Bidirectional Evolutionary Structural Optimization Algorithm For Multi-level Materials And Its Application In The Design Of D-Regions

Reinforced concrete deep beams,shear walls and other D-region members have been widely used in engineering,but the difficulties of design caused by complex stress mechanism and unclear stress distribution have not been well solved.In recent years,topology optimization provides a new idea for the design of RC D-region members.Evolutionary structural optimization（ESO）is one of the most commonly used topology optimization method because of its easy implementation and high efficiency.In this paper,the optimization direction and the certainty and probability of optimization criterions are used to classify ESO-type algorithm.At the same time,taking a simply supported deep beam with concentrated load in the middle of the span as an example,the optimization results of forward ESO and BESO are compared The optimization results of forward and backward（GESO and GAESO）are compared with those of single and bidirectional evolutionary structural optimization algorithms（GESO,GAESO and GBESO）.The results show that the bi-direction optimization algorithm has the strongest ability to obtain optimal solution;the efficiency of the backward optimization algorithm is higher than the forward optimization algorithm,and the bi-direction optimization algorithm is the lowest.Finally,the existing problems of evolutionary structural optimization are discussed,and the future development of evolutionary structural optimization algorithms is prospected.To further improve the optimization ability of BESO,by linear interpolation,multiple levels of materials are introduced between the 0-1 materials of BESO.It is developed by taking the utilization of materials as the evaluation parameter to determine the rise and fall of the element between different material levels.The new algorithm can obtain a better solution than the classical,which,on the one hand,has lower compliance with the optimization objective;on the other hand,the topology are more clear and the material utilization rate is higher,and the stress mechanism of the members is further reflected by the distribution of different grades of materials.When discussing the influence of material numbers,it is found that the more the optimized material numbers are,the more the results of the new algorithm can be used to observe details,but it will also lead to the increase of optimization time.Therefore,in practical application,the optimization accuracy and efficiency should be weighed to select the appropriate material scale.At the same time,the optimization results obtained by this algorithm include many kinds of materials with different elastic modulus.At present,there is no method to transfer it into the model of struct and tie model and further complete the reinforcement layout design,so it is not operable in practical engineering.To obtain the optimal reinforcement layout method with strong operability,this paper completes the multi-level BESO based on the separate reinforcement mode.In the optimization,a variety of reinforcement diameter are introduced to determine the rise and fall of different reinforcement materials by stress constraints.The algorithm can intuitively evolve the optimal reinforcement layout to reflect the core tension area of the component and describe the stress degree.The multi-level BESO of reinforcement diameter is more dependent on the preset initial feasible domain of reinforcement.When the wider feasible domain such as the more angle of reinforcements arrangement is used for optimization,the optimization result can be closer to the optimization goal of maximizing the utilization rate of steel bar,but the optimization efficiency will be reduced at the same time.To further verify the optimized reinforcement design,this paper completed the verification and simulation analysis of nonlinear FE model of RC deep beam.The results show that,compared with the empirical method,the component designed according to the optimization results has higher ultimate bearing capacity,and the bearing capacity of the normal section and the inclined section is close to each other.The failure mode can be controlled by adjusting the feasible region of reinforcement,and then adding distributed reinforcement can continue to improve.However,it may cause the change of the relationship between the bearing capacity of the normal section,the inclined section and ultimate failure mode.At the same time,it may also cause the increase of the component stiffness and reduce the deformation capacity.Therefore,in the future,the distribution of diagonal reinforcement can be optimized in the area affected by both normal stress and shear stress or dominated by shear stress,and then the distributed reinforcement can be reasonably added to ensure that the components have the desired ductile failure mode.In general,this paper proposes a multi-level BESO algorithm to improve the optimization capability of ESO-type algorithm,and in this basis,the separation mode is introduced to reinforcement optimization design.Finally,the nonlinear finite element simulation analysis of RC deep beam was completed,and the reinforcement suggestions for RC deep beam were given according to the results of the analysis.