A mathematical programming method to optimize the distribution field of a truss-like material is presented. The densities and angles of members are optimized in two separate procedures in each iteration. An explicit sub-problem in a variable separation form is established at every iteration procedure. At each sub-problem, the stress constraint function is expanded into a trigonometric series of the member angles. According to the extreme condition, the optimal orientations of members are determined. The member densities are optimized using the method of moving asymptotes (MMA). Two examples demonstrate that the optimal truss-like structures are very close to analytic solutions.
During the oil drilling process, the eccentric rotation of rotating devices such as rotary table may excite abnormal vibration of the drilling rig which will worsen the working condition of the rig and cause structure failure. In this paper, a ZJ70 drilling rig is taken as the study object, the harmonic response analysis of which is conducted by using FEM software and the frequency response characteristic of the substructure is obtained. Result shows the stiffness of rear substructure is insufficient. On the basis of harmonic response analysis, the modification of the substructure is carried out through enlarging the rear connection frame. Further calculation shows the first 3 order natural frequencies of the substructure are increased, thus the abnormal vibration of the substructure caused by the rotary table with certain rotation speed can be effectively reduced. In addition, the displacement response of both first two orders are greatly decreased with that of central and rear positions are respectively decreased by 17.5% and 42.1%, which demonstrates the dynamic characteristic of the substructure is significantly improved.
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