Structural Topology Optimization Algorithm Analysis Of Lattice Tower Under Wind Loading

With the rapid development of China’s economic system,the height of lattice tower structures such as transmission tower is constantly increasing,the shape and its structural layout is becoming more complicated.Due to their light weight,the damping of the structural system of lattice tower is also very small,which indicate that the lattice tower in very sensitive to wind loading.Therefore,it is very important to conduct topology optimization for such high-rise structures under wind loading.Although the topology optimization design is more widely developed in the mechanical and aviation industry,its application in the civil engineering industry is still relatively lacking.Although there have been some examples of topology optimization for simple components such as cantilever beams and simply supported beams,the topology optimization for the entire structural system are still relatively few,especially for the structural topology optimization under wind loading.The basic theory of the variable density method adopted for topology optimization procedure was first investigated and its optimization principles and implemental procedure was discussed.Then the phenomenon of numerical instability in the topology optimization process,such as checkerboard effect and grid independence was intoduced.The theoretical basis of three topology optimization algorithm--Optimality Criterion method(OC),Method of Moving Asymptotic(MMA)and interior point method were discussed,then the three optimization algorithms were adopted in the topology optimization on a beam structure for a single constraint to verify its effectiveness and correctness.Utilizing the variable density method,the topology optimization procedure was described by selecting the overnall stiffness,the total volume or the fundamental frequency of the optimized structure as the optimization object and selecting the total volume and/or displacement as the single or multiple constraints.The OC,MMA and interior point method were then adopted to solve the various topology optimization problems in this disertation,and detailed comparative analysis was also conducted for the optimized results from the three optimization algorithms.Meanwhile the application of fixed point iteration for OC based topology optimization algorithm was investigated to speed up the optimization process.Finally,by taking a self-standing lattice tower as an example,the wind-induced response and its equivalent static wind loading were obtained by the SAP2000 Application Programme Interface(API)with MATLAB software.By adopting the overall and decomposition method,topology optimization were conducted for the lattice tower under wind loading by updating the equivalent static wind load due to the change in structural layout and member size during the optimization procedure.In the variable density method in topology optimization,the numerical instability phenomena such as the checkerboard effect and grid independence were discussed.The topology optimization of a beam structural system for a single constraint such as volume or displacement wsa carried out with OC,MMA and interior point algorithms.The comparison and analysis on optimization results from these three methods verify the effectiveness of the three optimization methods in the topology optimization design procedure.Based on the topology optimization algorithm for single constraint,the methodology of the variable density method in topology optimization for multiple constraints was then conducted.Three types of topology optimization problems were analyzed separately:1)Volume optimization for displacement and frequency constraints 2)Stiffness optimization for volume and displacement constraints 3)Volume optimization for multiple displacement constraints.The OC,MMA and interior point methods were also adopted for sloving the above topology optimization cases,and topology optimization results from these three methods were then compared to investigate the effectiveness and degree of convergence in the optimal solution algorithmThe application of fixed-point iterative method for OC based topology optimization algorithm was investigated to accelerate the optimization process.The principle of three different fixed-point iterative methods were described,which includes simple mixing method,Anderson mixing method and periodic Anderson extrapolation method.By comparing the topology optimization results for the same optimization case,it was verified that the application of periodic Anderson extrapolation method in OC method could obtain the higher efficiency optimization resultsFinally,a 27-meter self-standing lattice tower is taken as an example for topology optimization on this type of structure under wind loading by upating the equivalent static wind loading during the iteration procedure in topology optimization.The concept of hierarchical and decomposition method for topology optimization and its implementing procedure were introduced.At the same time,the topology optimization for the lattice tower by both overall and decomposition method were conducted,and the topology optimization results from these two methods were compared.For this self-supporting lattice tower,the maximum overall stiffnes is considered as the optimization object,and the volume and/or displacement are selected as the constraints.The wind resistant topology optimization results for the lattice tower under single and multiple constraints were analyzed and discussed in detail.