Research Of The Topology Optimization Design Method Based On The Level Set Theory

In order to obtain a new machine with better functions, lower cost and meetingmore personalized market demands, structure optimization design has become one ofthe mainstream methods of modern mechanical design. Structure optimization designhas three methods, which are: size optimization, shape optimization and topologyoptimization, compared with the other two methods, topology optimization has moredesign freedom and larger design space, which could provide an optimal layout designproject in the early stage of design. Topology optimization has been considered to be themost promising optimization method. In the current topology optimization designmethods, level set method can avoid the grid dependency and the phenomenon ofcheckerboard lattice more effectively. The level set method could achieve more difficultshape and topology optimization design at the same time. However, the theory of levelset method needs further development. Since the range of applications has been limitedin two dimensional structure optimization. To apply this method into engineering, needsfurther research definitely.The paper will further develop the level set theory, using the level set method to theproblem of three dimensional elastic structure with concentrated load or body loadtopology optimization. The research contents are carried out as the following aspects:1. Firstly, establishing the finite element analysis model of the level set topologyoptimization method, according to finite element statics analysis theory, by softwareimplementation. Compairing the results of two different examples with ANSYSsoftware results, the relative errors are0.094%and0, which have proved the correctnessof the model. Secondly, according to the level set theory, achieves the method forsolving the level set function and deduce the level set evolving model, and implementby software, in the meantime verify the correctness of the algorithm. Thirdly, accordingto augmented multiplier method theory, establish augmented multiplier method modelof the level set topology optimization method. comparing with theoretical resultsthrough an examples, the relative errors are0, proved the correctness of this model.2. Build the optimization models with flexibility as the objective function andvolume ratio as constraint for two dimension structures with concentrated load and threedimension structures with concentrated load or body loads. Solve the time derivatives ofthe optimization model, and achieve the level set evolution velocity field ofoptimization models. In order to facilitate programming, provide the numerical form ofvolume, evolution velocity field, and other parameters, and the processing method ofthe body load. Comparing various ways of generating holes, present a simple ways of generating holes for level set method.3. Based on the theoretical derivation above, establish the solving method of thelevel set topology optimization method. Through six typical examples, including twodimensional and three dimensional structures, verify the validity of level set topologyoptimization model. Two dimensional structures all meet the condition that thedifference between volume ratio of optimization results and required volume ratio issmaller than5×10-3. Three dimensional structures also meet the condition that thedifference between volume ratio of optimization results and required volume ratio issmaller than3×10-3. All examples have reached the required volume ratio.4. Design the ways to test the effectiveness of the builded topological optimizationmodel based on level set. Process a typical cantilever structure (example3), build theexperiment platform, and measure the structural displacement. the experimental resultshave shown that the displacement of comparative structural is twice as much as theoptimization result. Use ANSYS software to test the optimized results effect of otherexamples. All results have shown that the objective functions of comparative structuralare larger than optimization results.Comprehensive experimental results and ANSYS software simulation results haveshown that the builded topological optimization model and solving method based onlevel set in the paper is reasonable and effective for two and three dimensional elasticstructures which only occur elastic deformation and keep the state of equilibrium underthe action of static.