Research On Hybrid Optimization Method Of Structural Topology And Size Based On Skeleton Extraction Algorithm

Topology optimization is an important branch of structural optimization,which can seek the optimal material density distribution under the condition of definite load and constraint,so as to make full use of the material bearing capacity to enhance the mechanical performance of the structure and minimize the waste of unnecessary materials.Consequently,the structural design has good mechanical properties and economic benefits.Solid Isotropic Microstructures with Penalization（SIMP）is one of the most widely used continuum topology optimization methods,which is easy to program and has fast iterative convergence.However,on the one hand,due to the large number of middle gray units and serious serration of boundary,SIMP is not suitable for direct industrial design and manufacture.On the other hand,for building structures,the topology configuration obtained by continuum topology optimization methods such as SIMP method often needs to be transformed into bar system structures in order to be more conducive to standardized structural design and construction,to reduce the cost of building the structure.In order to solve the above problems,a hybrid optimization method based on skeleton extraction algorithm is proposed.That is the result of continuum topology optimization is transformed into a good manufacturability bar structure and the size of the bar is further optimized.This method not only makes full use of the advantages of the continuum topology optimization,such as high efficiency and convergence speed,but also can directly provide the optimized topology and bar section size for the structural design.The main work and innovations of this paper are as follows:1.A skeleton extraction algorithm is proposed,which is in line with the structural features of the building.From the mathematical morphology point of view,skeleton is considered to be the most effective method to analyze and determine the shape of an object,because it preserves the topology configuration of the original structure and eliminates redundant information.In order to give full play to the advantages of structural skeleton and apply it to the field of structural topology optimization,according to the basic principles of topology optimization and the basic theory of mathematical morphology,a method for extracting structural skeleton based on SIMP topology optimization results is proposed.Based on the definition of skeleton and the theory of excellent skeleton properties,this method extracts the skeleton of the topology optimization image and effectively filters the redundant information in the image,the extracted skeleton is refined to avoid the suspension of the skeleton structure（that is,losing the support）and the suspension of the loading point（that is,the loading point loses contact with the skeleton）,the extracted skeleton conforms to the structural characteristics of the building and reflects the optimal topology of the structure more effectively.Finally,the heuristic optimization iterative scheme of design variables with volume and displacement constraints is constructed,so that the optimization criterion method can adapt to the topology optimization problem with multiple constraints（volume and displacement constraints）.Finally,the influences of different parameters,including penalty factor,filter radius and cell mesh division,on the results of continuum topology optimization are studied,and the parameter values that are in line with engineering practice are summarized.2.The algorithm of node identification and the generation of the skeleton is presented.Among the existing design methods of the skeleton structure based on topology optimization and skeleton extraction,the extracted skeleton node diagram is rather rough.Moreover,the process of connecting the joint to form the bar system structure needs manual intervention,which will greatly increase the workload for the complex three-dimensional structure.Therefore,based on the structure skeleton extracted in the first step,this paper further proposes a node extraction and member recognition algorithm,which can automatically extract the structure skeleton node through the judgment model of the structure skeleton node by computer programming,according to the criterion of merging the adjacent nodes,the adjacent nodes are automatically merged to eliminate the short bars.Then,the self-developed bars recognition algorithm is used to identify and generate the bars based on the structural skeleton diagram,the computer automatic processing of the whole process from the result of continuum topology optimization to the bar system structure with good manufacturability is realized.3.A complete structure topology and dimension hybrid optimization design framework is proposed.Due to the large number of permutations and combinations of discrete topology optimization node connections,such topology optimization calculation often takes several days or even longer.Based on the above work,a complete structure topology and dimension hybrid optimization design framework is proposed in this paper.This method firstly uses any continuum topology optimization method including SIMP method to obtain the topology configuration of the structure,which usually takes only minutes to tens of minutes.Then,the structure topology of the rod system is obtained based on the above methods of skeleton extraction,node extraction and rod recognition.Finally,the section size of the rod system is optimized.This hybrid optimization design method is a bridge between continuum topology optimization and lattice structure size optimization,and builds a complete framework of structural topology and size hybrid optimization design,which creatively connects topology optimization to component size optimization.The overall calculation time is usually tens of minutes,which is superior to the calculation time of several days in discrete topology optimization,and provides a new idea for structural optimization design.