Optimal Design Of Stiffened Plates Based On Elastic Foundation Via Meshless Method

The slab-shell structures on the elastic foundation are widely used in many constructions,such as beam-slab raft foundation and rigid pavement slab of concrete,etc.Due to inevitable uneven loads,however,these structures actually often get partly over-deformed,which prevents them from working normally and poses a big challenge to the building.The thesis argues that the whole structure could be strengthened by changing the position of ribs via the element-free Galerkin method and genetic algorithm.Firstly,based on the guidance of the element-free Galerkin method,a grid-free model of ribbed plate on the elastic foundation is established.The foundation is simulated by springs and then connected with the plate.The stiffness of spring is calculated by the coefficient of the foundation bed.And the stiffened plate on the elastic foundation is regarded as a composite structure of ribs and plates,not only the first order shear deformation theory but also the moving least squares approximation method is used to establish the total potential energy functional of the whole ribbed plate on elastic foundation,and then the complete transformation method is introduced to deal with and treatment of rib and grade slab displacement coordination problems,then according to the energy method,the governing equation of the bending of the structure is solved.Among them,the meshless method is based on the discrete nodes of foundation ribbed slab to obtain approximate numerical solutions.There is no need for element or grid connection between the nodes.The calculation efficiency is so high because of the plate nodes do not need to be rearranged even if the rib position changes.Secondly,the genetic algorithm is introduced into the structural optimization design to optimize the location of the rib.The ribbed panel is redesigned with the ribs position as the variable,the pivot deflection as the objective function,and the panel size as the constraint condition,the stiffened plate on the elastic foundation is optimized for the purpose of minimizing the deflection of the center control point of the foundation plate.The results show that the global optimization ability of genetic algorithm is strong,but the calculation repetition rate is high in the process of optimization,and the problem of premature convergence is easy to occur.Therefore,in order to improve the shortcoming of genetic algorithm,simulated annealing algorithm is adopted.The simulated annealing algorithm,which holds Metropolis criteria as its core concept,has a gift for escaping the local optimization and runs towards the global optimization.In the selection operation of the genetic algorithm,the core theory of the simulated annealing algorithm,Metropolis acceptance criterion,was added,supplemented by the optimal preservation scheme,to become the hybrid genetic algorithm.Furthermore,the modification of the mutation operator in genetic algorithm helps create an even better hybrid genetic algorithm:faster and stronger.Finally,in this paper,the optimum placement of rib in several common elastic foundation ribbed plates is calculated,such as the single rib(parallel ribs and vertical ribs)stiffened plate on the elastic foundation under uniform load or partial load.Putting together those calculations and the analysis output by the software ABAQUS,one will be delighted to see both the accuracy and the effectiveness of the thesis argument are well proved.