Abstract
This chapter presents refined shell finite element models with variable kinematics for the analysis of multi-layered structures involved in four physical fields: mechanical, electric, thermal, and hygroscopic. Variable kinematic models in the framework of Carrera Unified Formulation (CUF) with various kinematic assumptions are discussed. An efficient tool to realize adaptable refinement in finite element models, Node-Dependent Kinematics approach, is introduced. Refined doubly curved shell finite element formulations derived from the principle of virtual displacements accounting for multi-field coupling effects are presented.
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References
Altay G, Dökmeci MC (2008) Certain hygrothermopiezoelectric multi-field variational principles for smart elastic laminae. Mech Adv Mater Struct 15(1):21–32
Bucalem ML, Bathe KJ (1993) Higher-order MITC general shell elements. Int J Numer Methods Eng 36(21):3729–3754
Carrera E (2002) Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Methods Eng 9(2):87–140
Carrera E, Büttner A, Nali P (2010) Mixed elements for the analysis of anisotropic multilayered piezoelectric plates. J Intell Mater Syst Struct 21(7):701–717
Carrera E, Cinefra M, Li G (2018) Refined finite element solutions for anisotropic laminated plates. Compos Struct 183:63–76
Carrera E, Cinefra M, Li G, Kulikov GM (2016) MITC9 shell finite elements with miscellaneous through-the-thickness functions for the analysis of laminated structures. Compos Struct 154:360–373
Carrera E, Cinefra M, Petrolo M, Zappino E (2014) Finite element analysis of structures through Unified Formulation. Wiley, New Jersey
Carrera E, Fagiano C (2007) Mixed piezoelectric plate elements with continuous transverse electric displacements. J Mech Mater Struct 2(3):421–438
Carrera E, Robaldo A (2010) Hierarchic finite elements based on a unified formulation for the static analysis of shear actuated multilayered piezoelectric plates. Multidiscip Model Mater Struct 6(1):45–77
Cinefra M, Petrolo M, Li G, Carrera E (2017) Variable kinematic shell elements for composite laminates accounting for hygrothermal effects. J Therm Stress 40(12):1523–1544
Dökmeci M (1973) Variational principles in piezoelectricity. Lettere al Nuovo Cimento (1971–1985) 7(11):449–454
D’Ottavio M, Kröplin B (2006) An extension of Reissner mixed variational theorem to piezoelectric laminates. Mech Adv Mater Struct 13(2):139–150
Heyliger P (1994) Static behavior of laminated elastic/piezoelectric plates. AIAA J 32(12):2481–2484
Ikeda T (1996) Fundamentals of piezoelectricity. Oxford University Press, Oxford
Koiter W (1970) On the foundations of the linear theory of thin elastic shell. Proc Kon Nederl Akad Wetensch 73(3):169–195
Leissa AW (1973) Vibration of shells, vol 288. Scientific and Technical Information Office, National Aeronautics and Space Administration Washington
Li G, Carrera E, Cinefra M, de Miguel A, Pagani A, Zappino E (2019) An adaptable refinement approach for shell finite element models based on node-dependent kinematics. Compos Struct 210:1–19
Li G, Carrera E, Cinefra M, de Miguel A, Kulikov GM, Pagani A, Zappino E (2019) Evaluation of locking in refined hierarchical shell finite elements for laminated structures. Advanced modeling and simulation in engineering sciences. Accepted manuscript
Mindlin RD (1951) Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech 18:31–38
Murakami H (1986) Laminated composite plate theory with improved in-plane responses. J Appl Mech 53(3):661–666
Reddy J (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton
Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech A69–A77
Sih GC, Michopoulos J, Chou SC (2012) Hygrothermoelasticity. Springer Science & Business Media, Berlin
Sung C, Thompson B (1987) A variational principle for the hygrothermoelastodynamic analysis of mechanism systems. J Mech, Transm, Autom Des 109(3):294–300
Suri M (1996) Analytical and computational assessment of locking in the hp finite element method. Comput Methods Appl Mech Eng 133(3–4):347–371
Szabó B, Düster A, Rank E (2004) The p-version of the finite element method. Wiley Online Library, New Jersey
Tsai SW (1988) Composites design, vol 5. Think composites, Dayton
Smittakorn W, Heyliger PR (2000) A discrete-layer model of laminated hygrothermopiezoelectric plates. Mech Compos Mater Struct 7(1):79–104
Zappino E, Li G, Pagani A, Carrera E (2017) Global-local analysis of laminated plates by node-dependent kinematic finite elements with variable ESL/LW capabilities. Compos Struct 172:1–14
Zappino E, Li G, Pagani A, Carrera E, de Miguel AG (2018) Use of higher-order Legendre polynomials for multilayered plate elements with node-dependent kinematics. Compos Struct 202:222–232
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Li, G., Carrera, E., Cinefra, M., Zappino, E., Jansen, E. (2019). Variable Kinematic Shell Formulations Accounting for Multi-field Effects for the Analysis of Multi-layered Structures. In: Petrolo, M. (eds) Advances in Predictive Models and Methodologies for Numerically Efficient Linear and Nonlinear Analysis of Composites. PoliTO Springer Series. Springer, Cham. https://doi.org/10.1007/978-3-030-11969-0_2
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