On the Formulation of a Hybrid Discontinuous Galerkin Finite Element Method (DG-FEM) for Multi-layered Shell Structures
| dc.contributor.author | Li, Tianyu | en |
| dc.contributor.committeechair | Kapania, Rakesh K. | en |
| dc.contributor.committeemember | Patil, Mayuresh J. | en |
| dc.contributor.committeemember | Seidel, Gary D. | en |
| dc.contributor.department | Aerospace and Ocean Engineering | en |
| dc.date.accessioned | 2018-05-02T06:00:18Z | en |
| dc.date.available | 2018-05-02T06:00:18Z | en |
| dc.date.issued | 2016-11-07 | en |
| dc.description.abstract | 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. | en |
| dc.description.abstractgeneral | A novel computational method is developed for the composite structures withmultiple layers and stiffeners, which possess high ratio of strength-to-weight andhave wide applications in the aerospace engineering. The present method has thepotential to use fewer calculations to obtain high accuracy. Five typical andimportant problems are solved by this method and the results are also verifiedbyother papers or commercial software. For the first problem, the Sandwichplateproblem, the water pressure is applied on the top surface and the deformationaswell as stress field are both analyzed. The second problem is a two-dimensional multi-layered pipe’s collapse. The critical collapse failure point is found as a functionof geometrical imperfection. The third problem is the three-dimensional multilayered pipe’s unstable deformation analysis. The critical point of the unstabledeformation is found and a device is also analyzed to increase the strength. For thelast two problems, they are the stiffened plates and shells. In this case, weusestiffeners to increase the strength of the structure and the deformationof thestiffened plates/shells is analyzed. For the stiffened plate problem, we analyzearectangular plate reinforced by a parabolic stiffener. For the stiffened shell problem, we analyze the airfoil/hydrofoil structure stiffened by ribs. All these problems areimportant for aerospace vehicles. | en |
| dc.description.degree | Master of Science | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:9045 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/82962 | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | hybrid discontinuous Galerkin finite element method | en |
| dc.subject | Multi-layered and stiffened plates and shells | en |
| dc.subject | large deformation and strain | en |
| dc.subject | Dirac's delta function | en |
| dc.subject | Orthogonal basis function | en |
| dc.title | On the Formulation of a Hybrid Discontinuous Galerkin Finite Element Method (DG-FEM) for Multi-layered Shell Structures | en |
| dc.type | Thesis | en |
| thesis.degree.discipline | Aerospace Engineering | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | masters | en |
| thesis.degree.name | Master of Science | en |
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