On the Formulation of a Hybrid Discontinuous Galerkin Finite Element Method (DG-FEM) for Multi-layered Shell Structures

A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak form of the DG-FEM is next presented. In this case, the discontinuous basis functions can be employed for the displacement basis functions. The implementation details of the nonlinear FEM are next presented. Then, the Consistent Orthogonal Basis Function Space is developed. Given the boundary conditions and structure configurations, there will be a unique basis function space, such that the mass matrix is an accurate diagonal matrix. Moreover, the Consistent Orthogonal Basis Functions are very similar to mode shape functions. Based on the DG-FEM, three dedicated finite elements are developed for the multi-layered pipes, curved stiffeners and multi-layered stiffened hydrofoils. The kinematics of these three structures are presented. The smooth configuration is also obtained, which is very important for the buckling analysis with large deformation and finite strain. Finally, five problems are solved, including sandwich plates, 2-D multi-layered pipes, 3-D multi-layered pipes, stiffened plates and stiffened multi-layered hydrofoils. Material and geometric nonlinearities are both considered. The results are verified by other papers' results or ANSYS.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Aerospace Engineering

Department dc:contributor.department

Aerospace and Ocean Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2016

Author dc:creator

• Li, Tianyu

Chair dc:contributor.committeechair

• Kapania, Rakesh K.

Committee members dc:contributor.committeemember

• Patil, Mayuresh J.
• Seidel, Gary D.

• hybrid discontinuous Galerkin finite element method
• Multi-layered and stiffened plates and shells
• large deformation and strain
• Dirac's delta function
• Orthogonal basis function

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:9045

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/82962