矩形加肋板线性弯曲的无网格模拟与实验分析

Meshless simulation and experimental analysis for linear bending of stiffened rectangular plates

为了研究加肋板线性弯曲行为以及肋条对整个加肋板抗弯性能的影响,基于移动最小二乘近似,给出了加肋板线性弯曲的无网格法。将肋条看作梁,紧贴于平板的一侧而形成的组合。由一阶剪切变形理论以及移动最小二乘近似,分别建立板与肋条的势能泛函,然后根据位移协调条件把两者的势能泛函进行叠加,运用最小势能原理最终得出加肋板线性弯曲的控制方程,进行了加肋板三点弯曲实验,并将实验结果与理论解作比较。研究结果表明,加肋板较平板而言优势明显,实验中发现简支边界下的平板与单肋板上作用2 k N荷载时,平板中点挠度为0.791 mm,明显大于单肋板中点的挠度0.496 mm。运用无网格解得出的结果与加肋板三点弯曲实验的结果吻合良好。无网格解与运用ANSYS有限元求解出的结果相比,两者的值非常接近,均未超过5%的误差,从而验证无网格法的准确性。

In order to study the flexure behaviors of stiffened plates and the impact of stiffeners on the bending performance of stiffened plates, a meshless method was proposed based on the moving least-square approximation. A stiffened plate was considered as a composite structure of a plate and stiffeners, and the stiffeners were simulated as beams attached to the plate. The potential energy functions of plate and stiffeners were established by the moving least-square approximation and the first-order shear deformation theory, and they were superposed by applying the displacement compat-ible conditions between the plate and stiffeners. The governing equation of stiffened plate was given by implementing the theory of minimal potential energy. The three points bending test was carried out on the stiffened plates. Research shows that stiffened plates have more superiority comparing to flat plate. In the tests, when the force 2 kN is applied to the two types of simply supported plates, the central deflection of the flat plate is 0. 791 mm, and that of the stiffened plate is 0. 496. Moreo-ver, the results from meshless method and the tests are close. The solutions given by the proposed method are compared with the results from ANSYS, and the error is always less than 5%. The＆amp;nbsp;agreement proves the reliability of the proposed method.