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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Shape determination of wind-resistant wings attached to an oscillating bridge using adjoint equation method
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Shape determination of wind-resistant wings attached to an oscillating bridge using adjoint equation method

机译：伴随方程法确定摆臂上防风翼的形状

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The purpose of this study is to determine the angle of a wing that is attached to an oscillating bridge located in transient incompressible viscous flows, using the arbitrary Lagrangian-Eulerian (ALE) finite element method and optimal control theory, in which a performance function is expressed by the displacement of the bridge. Currently, some bridges have wings attached to them to prevent oscillation caused by wind flows. When the angle of the wing changes, the state of oscillation also changes. Therefore, the angle of the wing is a very important parameter to consider the minimization of the oscillation of the bridge. In this research, the angle of the wing is determined based on optimal control theory. To minimize the oscillation of a bridge, the performance function is introduced as the minimization index. The performance function is defined by the square sum of the displacements of a bridge. This problem can be transformed into a unconstrained minimization problem by the Lagrange multiplier method. The adjoint equations can be obtained by using the stationary condition of the extended performance function. The gradient used for updating the angle of the wing can be derived by solving the adjoint and state equations. The weighted gradient method is applied as a minimization technique. In this study, the determination of the angle at which the oscillation of the bridge is minimized is presented using this theory. To express the motion of fluids around a bridge, the Navier-Stokes equations described in the ALE form are employed as the state equations. The motion of the bridge is expressed by the motion equations by using the displacements and rotational angle of the body supported by springs. As a numerical study, the optimal control of the angle of the wing is demonstrated at low Reynolds number flows. Thus, the angle of the wing at which the oscillation of the bridge becomes minimum can be determined. Numerical results obtained correspond to the angle of actual bridge wing.
机译：这项研究的目的是使用任意Lagrangian-Eulerian（ALE）有限元方法和最优控制理论来确定机翼连接到位于瞬态不可压缩粘性流中的振荡桥的角度。用桥的位移表示。当前，一些桥梁附接有翼以防止由风引起的振动。当机翼角度改变时，摆动状态也会改变。因此，机翼的角度是考虑最小化桥梁振动的一个非常重要的参数。在这项研究中，机翼的角度是根据最佳控制理论确定的。为了使电桥的振动最小，引入性能函数作为最小化指标。性能函数由桥位移的平方和定义。该问题可以通过拉格朗日乘数法转换为无约束最小化问题。可以通过使用扩展性能函数的平稳条件来获得伴随方程。可以通过求解伴随和状态方程来导出用于更新机翼角度的梯度。加权梯度法被用作最小化技术。在这项研究中，使用该理论确定了最小化桥梁振动的角度。为了表示桥梁周围的流体运动，将ALE形式中描述的Navier-Stokes方程式用作状态方程式。通过使用弹簧支撑的车身的位移和旋转角度，通过运动方程式来表达桥的运动。作为数值研究，在低雷诺数流下证明了机翼角度的最佳控制。因此，可以确定机翼的振动最小的机翼角度。获得的数值结果与实际机翼的角度相对应。

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