Gas holdup is one of the key parameters in flotation process. Gas holdup as measured by a differential pressure method was investigated and the relative errors compared to the average gas holdup from the volume expans...Gas holdup is one of the key parameters in flotation process. Gas holdup as measured by a differential pressure method was investigated and the relative errors compared to the average gas holdup from the volume expansion method. The errors were used to establish optimum measurement positions. The results show that the measurement position should be in the middle of the column and in the region half way from the center to the wall (the half-radius). The gas holdup along the axial direction is lower at the bottom and higher at the top of the floatation column. The gas holdup along the radial direction is lower near the wall and higher near the center of the flotation column. The average gas holdup measure- ment can be replaced by regional gas holdup values.展开更多
The nonlinear finite element（FE） analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities（or gradients） to the model parameters are of significant i...The nonlinear finite element（FE） analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities（or gradients） to the model parameters are of significant importance in these realistic engineering problems.However the sensitivity calculation has lagged behind,leaving a gap between advanced FE response analysis and other research hotspots using the response gradient.The response sensitivity analysis is crucial for any gradient-based algorithms,such as reliability analysis,system identification and structural optimization.Among various sensitivity analysis methods,the direct differential method（DDM） has advantages of computing efficiency and accuracy,providing an ideal tool for the response gradient calculation.This paper extended the DDM framework to realistic complicated soil-foundation-structure interaction（SFSI） models by developing the response gradients for various constraints,element and materials involved.The enhanced framework is applied to three-dimensional SFSI system prototypes for a pilesupported bridge pier and a pile-supported reinforced concrete building frame structure,subjected to earthquake loading conditions.The DDM results are verified by forward finite difference method（FFD）.The relative importance（RI） of the various material parameters on the responses of SFSI system are investigated based on the DDM response sensitivity results.The FFD converges asymptotically toward the DDM results,demonstrating the advantages of DDM（e.g.,accurate,efficient,insensitive to numerical noise）.Furthermore,the RI and effects of the model parameters of structure,foundation and soil materials on the responses of SFSI systems are investigated by taking advantage of the sensitivity analysis results.The extension of DDM to SFSI systems greatly broaden the application areas of the d gradient-based algorithms,e.g.FE model updating and nonlinear system identification of complicated SFSI systems.展开更多
The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody sys...The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.展开更多
基金supports for this work provided by the NationalKey Technology R&D Program in the 11th Five-Year Plan of China(No. 2008BAB31B03)
文摘Gas holdup is one of the key parameters in flotation process. Gas holdup as measured by a differential pressure method was investigated and the relative errors compared to the average gas holdup from the volume expansion method. The errors were used to establish optimum measurement positions. The results show that the measurement position should be in the middle of the column and in the region half way from the center to the wall (the half-radius). The gas holdup along the axial direction is lower at the bottom and higher at the top of the floatation column. The gas holdup along the radial direction is lower near the wall and higher near the center of the flotation column. The average gas holdup measure- ment can be replaced by regional gas holdup values.
基金National Key Research and Development Program of China under Grant No.2016YFC0701106Natural Sciences and Engineering Research Council of Canada via Discovery under Grant No.NSERC RGPIN-2017-05556 Li
文摘The nonlinear finite element（FE） analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities（or gradients） to the model parameters are of significant importance in these realistic engineering problems.However the sensitivity calculation has lagged behind,leaving a gap between advanced FE response analysis and other research hotspots using the response gradient.The response sensitivity analysis is crucial for any gradient-based algorithms,such as reliability analysis,system identification and structural optimization.Among various sensitivity analysis methods,the direct differential method（DDM） has advantages of computing efficiency and accuracy,providing an ideal tool for the response gradient calculation.This paper extended the DDM framework to realistic complicated soil-foundation-structure interaction（SFSI） models by developing the response gradients for various constraints,element and materials involved.The enhanced framework is applied to three-dimensional SFSI system prototypes for a pilesupported bridge pier and a pile-supported reinforced concrete building frame structure,subjected to earthquake loading conditions.The DDM results are verified by forward finite difference method（FFD）.The relative importance（RI） of the various material parameters on the responses of SFSI system are investigated based on the DDM response sensitivity results.The FFD converges asymptotically toward the DDM results,demonstrating the advantages of DDM（e.g.,accurate,efficient,insensitive to numerical noise）.Furthermore,the RI and effects of the model parameters of structure,foundation and soil materials on the responses of SFSI systems are investigated by taking advantage of the sensitivity analysis results.The extension of DDM to SFSI systems greatly broaden the application areas of the d gradient-based algorithms,e.g.FE model updating and nonlinear system identification of complicated SFSI systems.
基金supported by National Defense Pre-research Foundation of China during the 12th Five-Year Plan Period(Grant No.51036050107)
文摘The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.
