Abstract
Abstract The current paper implementates a simple fully non-linear Kirchhoff-lovel shell penalty based finite element. The 6 nodes and 21 DoF triangular element developed in this work has a quadratic displacement field associated to it and the C1 continuity required by Kirchhoff-Love Hyphotesis is approximated by an internal penalty. The biggest novelty in this article is the simultaneous use of penalty and a Rodrigues incremental Rotation parameter (scalar DOF) between neighboring elements further explained in the text. The nonlinear finite element model developed in this article is compared to analytical results, commercial finite element code and another FEM model developed in bibliography. Simulations have demonstrated consistency when comparing results to other models and it is deemed that reliable mesh generation together with a powerfull triangular finite element is a good option for trustworthy thin shell simulations.
Highlights
A numerical approach solution usually is an effective method of obtaining the structural response for situations where the load distribution, material non-linearity or geometrical properties are complex, turning the attainment of an analytical solution into a real challenge
The simulation has been executed for different mesh discretization and for different Thickness and its output is compared to analytical results and to commercial software Nastran Triangular Shell Element – Ctria6 (See Autodesk Inc, 2019)
The present article develops analytically a very simple finite element and presents results in 3 different simulations comparing it to other FEM models and to linear analytical models
Summary
A numerical approach solution usually is an effective method of obtaining the structural response for situations where the load distribution, material non-linearity or geometrical properties are complex, turning the attainment of an analytical solution into a real challenge. Shells are a very important structural model, which can be regarded as a MOR (Model Order Reduction) of Solid Mechanics (Nigro et al, 2019) and are consistently applicable to engineering structural problems. Theories for Plates, Shells and Membranes have been developed in the past decades by many researchers due to its importance in mechanics. Kirchhoff-Love and Reissner–Mindlin theories are example of shell/plate models used in engineering. The authors address a non-linear Kirchhoff-Love element implemented in the AceGEN / AceFEM code environment, which is a Mathematica based code suitable for developing optimized code for computational mechanics (Korelc, J.A., Wriggers, P., 2016). In Finite Element Methods, this structural problem may be implemented and studied by three-dimensional elements. Special attention must be taken regarding the interpolation of 3-D elements for Shell modeling
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