Abstract
In recent past, isogeometric analysis (IGA) has gained significant popularity as a numerical technique in computational mechanics. The systematic framework of IGA allows maintaining the exact geometry during discretization regardless of how coarse the mesh is, and furthermore, it also eliminates the dependency on computer-aided design (CAD) once the initial mesh is created. IGA often referred as a generalized version of finite element analysis (FEA) or with a different perspective FEA can be seen as a special case of IGA. Though IGA performs superior to FEA in several ways, it does exhibit similar limitations sooner or later like its FE counterpart. One such limitation is locking which appears during the analysis of thin structural parts and for incompressible or nearly incompressible material. However, on the promising side, the techniques available in FEA to tackle such limitations can be successfully modified to work with IGA as well. In the present work, a two-field hybrid formulation is explored in the framework of IGA which performs convincingly well in situations where the problem demands incompressibility or near incompressibility of material or to solve problems of beam/plate/shell geometries and so on. As per our best knowledge, the stated method is yet to be studied in context of IGA, despite the fact that the same formulation will eliminate different types of locking. Finally, the proposed formulation has been successfully implemented on several examples with promising results.
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References
Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195
Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, NewYork
Echter R, Bischoff M (2010) Numerical efficiency, locking and unlocking of NURBS finite elements. Comput Methods Appl Mech Eng 199:374–382
Jog CS (2005) A 27-node hybrid brick and a 21-node hybrid wedge element for structural analysis. Finite Elem Anal Des 41:1209–1232
Jog CS, Kelkar PP (2006) Non-linear analysis of structures using high performance hybrid elements. Int J Numer Methods Eng 68:473–501
Jog CS (2010) Improved hybrid elements for structural analysis. J Mech Mater Struct 5:507–528
Agrawal M, Nandy A, Jog CS (2019) A hybrid finite element formulation for large-deformation contact mechanics. Comput Methods Appl Mech Eng 356:407–434
Roychowdhury A, Nandy A, Jog CS, Pratap R (2014) Hybrid elements for modelling squeeze film effects coupled with structural interactions in vibratory MEMS devives. CMES 1:1–15
Jog CS, Nandy A (2015) Conservation properties of the trapezoidal rule in linear time domain analysis of acoustics and structures. J Vib Acoust Trans ASME 137:1–17
Bathe KJ (1996) Finite element procedures. Prentice-Hall, New Jersey
Agrawal V, Gautam SS (2018) IGA: a simplified introduction and implementation details for finite element users. J Inst Eng Ser C
Elguedj T, Bazilevs Y, Calo VM, Hughes TJR (2008) B bar and F bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements. Comput Methods Appl Mech Eng 197:2732–2762
Nguyen VP, Anitescu C, Bordas SPA, Rabczuk T (2015) Isogeometric analysis: an overview and computer implementation aspects. Math Comput Simul 117:89–116
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Bombarde, D.S., Nandy, A., Gautam, S.S. (2021). A Two-Field Formulation in Isogeometric Analysis to Alleviate Locking. In: Joshi, P., Gupta, S.S., Shukla, A.K., Gautam, S.S. (eds) Advances in Engineering Design. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-33-4684-0_20
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DOI: https://doi.org/10.1007/978-981-33-4684-0_20
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