| Modle updating can effectively reduce the errors of models and actual structures.It is widely used in civil engineering fields and is currently a relatively popular research direction.The research on the existing model updating is mostly based on component stiffness parameter as the updating.There are few studies on the update of constitutive parameters from the perspective of material constitutive model.Therefore,based on the existing research,this paper derives the equilibrium equations of axial force and bending moment to obtain the static response based on the plane section assumption,and establish the relationship between the constitutive parameters and the static response(strain,stiffness,deflection),and conducts a study on the constitutive parameters updating of the model from the constitutive level.The main contents are as follows:1.To update constitutive material model parameters of the structure,the two-type parameter correction method is proposed based on the theoretical model and the response surface model:(1)A method of constitutive material model parameter updating based on the theoretical model.Based on the material constitutive model,the geometric characteristics of the structure and the loading state,the axial force and moment balance equation are deduced from the plane section assumption to calculate the structural response(the method mainly uses the bending stiffness EI),then use Matlab software to establish the theoretical model between response and parameters,and correct the constitutive parameters based on the optimization theory.The example of UHPC constitutive parameter updating shows that the error of constitutive parameters updating is almost zero,indicating that the theoretical model based on EI response can accurately update the nonlinear material constitutive model.(2)A method of constitutive material model parameter updating based on response surface model.According to the material constitutive model,structural geometric characteristics and stress state,the central composite experimental design method(CCD)or Box-Behnken design method(BBD)is used to calculate the structural response from the plane section assumption,and then the polynomial response surface model between the response and parameters is established.The example shows that the error of constitutive parameters updating can be controlled at about 5%,and the correction effect is slightly worse than the theoretical model.2.The EI response is used to analyze the material constitutive parameters updating based on the theoretical model,and the discrimination method for whether the constitutive parameters of flexural beams can be corrected is proposed.When the height of the compression zone is fixed and the discriminant EIB≠O is satisfied,the selected constitutive model can correctly correct the constitutive parameters based on the theoretical model;When the height of the compression zone is not constant,the constitutive group can be corrected accurately based on the theoretical model if there are two parameters to be corrected and the discriminant EIA is>0.4%,three parameters to be corrected and the discriminant EIR is>0.7%,and four parameters to be corrected and the discriminant EIR is>1.5%.3.The parameters of the constitutive models of rebar and concrete commonly used in engineering are optimized,and the feasibility of parameter correction and discrimination methods in engineering applications based on the theoretical model and response surface model is further verified.The constitutive parameters of plain concrete rectangular cross-section beams,reinforced concrete rectangular cross-section beams,plain concrete T-section beams and reinforced concrete T-section beams are corrected by numerical examples.(1)The calculation example shows that the selected constitutive model can be corrected by constitutive parameters when the discriminant is satisfied,which further verifies the feasibility of the discriminant method.(2)Taking EI response,w response and transformed w-1 response as response values respectively,the parameters of the material constitutive model of simple supported rectangular section plain concrete beams are corrected by using the method of parameter updating based on the theoretical model or response surface model.The errors of parameter updating based on the theoretical model and the response surface model can be controlled within 1%and 2%,respectively.The errors of parameter updating based on the response surface model can be controlled within 7%and 3%in response to w and w-1,respectively.(3)Taking EI response,w response and transformed w-1 response as response values respectively,the parameters of the material constitutive model of simply supported beams with rectangular section of reinforced concrete are corrected by using the method of parameter updating based on the theoretical model or response surface model.The errors of parameter updating based on the theoretical model and the response surface model can be controlled within 1%and 5%,respectively.The errors of parameter updating based on the response surface model can be controlled within 9%and 6%in response to w and w-1,respectively.(4)With EI as the response value,the material constitutive model of simple supported beam structure with T-section of plain concrete and reinforced concrete is corrected by the parameter correction method based on the theoretical model.The errors of parameter updating can be controlled within 1%.4.The parameters of the material non-linear constitutive model under the state of compression(tension)are modified,and the discriminant method for whether the model can be corrected is presented.Force analysis and theoretical derivation of the constitutive model are used to establish a theoretical solution model between the material constitutive parameters and the structural strain response ε,and the constitutive parameters can be modified.At the same time,based on the singularity of coefficient matrix,it is proposed to judge whether the material constitutive model can be modified in the state of compression(tension). |
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