Optimization of initial stress and equilibrium shape of membrane structures considering fundamental frequency as a measure of stiffness

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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
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EŒbecause the fundamental eigenmode is considered the weakest mode of deformation. The membrane is discretized by using the finite element methodEŒwhere the triangular elements with constant strains is used. In the first stage of proposed methodEŒthe 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EŒand the optimal stresses are found by sequentially solving simultaneous linear equations. In the second stageEŒthe 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EŒthe 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.