An enhanced 4-node shell element for laminated composites

Gall Trabal, Guillem ; Capella Pujol, Pau

4. term

Design of Mechanical Systems, Master

2018

2018-05-31

92 pages

Laminated composite shell structures are becoming increasingly popular because of their mechanical properties versus weight benecial relation. The aim of this study is to develop a robust nite shell element formulation for the analysis of laminated composites. The 4-node shell element coded in this work is desired to solve for linear static analysis, linear buckling and geometrically non-linear analysis. The element routine is implemented in the MUltidisciplinary Synthesis Tool (MUST), under development at the Department of Materials and Production at Aalborg University since 1998. MUST is a system used for design, analysis and optimization for structural, uid and thermal problems coded in Fortran90. Therefore, the 4-node shell element of this thesis is implemented in Fortran90 and tted adequately in the system. The starting point of this project is a 4-node at shell element enhanced with the EAS (Simo and Rifai, 1990) and MITC (Dvorkin and Bathe, 1984) methods. It was coded in Matlab as a 3rd semester project in the DMS master's program. The aforementioned element can solve linear static problems and it is not generalized to the 3D space. Thus, a generalized, non-linear enhanced formulation is needed. The thesis derives the continuum based theories needed to model shell elements and laminated structures. From there, a derivation of the continuum mechanics in curvilinear is done so that the reader gathers all the needed tools to understand the three-eld variational derivation (Washizu, 1975) of the element's governing equation. Once the governing equations are obtained, they are discretized to formulate the nite elements solution. Finally, the discrete equations to be solved are obtained and they describe a 4-node nite element capable of modeling multi-layered structures. It is enhanced with the EAS and MITC methods to tackle, in this way, the in-plane and out-of-plane locking the isoparametric element displays before any improvement implementation. The 4-node shell laminated element passes all patch tests for both membrane and bending loading situations. Good results are obtained for laminated and non-laminated elements in both linear and linear bucking tests, regardless the geometry and orientation of the structure. In the case of geometrically non-linear situations the element performs well when bending is not involved and the structure's geometry is not curved. Therefore, a bug in the code appears to be in the geometrically non-linear (GNL) implementation regarding the rotation degrees of freedom or a mistake in transforming the mesh to the local element base. Further work is to be done on debugging the GNL implementation of the element.

Finite element method ; MITC ; EAS ; Shell ; 4 node ; Enhanced ; Continuum mechanics ; Composite materials

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