Layout Optimization Of Stiffener Of Plate And Shell Structure By The Weight-guide Method

Structural topology optimization based on finite element analysis has become one of the research hotspots of structural optimization design.The Weight-Guide method is a new optimization method which combines the mathematical programming method and the optimization criterion method.At the same time,it has the advantages of fast iterative speed,high accuracy and rigorous theory of the optimization criterion method.At present,the WeightGuide method has been widely used in the size and shape optimization design of general engineering structures,but there are few researches and applications in the field of topology optimization.Therefore,on the basis of the theory of Weight-Guide method,this paper extends the application scope of Weight-Guide method and optimizes the layout of structural stiffeners,so that it can be applied to the topology optimization design of different optimization objectives from static to dynamic,which has great theoretical significance and engineering application value.First of all,the basic theory of the Weight-Guide method is described.The Lagrange multiplier and the iterative formula are solved by the combination of the plate beam coupling model and the SIMP interpolation method,which are applied to the optimization of the layout of the cantilever beam and the stiffener of the thin plate with the minimum flexibility of the static load of the foundation.In this paper,numerical examples of MATLAB is used to show that the Weight-Guide method can achieve better topology and optimization efficiency,and compared with the fixed point iteration method,it embodies the advantages of the weight-guide method.Secondly,considering that there are few applications of the Weight-Guide method in the dynamic optimization,this paper introduces the Weight-Guide optimization criteria of the previous chapter into the dynamic optimization analysis,and carries out the topology optimization of dynamic Rayleigh damping power flow response and Mode power flow response.Based on the traditional power flow theory,this paper analyzes the modal power flow theory based on the inherent damping distribution,and describes the power flow of the system by constructing the Characteristic damping matrix and using its eigenvector as a set of basis vectors in the power flow space of the system.Through numerical examples,the final topological structure of the two power flow models is very similar,and the values of the objective function is very close.The power flow of the stiffened plate optimized by the WeightGuide method is effectively reduced in the low and medium frequency band,and the structural dynamic performance is significantly improved.Finally,the Weight-Guide method is applied to the optimization design of radiated sound power flow of structure vibration.The Rayleigh integral method derived from Helmholtz equation is used to integrate the sound intensity of structure to obtain radiated sound power flow,and the sensitivity of objective function is calculated by explicit approximation technique.The Weight-Guide method is used to update the design variables,optimize the layout of stiffeners,change the shape of vibration structure,transform the structure into a weak radiator,and reduce the acoustic radiation.The optimized structure not only reduces the local frequency band of the optimized frequency,but also optimizes the whole band of the sound power spectrum by changing the number and position of the peaks.