| The in-depth contents |
| Publication year |
1999 |
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| Title |
Optimization of initial stress and equilibrium shape of membrane structures considering fundamental frequency as a measure of stiffness |
| Author |
Jun Fujiwara,Makoto Ohsaki,Tomonori Kitaori
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| Summary |
An inverse method for specified lowest eigenvalue (square of the lowest natural frequency) is proposed for finding the optimal cutting pattern and the optimal stresses of a frame-supported membrane structure. The lower bound of stiffness is guaranteed by specifying the lowest eigenvalue�E�because the fundamental eigenmode is considered the weakest mode of deformation. The membrane is discretized by using the finite element method�E�where the triangular elements with constant strains is used.
In the first stage of proposed method�E�the optimal stresses to minimize the standard deviation are found for specified eigenvalue and nodal coordinates. The lowest eigenvalue which is a nonlinear function of stresses is linearized�E�and the optimal stresses are found by sequentially solving simultaneous linear equations. In the second stage�E�the optimal locations of nodes are found by using the optimizing method based on the sensibility analysis with respect to the nodal coordinates.
In the examples�E�the proposed method is applied to an HP-type membrane structure supported b y a frame. It is confirmed by carrying out nonlinear shape analysis that the eigenvalue constraint is satisfied within good accuracy.
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