## An enhanced 4-node shell element for laminated composites

Student thesis: Master Thesis and HD Thesis

• Guillem Gall Trabal
• Pau Capella Pujol
4. term , Design of Mechanical Systems, Master (Master Programme)
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.
Language English 1 Jun 2018 92
Keywords Finite element method, MITC, EAS, Shell, 4 node, Enhanced, Continuum mechanics, Composite materials
ID: 280225329