Modification Of Nonlinear Model Of Concrete Beam Based On Response Surface Method

As a numerical structural analysis method,finite element method has been widely used in civil engineering.Due to finite element modeling errors and experimental errors,there are some differences between the calculation results of the finite element model and the measured results.Therefore,the finite element model is update based on the measured data to establish an accurate finite element model.The modified finite element model is beneficial to the detection,maintenance and reinforcement of the bridge.Based on the assumption of a plane section,the strip method is used to compile the nonlinear program of the material of the flexural beam.The strain of each strip in the section under the corresponding curvature can be obtained by the assumption of the plane section.Strip stresses and the internal force is obtained by the constitutive relation of the material.Then the axial position of the section is calculated by the axial force balance equation,and the section bending moment is calculated.The calculation of the moment-curvature relationship is completed,and the load-displacement relationship of the member is obtained by the conjugate beam method.The relationship between the constitutive parameters of the material and the deflection is built by this finite element analysis.The model was modified based on the response surface method.The experimental design was conducted by Box-Behnken-Designs.The design of the constitutive parameters of concrete,steel bars and prestressed tendons was analyzed by Design Expert 8.0 software,and the sensitivity of the deflection response was selected.The parameters are constructed,and the response surface equation is fitted by quadratic polynomial.The measured data is taken as the target value,and the constitutive parameters of the material are corrected.The main conclusions are as follows:1?The variance of the constitutive parameters of the material was analyzed by Design Expert 8.0.The results show that the constitutive parameters of the reinforced concrete beam material have significant influence on the deflection value of f_c,f_t,E_c and E_s.f_y has no significant effect on the deflection value.The constitutive parameters of prestressed reinforced concrete beams have significant effects on the deflection values of f_c,f_t,E_c,E_s,E_p and f_b.f_y has no significant effect on the deflection value,and f_t,E_p and f_b are sometimes not significant.According to the specific analysis of the stress state of the beam.2?The response surface equation is quadratic polynomial,and the 2R criterion is utilized to test the accuracy of each response surface equation.It is noted that the correlation coefficients R² and R²_adj of each response surface equation are close to 1,indicating that the accuracy of the response surface equation is good.Therefore,the material constitutive The response surface equation for parameters and deflection values can be provided with a quadratic polynomial.3?Through the numerical simulation of reinforced concrete beams and prestressed concrete beams,the correction results show that the error of the parameters to be corrected is reduced to about 3%after the reinforced concrete simply supported beam is rectified by the response surface model.The corrected deflection value is compared with the actual value.The error is within 1%;the prestressed reinforced concrete simply supported beam,after correction by the response surface model,except for the parameter f_t,the error of other parameters to be corrected is reduced to about 3%,and the relative error of the deflection value is reduced from 51%to within 1%.Verify that this method is correct.4?By comparing the material linearity and nonlinear model correction,it can be seen that when the material linear model is modified,the modified parameters are substituted into the finite element model,and the calculated response value can only predict the deflection value of the simply supported beam without cracking.The deflection value after cracking is large and cannot be predicted well.When the material nonlinear model is modified,the modified parameters are substituted into the finite element model to calculate the mid-span deflection corresponding to the force.The curve shows that the modified parameters can well predict the entire process of the simply supported beam.5?The constitutive parameters of the material in the initial finite element model were corrected by the measured data of a 2m span reinforced concrete simply supported beam and a prestressed reinforced concrete simply supported beam with a span of 8m.The mid-span deflection under the grading load is used as the response value.The correction results show that the reinforced concrete simply supported beam is substituted into the finite element software to calculate the deflection value.The deviation between the deflection value and the true value is equal to 5%.Meet the accuracy requirements of the project.For the prestressed reinforced concrete simply supported beam,the corrected deflection value is within 3%of the actual value,indicating that the correction method can be implemented in actual engineering.