RIB MESHLESS OPTIMIZATION OF STIFFENED PLATES RESTING ON ELASTIC FOUNDATION BASED ON GENETIC ALGORITHM

Based on the genetic algorithm and the first-order shear deformation theory, a meshless method is proposed to optimize the position of ribs of the stiffened plate resting on elastic foundation. Firstly, the meshless model of the stiffened plate is obtained by discretizing the plate and ribs with a series of points and by simulating the elastic foundation with springs. Secondly, the displacement field is approximately obtained based on the first-order shear deformation theory and the moving-least square approximation, and the total potential energy of the stiffened plate resting on the elastic foundation is derived. Then, the boundary conditions are dealt with the full transformation method, and the governing equation of the structure is derived from the Hamilton principle. Finally, the genetic algorithm and the improved genetic algorithm are introduced with the location of ribs as the design variable and the minimal deflection of the center point of the stiffened plate as the objective function. The arrangement of ribs is optimized to achieve the minimum center point deflection of the stiffened plate resting on the elastic foundation. Taking some ribbed plates resting on elastic foundation with different parameters and load distribution as the numerical examples, the comparison with the finite element results given by ABAQUS is carried out. The results show that the proposed meshless model can effectively analyze the bending problem of stiffened plate on elastic foundation. Meanwhile, the meshless optimization method based on the genetic algorithm and the improved genetic algorithm both can effectively optimize the position of the ribs of the stiffened plate on elastic foundation, the latter is relatively efficient, and the stable optimal solution can be obtained after only three iterations. Additionally, when the position of the rib changes during the optimization process, only the displacement transformation matrix needs to be recalculated, and the mesh reconstruction is totally avoided.