Research Based On SIMP Method On Dynamic Topology Optimization Of Cylindrical Shell Structure Rib

Structural optimization is a preliminary design for material distribution optimization problems,which has a great impact on the conceptual design stage of the structure.The correct choice of the optimization method can greatly improve the performance index of the structure,so as to effectively save costs and obtain greater economic benefits.In terms of structural optimization,topology optimization has a larger design limit than other traditional size optimization and shape optimization,and has a wider application range.At present,the topology optimization method still has the problem of simple optimization structure,which is limited by the long calculation time and low precision in the high frequency vibration caused by the traditional finite element method.Aiming at these problems,this paper optimizes the cylindrical shell rib structure based on SIMP structural topology optimization,and extends the topology optimization application field to the complex coupling structure and high frequency energy finite element problem research.Firstly,the basic theory of static stiffness topology optimization based on SIMP method is studied.Through the mathematical modeling of the cylindrical shell rib structure,the traditional finite element is used to calculate it.The optimization criterion algorithm based on the SIMP interpolation model is used to establish the minimum structural flexibility,that is,the maximum stiffness is the objective function.The optimization model of the constraint optimizes the ribs on the surface of the shell.The program is written in Matlab,and the optimization results of the structure under low frequency static load are shown by numerical examples.Secondly,aiming at the most common dynamic mechanics problems in real engineering,the mathematical models and optimization methods established in the previous chapter are used.The dynamic load is transformed into the instantaneous static load by the equivalent static load principle,and the problem is transformed into the static optimization problem.The dynamic topology optimization results of the surface stiffener of the cylindrical shell structure are demonstrated by an example.Thirdly,in order to improve the applicability of topology optimization in high frequency domain and solve the problem of dense meshing and high computational time cost of traditional finite element method in high frequency domain,an energy finite element method based on adjoint variable method is proposed.Then the sensitivity of the structure is calculated and analyzed by energy control equation.With the objective function is to minimize the energy compliance of the structure,the plate structure is optimized and its optimal configuration is displayed,which provides useful information for material layout design of structural system.Finally,in order to obtain the optimal configuration of the rib reinforcement of the cylindrical shell under high-frequency vibration,an energy finite element method is introduced to solve the energy density response.The elemental matrix is obtained by the traditional finite element method,then the energy transfer coefficient between the beam and the plate is calculated and the coupling matrix is obtained.And the unit matrix is integrated into the overall matrix through the coupling matrix.In order to achieve the structural optimization of the goal of minimizing the energy flexibility,the sensitivity of the energy flexibility is derived,and the topology optimization of the ribs of the cylindrical shell structure is finally completed.