Topology Optimization Design Of Box Girder Based On Dynamic Characteristics

The box beam structure is a common bearing component in the mechanical equipment,but the use of traditional design methods leads to its structure cumbersome and low market competitiveness.Based on the theory of variable density method,this thesis is to study the dynamic topology optimization after completing the static topology optimization.The static performance of the structure is considered while its dynamic performance is also taken into account to solve the optimization model and get a new structure by programming the codes.The main studies of this thesis are as follows:1.The topological theory of variable density method is used to establish the mathematical models to describe the topology problem.In accordance with the relationship between design variables and material properties,the density-stiffness interpolation model is built.2.Different filtering functions are employed to solve the numerical problems such as the checkerboard and the grid dependency in the optimization process.The localized mode problem in the dynamic topology optimization problem is solved by modifying the SIMP interpolation model and the OC criteria method is applied to realize the iterative calculation of the design variables.3.The finite element method is adopted to analyze the mechanical behavior of the box-beam structure.Four-node rectangular element and eight-node rectangular box element are selected respectively to discrete the two-dimensional and the three-dimensional continuum structure.After deriving the total stiffness matrix and mass matrix,the boundary conditions and loads,the static parameters are acquired.The method of MATLAB function,vector inverse iteration and subspace method are used to calculate the low-order natural frequency of the structure.4.For the problem of static optimization,the minimum compliance optimization model is established.Problems of the two-dimensional and three-dimensional structure are analyzed through examples,while penalty factor and filter radius are also done.The topology problem of special geometric constraint structure and optimization problem meshed under large scale are studied too.5.As to the dynamic optimization problem,the mathematical model of displacement-fundamental frequency constraint is established based on the static.The change of displacement,fundamental frequency and structure quality during topology optimization is analyzed with examples.At the same time,various topology problems are summarized to design a simple interface to facilitate the program intuitively and conveniently.This thesis has a certain reference value for the static and dynamic topology optimization of continuum structure.The optimal topology can guide the design of engineering equipment related to box beam structure thereby improving the market competitiveness.