Shape and stress optimization of membrane structures considering material nonlinearity

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Publication year 1998
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Title Shape and stress optimization of membrane structures considering material nonlinearity
Author Makoto Ohsaki,Jun Fujiwara
Summary An inverse formulation is presented for simultaneously finding optimal cutting patterns and the optimal initial stresses of a frame-supported membrane structureĀEĆwhere explicit developability conditions are incorporated for a curved surface to be reduced to a set of plane cutting patterns after removing the initial stresses. The membrane is modeled as an orthotropic materialĀEĆand the rigid body rotation of the principal axes is considered in the developability conditionĀEĆalthough the effect of shear deformation on the directions of the principal axes is neglected. Nonlinear polynomial functions are used for the stress-strain relations in the principal axes. The membrane is discretized by using the finite element methodĀEĆwhere the triangular unit with constants trains is used. In the first stage of the proposed methodĀEĆan inverse problem is formulated to directly find prestresses as well as the cutting patterns for specified nodal coordinates so as to minimize the variation of stresses at the initial shape from the desired values. Then the distribution of the stresses is further improved by considering the nodal locations as the design variables. Optimal orientations of principal axes is also found for each cutting sheet. In the examplesĀEĆthe optirnal shapeĀEĆinitial stresses and cutting patterns are found simultaneously for an HP-type membrane structure supported by a frame. The optimal locations of the internal nodes are found by using the sequential quadratic programming method. It is confirmed by carrying out nonlinear shape analysis that accurate optimal solutions are found by incorporating material nonlinearity in the developability conditions. It is also shown that the distribution of initial stresses is slightly improved by varying the directions of the principal axes of the cutting sheets.