A Finite Circular Arch Element Based on Trigonometric Shape Functions
The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordina...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2007-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2007/78507 |
| Summary: | The curved-beam finite element formulation by trigonometric function
for curvature is presented. Instead of displacement function, trigonometric function
is introduced for curvature to avoid the shear and membrane locking
phenomena. Element formulation is carried out in polar coordinates. The element
with three nodal parameters is chosen on curvature. Then, curvature field in
the element is interpolated as the conventional trigonometric functions. Shape
functions are obtained as usual by matrix operations. To consider the boundary
conditions, a transformation matrix between nodal curvature and nodal displacement
vectors is introduced. The equilibrium equation is written by minimizing the total
potential energy in terms of the displacement components. In such equilibrium
equation, the locking phenomenon is eliminated. The interesting point in this method
is that for most problems, it is sufficient to use only one element to obtain
the solution. Four examples are presented in order to verify the element formulation
and to show the accuracy and efficiency of the method. The results are compared
with those of other concepts. |
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| ISSN: | 1024-123X 1563-5147 |