Study On Multi-scale Modeling Method Based On Multi-point Constrained Equation

In recent years,the damage of large-scale structures has also occurred from time to time.Research shows that the damage of structures is the result of gradual evolution from the detail level to the overall level.It is also necessary to analyze and study the local details.However,the single-scale modeling and analysis of large-scale structures can not meet the requirements of computational efficiency and accuracy at the same time.The multi-scale modeling method will establish the micro-element of nodes and the macro-element of the whole.By effectively connecting the interface of different-scale elements,the response of detail parts can be more accurately obtained.In this paper,multi-point constraint equation method is used for multi-scale modeling and analysis.Different interface constraint equations are established by different principles,and the advantages and disadvantages of different connections are analyzed by numerical examples.At the same time,it is applied to practical engineering to further verify its rationality.Combined with the dynamic analysis of transmission tower structure,the application of multi-scale modeling method in dynamic analysis of large-scale structure is studied.The main research results are as follows:(1)Three theoretical methods of establishing multi-point constraint equation based on displacement coordination,work equality and combination of displacement coordination and work equality are expounded.According to three different theories,the node constraint equation of multi-scale connection interface is deduced,and the multi-scale connection of beam-solid element and beam-plate element is realized.(2)The examples of beam-solid element connection and beam-plate element connection are analyzed.Based on three different theories,the multi-scale analysis model of cantilever beam is established.By comparing with the results of the fine model,it is found that the multi-scale model based on displacement coordination principle appears discontinuous stress distribution at the interface of multi-scale connection under the action of axial force;and the multi-scale model is based on the principle of equal work.The multi-scale model,which is based on the combination of displacement coordination and work equivalence,avoids the shortcomings of the first two models and achieves better simulation results.The effects of interface mesh size and interface location on the validity of multi-scale model are studied.The mesh size should be less than 1/3 of the cross-section edge length and the multi-scale interface should avoid the plastic area in order to ensure the accuracy of the multi-scale model analysis.(3)A multi-scale model of semi-rigid T-beam-to-column connections is established.Compared with the force-displacement curves and failure modes obtained by monotonic loading tests,and combined with the results of fine element model analysis,the multi-scale model is proved to be of high accuracy and efficiency.(4)The multi-scale wind-resistant dynamic time history analysis of transmission tower structure is carried out.Firstly,the beam element model is established to analyze the dynamic time history under wind load.Then,the fine element region is coupled with the macro element by the multi-point constraint equation method,and the multi-scale model of the transmission tower is obtained.Further,the multi-scale model is analyzed to obtain the stress and strain of the fine member.Compared with the dynamic analysis results of the beam element model,it is found that the response of the two models in the elastic stage is close,but the response of the multi-scale model in the plastic stage is larger than that of the beam element model,and the bearing capacity of the multi-scale model is also lower than that of the beam element model.