the patch test: an example. Computer methods in applied mechanics and engineering, 140(1-2), 183-199.
Bathe, K. J.(1996). Finite Element Procedures In Engineering Analysis. Prentice-Hall Englewood Cliffs.
Castro, L. M. S. (2010). Polynomial wavelets in hybrid‐mixed stress finite element models. International journal for numerical methods in biomedical engineering, 26(10), 1293-1312.
Castro, L. S., & Barbosa, A. R. (2006). Implementation of an hybrid-mixed stress model based on the use of wavelets. Computers & structures, 84(10-11), 718-731.
Castro, L. M. S., & de Freitas, J. A. T. (2001). Wavelets in hybrid-mixed stress elements. Computer Methods in Applied Mechanics and Engineering, 190(31), 3977-3998.
Cen, S., Fu, X. R., & Zhou, M. J. (2011). 8-and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes. Computer Methods in Applied Mechanics and Engineering, 200(29-32), 2321-2336.
Cen, S., Zhou, M. J., & Fu, X. R. (2011b). A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions. Computers & Structures, 89(5-6), 517-528.
Clough, R. W., & Wilson, E. L. (1999, August). Early finite element research at Berkeley. In Fifth US National Conference on Computational Mechanics (pp. 1-35).
Comi, C., & Perego, U. (2001). Numerical aspects of nonlocal damage analyses. Revue européenne des éléments finis, 10(2-4), 227-242.
Comi, C., & Perego, U. (2001). Symmetric and non-symmetric non-local damage formulations: an assessment of merits. In Proceedings of ECCM 2001 European conference on computational mechanics, (pp. 1-19). Cracow.
Cook, R. D. (2007). Concepts and applications of finite element analysis. John Wiley & Sons.
Cottrell, J. A., Hughes, T. J., & Bazilevs, Y. (2009). Isogeometric analysis: toward integration of CAD and FEA. John Wiley & Sons.
De Almeida, J. M., & De Freitas, J. T. (1991). Alternative approach to the formulation of hybrid equilibrium finite elements. Computers & Structures, 40(4), 1043-1047.
De Almeida, J. M., & Pereira, O. A. (1996). A set of hybrid equilibrium finite element models for the analysis of three‐dimensional solids. International Journal for Numerical Methods in Engineering, 39(16), 2789-2802.
Teixeira de Freitas, J. A. (1990). Mixed and hybrid symmetric formulations for the boundary integral method. European journal of mechanics. A. Solids, 9(1), 1-20.
de Freitas, J. T. (1999). Hybrid finite element formulations for elastodynamic analysis in the frequency domain. International journal of solids and structures, 36(13), 1883-1923.
Freitas, J. A. T., Almeida, J. P. B. M., & Pereira, E. M. B. R. (1993). Alternative hybrid formulations for the finite element method. In Proc. 7th World Congress Finite Element Method(pp. 264-271).
Freitas, J. A. T., Almeida, J. P. B. M., & Pereira, E. M. B. R.(1996). Non-conventional formulations for the finite element method. Structural Engineering and Mechanics, 4, 655–678.
Freitas, J. A. T., Almeida, J. P. B. M., & Pereira, E. M. B. R.(1999). Non-conventional formulations for the finite element method. Computational Mechanics, 23(1), 488-501.
Ghali, A., & Nevillle, A. M. (1997). Structural Analysis: A unified Classic and Matrix Approach. London, E & FN Spon.
Holzapfel, G. A.(2000). Nonlinear Solid Mechanics. Austria, Wiley and Sons LTD.
Hughes, T. J. R.(2003). The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. Dover.
Jirousek, J., & Leon, N. (1977). A powerful finite element for plate bending. Computer Methods in Applied Mechanics and Engineering, 12, 77-96.
Liu, G. R. (2003). Mesh Free Methods. USA, CRC Press.
Malkus, D. S., & Hughes, T. J. R.(1978). Mixed finite element methods - Reduced and selective integration techniques: A unification of concepts. Computer Methods in Applied Mechanics and Engineering, 1(15), 63-81.
Mazars, J.(1984) J.. Application de la mécanique de l’endommagement au comportement non lineaire et à la rupture du béton de structure. Paris, Université Paris 6. Ph.D Thesis
Mendes, L. A. M., & Castro, L. M. S. S.(2009) Hybrid-mixed stress finite element models in elastoplastic analysis. Finite Elements in Analysis and Design 45(12), 863-875.
Moes, N., Dolbow, J., & Belytschko, T.(1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46, 131-150.
Pereira, E. M. B. R., & Freitas, J. A. T. (1996a). A hybrid-mixed element model based on legendre polynomials for reissner-mindlin plates. Computer Methods in Applied Mechanics and Engineering 136(1-2), 111-126.
Pereira, E. M. B. R., & Freitas, J. A. T.(1996b). A mixed-hybrid finite element model based on orthogonal functions. International Journal for Numerical Methods in Engineering, 39(8), 1295-1312.
Pereira, E. M. B. R., & Freitas, J. A. T. (2000). Numerical Implementation of a Hybrid-Mixed Finite Element Model for Reissner-Mindlin Plates. Computer & Structures 74(3), 323-334.
Pereira, O. J. B. A.(1996). Utilização de Elementos Finitos de Equilíbrio em Refinamento Adaptativo. Lisbon, Instituto Superior Técnico. Ph.D Thesis
Pian, T. H. H., & Tong, P. (1969). Basis of finite element methods for solid continua. International Journal for Numerical Methods in Engineering, 1, 3-28.
Ruoff, G.(1973). Finite Elemente in der Statik. ch. Die praktische Berechnung der Kombination der Trefftzschen Metode und bei flachen Schalen: 242-259.
Santos, H. A. F. A. (2009). Duality in the geometricall exact analysis of frame structures. Lisbon, Instituto Superior Técnico. Ph.D Thesis
Shephard, M. S., Niu, O., & Baehmann, P. L.(1989). Some results using projectors for error indication and estimation. In Adaptive Methods for Partial Differential Equations, Philadelphia.
Silva, M. C., & Castro, L. M. S. S. (2004). Hybrid-mixed stress formulation with continuum damage models continuum damage models. XXV CILAMCE. Recife, Gráfica Bagaço
Silva, M. C., & Castro, L. M. S. S. (2006a). Hybrid-mixed stress formulation using continuum damage models. Communications in Numerical Methods in Engineering, 22, 605-617.
Silva, M. C., & Castro, L. M. S. S.(2006b). Hybrid and mixed finite element formulations for softening materials. European Conference on Computational Mechanics - Solids, Structures and Coupled Problems in Engineering, Lisboa, ECCM.
Spiegel, R. M., & Liu, J. (1999). Schaum's Mathematical Handbook of Formulas and Tables. New York, Schaum McGraw-Hill.
Stein, E. (1973). Finite Elemente in der Statik. ch. Die Kombination des modifizierten Treffzschen Verfahrens mit der Methode der Finiten Elemente: 172-185.
Veubeke, B. M. (1965). Displacement and Equilibrium models in the Finite Element Method. Stress Analysis: Wiley.
Zienkiewicz, O. C. (2000). Achievements and some unsolved problems of the finite element method. International Journal for Numerical Methods in Engineering, 47, 9-28.
Zienkiewicz, O. C., & Taylor, R. L. (2000). The Finite Element Method: Basis. Londres, 1, B-H.
Arruda, M. R., & Castro, L. M. S. S.(2011a). Hybrid mixed formulation in continuum damage mechanics. CFRAC. Barcelona
Arruda, M. R., & Castro, L. M. S. S.(2011b). Structural dynamic analysis using hybrid and mixed finite element models. Finite Elements in Analysis and Design, 57, 43-57.
Arruda, M. R. T., & Castro, L. M. S. (2013a). A new hybrid-mixed stress model for the analysis of concrete structures using damage mechanics. Computers & Structures, 125, 23-44.
Arruda, M. R., & Castro, L. M. S. (2013). Static and dynamic physically non-linear analysis of concrete structures using a hybrid mixed finite element model. Advances in Engineering Software, 65, 112-131.
Babuška, I., & Narasimhan, R. (1997). The Babuška-Brezzi condition and the patch test: an example. Computer methods in applied mechanics and engineering, 140(1-2), 183-199.
Bathe, K. J.(1996). Finite Element Procedures In Engineering Analysis. Prentice-Hall Englewood Cliffs.
Castro, L. M. S. (2010). Polynomial wavelets in hybrid‐mixed stress finite element models. International journal for numerical methods in biomedical engineering, 26(10), 1293-1312.
Castro, L. S., & Barbosa, A. R. (2006). Implementation of an hybrid-mixed stress model based on the use of wavelets. Computers & structures, 84(10-11), 718-731.
Castro, L. M. S., & de Freitas, J. A. T. (2001). Wavelets in hybrid-mixed stress elements. Computer Methods in Applied Mechanics and Engineering, 190(31), 3977-3998.
Cen, S., Fu, X. R., & Zhou, M. J. (2011). 8-and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes. Computer Methods in Applied Mechanics and Engineering, 200(29-32), 2321-2336.
Cen, S., Zhou, M. J., & Fu, X. R. (2011b). A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions. Computers & Structures, 89(5-6), 517-528.
Clough, R. W., & Wilson, E. L. (1999, August). Early finite element research at Berkeley. In Fifth US National Conference on Computational Mechanics (pp. 1-35).
Comi, C., & Perego, U. (2001). Numerical aspects of nonlocal damage analyses. Revue européenne des éléments finis, 10(2-4), 227-242.
Comi, C., & Perego, U. (2001). Symmetric and non-symmetric non-local damage formulations: an assessment of merits. In Proceedings of ECCM 2001 European conference on computational mechanics, (pp. 1-19). Cracow.
Cook, R. D. (2007). Concepts and applications of finite element analysis. John Wiley & Sons.
Cottrell, J. A., Hughes, T. J., & Bazilevs, Y. (2009). Isogeometric analysis: toward integration of CAD and FEA. John Wiley & Sons.
De Almeida, J. M., & De Freitas, J. T. (1991). Alternative approach to the formulation of hybrid equilibrium finite elements. Computers & Structures, 40(4), 1043-1047.
De Almeida, J. M., & Pereira, O. A. (1996). A set of hybrid equilibrium finite element models for the analysis of three‐dimensional solids. International Journal for Numerical Methods in Engineering, 39(16), 2789-2802.
Teixeira de Freitas, J. A. (1990). Mixed and hybrid symmetric formulations for the boundary integral method. European journal of mechanics. A. Solids, 9(1), 1-20.
de Freitas, J. T. (1999). Hybrid finite element formulations for elastodynamic analysis in the frequency domain. International journal of solids and structures, 36(13), 1883-1923.
Freitas, J. A. T., Almeida, J. P. B. M., & Pereira, E. M. B. R. (1993). Alternative hybrid formulations for the finite element method. In Proc. 7th World Congress Finite Element Method(pp. 264-271).
Freitas, J. A. T., Almeida, J. P. B. M., & Pereira, E. M. B. R.(1996). Non-conventional formulations for the finite element method. Structural Engineering and Mechanics, 4, 655–678.
Freitas, J. A. T., Almeida, J. P. B. M., & Pereira, E. M. B. R.(1999). Non-conventional formulations for the finite element method. Computational Mechanics, 23(1), 488-501.
Ghali, A., & Nevillle, A. M. (1997). Structural Analysis: A unified Classic and Matrix Approach. London, E & FN Spon.
Holzapfel, G. A.(2000). Nonlinear Solid Mechanics. Austria, Wiley and Sons LTD.
Hughes, T. J. R.(2003). The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. Dover.
Jirousek, J., & Leon, N. (1977). A powerful finite element for plate bending. Computer Methods in Applied Mechanics and Engineering, 12, 77-96.
Liu, G. R. (2003). Mesh Free Methods. USA, CRC Press.
Malkus, D. S., & Hughes, T. J. R.(1978). Mixed finite element methods - Reduced and selective integration techniques: A unification of concepts. Computer Methods in Applied Mechanics and Engineering, 1(15), 63-81.
Mazars, J.(1984) J.. Application de la mécanique de l’endommagement au comportement non lineaire et à la rupture du béton de structure. Paris, Université Paris 6. Ph.D Thesis
Mendes, L. A. M., & Castro, L. M. S. S.(2009) Hybrid-mixed stress finite element models in elastoplastic analysis. Finite Elements in Analysis and Design 45(12), 863-875.
Moes, N., Dolbow, J., & Belytschko, T.(1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46, 131-150.
Pereira, E. M. B. R., & Freitas, J. A. T. (1996a). A hybrid-mixed element model based on legendre polynomials for reissner-mindlin plates. Computer Methods in Applied Mechanics and Engineering 136(1-2), 111-126.
Pereira, E. M. B. R., & Freitas, J. A. T.(1996b). A mixed-hybrid finite element model based on orthogonal functions. International Journal for Numerical Methods in Engineering, 39(8), 1295-1312.
Pereira, E. M. B. R., & Freitas, J. A. T. (2000). Numerical Implementation of a Hybrid-Mixed Finite Element Model for Reissner-Mindlin Plates. Computer & Structures 74(3), 323-334.
Pereira, O. J. B. A.(1996). Utilização de Elementos Finitos de Equilíbrio em Refinamento Adaptativo. Lisbon, Instituto Superior Técnico. Ph.D Thesis
Pian, T. H. H., & Tong, P. (1969). Basis of finite element methods for solid continua. International Journal for Numerical Methods in Engineering, 1, 3-28.
Ruoff, G.(1973). Finite Elemente in der Statik. ch. Die praktische Berechnung der Kombination der Trefftzschen Metode und bei flachen Schalen: 242-259.
Santos, H. A. F. A. (2009). Duality in the geometricall exact analysis of frame structures. Lisbon, Instituto Superior Técnico. Ph.D Thesis
Shephard, M. S., Niu, O., & Baehmann, P. L.(1989). Some results using projectors for error indication and estimation. In Adaptive Methods for Partial Differential Equations, Philadelphia.
Silva, M. C., & Castro, L. M. S. S. (2004). Hybrid-mixed stress formulation with continuum damage models continuum damage models. XXV CILAMCE. Recife, Gráfica Bagaço
Silva, M. C., & Castro, L. M. S. S. (2006a). Hybrid-mixed stress formulation using continuum damage models. Communications in Numerical Methods in Engineering, 22, 605-617.
Silva, M. C., & Castro, L. M. S. S.(2006b). Hybrid and mixed finite element formulations for softening materials. European Conference on Computational Mechanics - Solids, Structures and Coupled Problems in Engineering, Lisboa, ECCM.
Spiegel, R. M., & Liu, J. (1999). Schaum's Mathematical Handbook of Formulas and Tables. New York, Schaum McGraw-Hill.
Stein, E. (1973). Finite Elemente in der Statik. ch. Die Kombination des modifizierten Treffzschen Verfahrens mit der Methode der Finiten Elemente: 172-185.
Veubeke, B. M. (1965). Displacement and Equilibrium models in the Finite Element Method. Stress Analysis: Wiley.
Zienkiewicz, O. C. (2000). Achievements and some unsolved problems of the finite element method. International Journal for Numerical Methods in Engineering, 47, 9-28.
Zienkiewicz, O. C., & Taylor, R. L. (2000). The Finite Element Method: Basis. Londres, 1, B-H.