Boundary element method for torsional analysis
In this paper a boundary element method is developed for calculating torsional rigidity of inhomogeneous shafts with arbitrary cross sections. One end of the shaft is attached to a fixed support and an arbitrarily distributed twisting moment is applied on the other end. Boundary element method is us...
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| Format: | Final Year Project |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10356/54129 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | In this paper a boundary element method is developed for calculating torsional rigidity of inhomogeneous shafts with arbitrary cross sections. One end of the shaft is attached to a fixed support and an arbitrarily distributed twisting moment is applied on the other end. Boundary element method is used to solve two-dimensional Laplace’s equation to determine warping function of certain cross section subjected to given boundary conditions in order to solve for the torsional rigidity of the shafts.
The torque is proportional to the angle of twist per unit length, θ, with a constant GJ, which is known as the torsional rigidity of the shaft. J is also known as the polar moment of inertia for the case of shafts with regular shapes such as circular shafts, whereas for non-regular shapes, the product GJ still retained as the torsional rigidity.
MATLAB is used to implement the boundary element procedure on the computer to solve for values of J such that it can be used in the calculation of the angle of twist per unit length for a given torque. Besides solid shafts, the J values of hollow shafts are considered as well in this project. The results obtained using MATLAB are compared to the exact solutions. |
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