Optimization Of Domes Against Instability Considering Joints' Mechanical Performance

Stability is the determinant factor in the design of domes,and it becomes more prominent as the span increases.However,the problem of stability is considered merely through verification according to current codes and specifications.The current design process can't consider the interaction between the designation of members and the global stability.This separation will lead to repeated design and verification,thus reducing the design efficiency.On the other hand,a large number of novel joints have been proposed for assembly in-situ with the industrialization of construction in our country.These new joints are neither rigid nor pinned.Nevertheless,joints are still assumed to be ideally rigid in the design process and stability verification.The performance of these newly-proposed joints can't be considered in the design process and stability verification,which limits the application and promotion of novel joints.With respect to the aforementioned problems,the instability mechanism of domes has been revealed from a new perspective,and then an optimization against instability with the assumption of rigid joint has been proposed.Afterwards,optimal design of joints has been carried out,and a collection of new joints with reasonable configurations has been obtained.Finally,the performance of joints has been introduced to the optimization of domes against instability.Thus,an optimization design of domes considering joints' stiffness has been proposed.External factors,such as load and supports,have been introduced to the classical theory of form vulnerability so that the defect of the theory is overcome.The extent of degradation of joint's stiffness has been represented quantitatively by the extended theory.And the instability mechanism has been revealed from the perspective of structural degradation.Three domes with different spans under full-span uniform load,half-span uniform load and vertex concentrated load have been studied to verify the instability mechanism.These case studies have come to conclude the most unfavorable load pattern from the perspective of stability as well.Based on the instability mechanism of space domes,an optimization model of domes against instability has been formulated with the the assumption of rigid joints.The objective of the optimization is to reduce the instability trend so that the stability is improved.Discrete member sections are taken as the optimization variables.Design requirements according to the specifications and steel consumption of members are taken as the optimization constraints.Conventional optimization algorithms generally fail to solve optimization models with a great amount of variables.The random mutation in canonical genetic algorithm has been modified to guided mutation to solve the optimization model with so many variables quickly.Finally,one small-span dome with a span of 22 meters,a medium-span dome with a span of 50 meters and a large-span dome with a span of 80 meters have been taken as illustrative examples to verify the optimization method.The optimal dome with a span of 22 meters consumes no more than 29.31kg/m2 steel,but its capacity of stability is 27.9% higher than that of the initial dome.The optimal dome with a span of 50 meters consumes no more than 24.46kg/m2 steel,but its capacity of stability is 22.1% higher than that of the initial dome.The optimal dome with a span of 80 meters consumes no more than 46kg/m2 steel,but its capacity of stability is 30.5% higher than that of the initial dome.To further verify the optimization design method,optimization against instability have been conducted upon two large-scale domes,which were constructed for shaking table collapse experiments.There are as many as 3660 optimization variables for each shell and 575 candidate sections for each variable.As for the two large-scale domes,the optimization design method have managed to get the optimal results which are solved by the modified GA.The stability of two optimal domes,whose steel consumption is limited to a given volume,has been elevated 1.732 times and 1.812 times,respectively.The elevation of the stability of two large-scale domes has verified the adaptability of the optimization method.On the other hand,determinant parameters of the two initial domes are the same except section designations.The two corresponding optimal domes finally consume nearly the same steel and have similar capacity of stability.It demonstrates that even though the initial domes are different in section designation,the algorithm manage to search out the optimal solution and keep convergent subjected to other identical conditions,such as supports,total steel consumption,material performance,geometric size and configuration.This demonstration has verified the robustness of the optimization method.Finally,to check the anti-collapse ability of the optimal domes subjected to intensive earthquake,the load-displacement curves of the optimal domes have been calculated via numerical simulation.And the load-displacement curves of the optimal domes have been compared to those of the initial domes via shaking table collapse experiment.The comparison has demonstrated that the anti-collapse ability of both optimal domes under intensive earthquake is 2 times higher than that of the initial domes,and the corresponding collapse mode is obviously improved.To enrich the form of connections for domes,optimal design of joints has been conducted from two aspects: increasing the rotational stiffness and improving the safety performance.To increase the rotational stiffness,an optimization model of the joint core has been formulated,and the technical problem of how to apply the equvilent concentrated force on the joint has been solved.Topology optimization has been performed on the joint core subjected to design requirements.At the same time,a universal connecting interface has been designed according to the requirements of prefabricated joints for assembly construction.This interface manages to connect members from different directions.To improve the security performance of joints,an index to evaluate the security performance of joints has been introduced.Based on this index,a security optimization of joints has been formulated,and the corresponding algorithm has been compiled.Two planar joints have been optimized to verify the security optimization.The classical theory of form vulnerability can not consider joint stiffness.This theory has been further extended by modifying the element stiffness matrix to consider joint stiffness.Furthermore,from the viewpoints of the degradation of semi-rigid joint's wellformedness and the stability bearing capacity of the dome,the influence of joint stiffness on stability has been studied quantitatively and the reasonable range of joint stiffness has been determined simultaneously.Optimal design has been conducted on joints with different sizes whose stiffness is within the reasonable range.In this way,a collection of optimal joints has been formulated.Afterwards,an optimization against instability considering joint stiffness has been proposed and the corresponding algorithm has been compiled.In the optimization against instability considering joint stiffness,reducing the instability trend is taken as the objective,members and joints are taken as the variables simultaneously.Member sections are chosen from the standard sections,and joints are chosen from the optimal joint collection.Design requirements according to design codes,limitations of joint steel consumption and member steel consumption are taken as the constraints.The identical large-span dome(80m span),the identical medium-span dome(50m span)and the identical small-span dome(22m span)have been selected as the verification examples as well.The determinant parameters of the three identical domes,such as span,ratio of span to height,configuration and total steel consumption,keep constant with those in the stability optimization based on rigid joint.The capacity of stability of the optimal 22m-span dome with semirigid joints is 2.03 times higher than that of the initial dome and nearly equal to that of the corresponding optimal dome with rigid joints,but the steel consumption for joint of the optimal dome with semi-rigid joints is 40.0% lower than that of the optimal dome with rigid joints.The capacity of stability of the optimal 50 mspan dome with semi-rigid joints is 1.52 times higher than that of the initial dome and nearly equal to that of the corresponding optimal dome with rigid joints,but the steel consumption for joint of the optimal dome with semi-rigid joints is 66.7% lower than that of the optimal dome with rigid joints.The capacity of stability of the optimal 80m-span dome with semi-rigid joints is 1.74 times higher than that of the initial dome and nearly equal to that of the corresponding optimal dome with rigid joints,but the steel consumption for joint of the optimal dome with semi-rigid joints is 64.8% lower than that of the optimal dome with rigid joints.Finally,the anti-collapse ability of optimal domes with semi-rigid joints under intensive earthquake has been checked as the joints are transferred from rigid connections to semi-rigid connections.The performance of the three optimal domes with semi-rigid joints has been compared with that of the corresponding optimal domes with rigid joints.The comparison illustrates that the critical collapse PGA of optimal domes with semi-rigid joints is lower than that of the optimal domes with rigid joints,but it is higher than the maximum acceleration of ground motion according to Chinese seismic codes.Thus,it is demonstrated that optimal domes with semi-rigid joints still have good anti-collapse ability under intensive earthquake.Main innovations:(1)Considering joint stiffness,load and supports are not taken into account in the classical theory of form vulnerability,the current theory is extended.And the instability mechanism of space domes is disclosed by the extended theory.(2)Considering the defect of current design method,an optimization design against instability aiming at improving the stability directly is proposed to increase the design efficiency.(3)An optimal design method combining topology optimization and design is proposed to develop rigid connections of space domes.As for the joint core which is subjected to complex forces,a topology optimization model is proposed to explore effective configurations via theoretical approach rather than experience.In addition,a solution to the technical problem how to apply the equivalent concentrated force upon the joint is proposed in the process of model building.As for the connecting surface which is linked to the members directly,a universal connecting interface is formulated according to the requirements of prefabricated joints for assembly construction so that members can be connected conveniently,reliably and accurately.(4)Because current design method cannot consider joint stiffness,an optimization design method against instability considering joint stiffness is formulated.This proposed design method takes the effects of members and joint stiffness into account and gives section designation and joints simultaneously.It improves the stability of domes subjected to very saving steel consumption.The optimization design method against instability considering joint stiffness manages to realize refined design and it is beneficial to the application and promotion of new semi-rigid joints.(5)Considering the difficulty of canonical GA to solve large-scale stability optimization problems of reallife buildings,random mutation in canonical GA is improved to guided mutation so that the speed of search is accelerated and the robustness of the algorithm is improved,which provides the algorithm base for the stability optimization of large-scale domes in this paper.