Reinforcement Layout Design Based On Topological Optimization For RC Deep Beams Under Multi-objective Of Stress Or Load

At present,the reinforcement layout design methods of reinforced concrete deep beams mainly include empirical design method and elastic stress design method.However,there are still some problems in their application.Although the absolute bearing capacity of deep beams designed by empirical design method is high,the mechanical support of this method is relatively scarce,and the design of deep beams with openings is not targeted;In addition,the design method of elastic stress is not mature,even the strut and tie model(STM)method which has been widely used and concerned,there are still many problems in the construction and calculation of the model,the drawing of reinforcement layout and the control of the actual failure form of the component.According to the stress distribution,it is a new idea to carry out the optimal reinforcement layout design of deep beams based on topological algorithm in recent years,which shows strong practicability and theoretical reliability of engineering design.However,this kind of method has not been able to solve the problem of multi-objective of stress or load condition that engineering design often needs to face.Therefore,this paper develops reinforcement layout design method based on topological optimization for RC deep beams under multi-objective of stress or load,in which the design method of multi-objective of stress should meet the requirements of various design limit states of deep beams,and be verified by static loading test.However,the optimization design method of multi-objective of load is mainly aimed at the reinforcement layout design of deep beams under multi-load conditions,and finally combined with the STM model method to achieve.The main content of the paper is as follows:Firstly,based on the model of discrete model,the multi-objective topological optimization algorithm of reinforcement stress is developed.In the structural optimization,the full stress state of the reinforcement is always the ideal state when the reinforcement is the optimization object,so the full stress state of the reinforcement is divided into two optimization objectives,that is,on the one hand,based on the sequence of stress values of reinforcements,the low stress elements of steel bars are deleted iteratively to realize the initial optimization of stress uniformity distribution of reinforcements;on the other hand,the corresponding sensitivity is constructed for the peak stress of the reinforcement element,and the deleted reinforcement elements causing the excessive peak stress in each iterative step are continuously revived,so as to achieve the secondary goal of the control of the peak stress of the reinforcement,obtain the topology of the reinforcement with higher optimization degree,and finally realize the full stress state of the reinforcement.After the algorithm is proposed,the optimal reinforcement layout design scheme can be constructed by referring to the corresponding topological solution.For this new design method,from optimization algorithm to reinforcement scheme,its good feasibility,stability and general applicability are verified by several numerical examples,such as simply supported deep beams,deep beams with openings and continuous deep beams.The results show that the new design method has lower subjectivity,higher accuracy and operability compared with the STM method.In order to further verify the ability of the multi-objective topological optimization of reinforcement stress in deep beam design and the reliability of design scheme,two groups contrast tests of deep beam are completed.The first group consists of two deep beams with openings.The empirical design method and the multi-objective topological optimization design method are used to complete the reinforcement layout design,and then the static contrast test is carried out.The test results show that the specimen designed by the multi-objective topological optimization of reinforcement stress can basically maintain the ultimate bearing capacity equivalent to the empirical design method under the condition of less steel consumption,and from the point of view of failure process and shape,the normal section cracks of the specimen designed by this new optimization design method are more fully developed,and the inclined section cracks can also be effectively limited at the same time,so as to show better deformation capacity and energy consumption capacity.The second group consisted of two deep beam specimens with solid web,which used the single-objective topological optimization design method and multi-objective topological optimization design method of reinforcement stress to complete the reinforcement layout design,and then carried out the static contrast test.The test results show that the two specimens are all in the form of normal section failure,but in contrast,the mechanical properties of the reinforcement are fully used in the multi-objective topological optimization design of the reinforcement stress,so the material utilization ratio is also higher,and the ultimate performance is certain advantages in the capacity of energy consumption and ductility of the specimens.After analysis,the concept of multi-objective topological optimization design method for reinforcement stress is in line with the requirements of current code for seismic design "strong shear and weak bending",and at the same time,the full stress utilization of steel bars is realized at a high level,that is,the goal of multi-objective topological optimization method for reinforcement stress is well practiced and basically realized.Finally,aiming at the design objective of multiple load cases,the paper proposes the load multi-objective topological optimization algorithm based on the integrated-elements model,and the design idea combined with the design method of STM.On the one hand,it is evolved from genetic evolutionary structural optimization(GESO)and extend it to the application mode of load multi-objective;on the other hand,based on the topological solution obtained by optimization,the STM model is constructed,the mechanical analysis of the model and the conceptual design of reinforcement layout are completed,and the link between topological optimization and engineering design is connected.Through three numerical examples of deep beams,it is proved that this new method of optimization design under multi-load condition has good feasibility and general applicability for deep beams under different boundary conditions.After research and discussion,starting from the referential and mechanical properties of the STM model,this new method is more suitable for the mechanical properties of deep beam members,and shows the good global optimization ability of the algorithm.In a word,through the research of this paper,the idea of topological optimization design of reinforced concrete deep beam is developed.At the same time,the optimization promotion on multi-objective problems of stress and load makes this optimization more close to the needs of engineering design,which provides an important reference for the design of reinforced concrete deep beam in the future.