The considered system is initially formed by four bars at which one adds the fifth bar. One knows the geometrical and mechanical parameters of the four bars, including here the errors of manufacturing too. For the fifth bar one also knows the geometrical and mechanical parameters and the error of manufacturing, but not the angle between the bar and the positive direction of the horizontal axis. The common point of the bars is acted in plan by a known force (its components on the two directions are also known). We determine the displacement of the common point (considered as the origin of the reference frame), the components of this displacement on the two directions, the forces in the bars, their minimum and maximum values, and the angle between the fifth bar with the positive direction of the horizontal bar for which these extreme values take place. The calculations are presented analytical and numerical. Some conclusions end the paper.

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Aspects Concerning the Optimization for a Planar System of Bars Cylindrically Jointed and Having One Common End

  • Valentin Răcășan,
  • Nicolae-Doru Stănescu

摘要

The considered system is initially formed by four bars at which one adds the fifth bar. One knows the geometrical and mechanical parameters of the four bars, including here the errors of manufacturing too. For the fifth bar one also knows the geometrical and mechanical parameters and the error of manufacturing, but not the angle between the bar and the positive direction of the horizontal axis. The common point of the bars is acted in plan by a known force (its components on the two directions are also known). We determine the displacement of the common point (considered as the origin of the reference frame), the components of this displacement on the two directions, the forces in the bars, their minimum and maximum values, and the angle between the fifth bar with the positive direction of the horizontal bar for which these extreme values take place. The calculations are presented analytical and numerical. Some conclusions end the paper.