Study On Topology Optimization Method For Minimum Flexibility Problem Of Two-dimensional Beam Structure

Compared with shape optimization and size optimization,topology optimization is considered to be a more difficult and challenging topic in the field of structural optimization.Moreover,the core part of structural optimization has changed from shape optimization to topology optimization.Therefore,topology optimization of continuum structure has become one of the frontier and hot issues in structural optimization.Structural topology optimization method involves multi-disciplinary knowledge,among which computational mathematics,structural mechanics and computer technology are the theoretical and practical basis of the method.The combination of computer technology and finite element analysis method can solve the mechanical analysis problems of complex structures in the optimization process,and provide new analysis ideas and technical means for the effective topology optimization design of structures.At present,the topology optimization method is not mature,and there are still many problems to be solved in this field.Moreover,the application prospect of topology optimization is very considerable,and its research will have a profound impact on the traditional optimization design.Foreign scholars have invested a lot of research in this field,and the domestic research in this field is just beginning.Firstly,based on the density penalty method,the paper studies the topology optimization design of two-dimensional beam structure under the minimum flexibility condition.The relative density is the design variable and the volume fraction is the constraint,and the topological optimization model aiming at minimizing the flexibility of continuum structure is established.In the traditional algorithm,the filter mechanism is introduced,and the optimization criteria method topology optimization system model and the mobile asymptote method topology optimization system model are established respectively based on the SIMP model(Solid isotropic microstructure with penalization).Then,the influence of key control parameters(penalty factor,volume ratio and filter radius)on the results based on density stiffness interpolation model and optimization criterion method is discussed by two-dimensional MBB beam(Messerschmitt-Bolkow-Blohm Beam)calculation example,and the appropriate range of values is given.Then,the numerical instability phenomena such as porous materials,which are often found in topology optimization are analyzed with the examples above,and the treatment strategies to overcome these instability phenomena are studied.The paper uses MATLAB programming language to analyze the structural topology optimization of two-dimensional beam model,and gets good results.Secondly,the shortcomings of traditional SIMP model are discussed and improved,and the improved modified SIMP model is finally obtained.Based on the model,the two-dimensional beam structure is analyzed and compared with the common numerical algorithm,which verifies the rationality and effectiveness of the improved method.Finally,based on the level set method,the paper studies the topology optimization design of twodimensional beam structure under the minimum flexibility condition,constructs the horizontal set model of structural topology optimization,develops the level set algorithm program of topology optimization of continuous structure in MATLAB,and realizes the topology optimization of cantilever beam,MBB beam and Michel structure by MATLAB programming.Then,the topology optimization is carried out by using the finite element analysis software,and the comparison and analysis are made with the optimization results of the model system established in this paper,which verifies the effectiveness and feasibility of the proposed model system.Through the topological optimization system models based on density penalty method and horizontal set method,the two-dimensional beam structure is optimized,and the results are compared and analyzed.The experiment shows that the horizontal set method overcomes the serrated boundary in density penalty method,obtains smooth structure boundary,and avoids chessboard phenomenon naturally.Through the system model and the corresponding calculation examples,it is found that a method can improve the iteration efficiency and the objective function better under the premise of ensuring the degree of discreteness,which has certain reference value for the actual project.