Common tools based on landmarks in medical image elastic registration are Thin Plate Spline (TPS) and Compact Support Radial Basis Function (CSRBF). TPS forces the corresponding landmarks to exactly match each other a...Common tools based on landmarks in medical image elastic registration are Thin Plate Spline (TPS) and Compact Support Radial Basis Function (CSRBF). TPS forces the corresponding landmarks to exactly match each other and minimizes the bending energy of the whole image. However, in real application, such scheme would deform the image globally when deformation is only local. CSRBF needs manually determine the support size, although its deformation is limited local. Therefore, to limit the effect of the deformation, new Compact Support Thin Plate Spline algorithm (CSTPS) is approached, analyzed and applied. Such new approach gains optimal mutual information, which shows its registration result satisfactory. The experiments also show it can apply in both local and global elastic registration.展开更多
The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The supp...The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.展开更多
In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable...In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.展开更多
In order to achieve refined precipitation grid data with high accuracy and high spatial resolution,hourly precipitation grid dataset with 1 km spatial resolution in Anhui Province from May to September (in the rainy s...In order to achieve refined precipitation grid data with high accuracy and high spatial resolution,hourly precipitation grid dataset with 1 km spatial resolution in Anhui Province from May to September (in the rainy season) in 2016 and from August 2017 to July 2018 was established based on thin plate smoothing spline (TPS),which meets the needs of climate change research and meteorological disaster risk assessment.The interpolation errors were then analyzed.The grid precipitation product obtained based on thin plate smoothing spline,CLDAS-FAST and CLDAS-FRT were evaluated.The results show that the interpolated values of hourly precipitation by thin plate smoothing spline are close to the observed values in the rainy season of 2016.The errors are generally below 0.9 mm/h.However,the errors of precipitation in the mountainous areas of eastern Huaibei and western Anhui are above 1.2 mm/h.On monthly scale,the errors in June and July are the largest,and the proportion of absolute values of the errors ≥2 mm/h is up to 2.0% in June and 2.2% in July.The errors in September are the smallest,and the proportion of absolute values of the errors ≥2 mm/h is only 0.6%.The root mean square (RMSE) is only 0.37 mm/h,and the correlation coefficient (COR) is 0.93.The interpolation accuracy of CLDAS-FRT is the highest,with the smallest RMSE (0.65 mm/h) and mean error ( ME =0.01 mm/h),and the largest COR (0.81).The accuracy of the precipitation product obtained by thin plate smoothing spline interpolation is close to that of CLDAS-FAST.Its RMSE is up to 0.80 mm/h,and its ME is only -0.01 mm/h.Its COR is 0.73,but its bias (BIAS) is up to 1.06 mm/h.展开更多
The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh disto...The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.展开更多
Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner m...Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.展开更多
In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these t...In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.展开更多
In this paper, Von Karman's set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection bein...In this paper, Von Karman's set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point (SFP) method and by the spline finite element (SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.展开更多
The spline finite strip method (FSM) is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing on...The spline finite strip method (FSM) is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems. To date, no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such, in this paper, the mathematical exact solutions of spline finite strips in the plate analysis are derived using a unitary transformation approach (abbreviated as the U-transformation method herein). These exact solutions are presented for the first time in open literature. Unlike the conventional spline FSM which involves assembly of the global matrix equation and its numerical solution, the U-transformation method decouples the global matrix equation into the one involving only two unknowns, thus rendering the exact solutions of the spline finite strip to be derived explicitly. By taking Taylor's series expansion of the exact solution, error terms and convergence rates are also derived explicitly and compared directly with other numerical methods. In this regard, the spline FSM converges at the same rate as a non-conforming finite element, yet involving a smaller number of unknowns compared to the latter. The convergence rate is also found superior to the conventional finite difference method.展开更多
基金the National Natural Science Foundation of China (No.60572101) the Natural Science Foundation of Guangdong Province (No.31789).
文摘Common tools based on landmarks in medical image elastic registration are Thin Plate Spline (TPS) and Compact Support Radial Basis Function (CSRBF). TPS forces the corresponding landmarks to exactly match each other and minimizes the bending energy of the whole image. However, in real application, such scheme would deform the image globally when deformation is only local. CSRBF needs manually determine the support size, although its deformation is limited local. Therefore, to limit the effect of the deformation, new Compact Support Thin Plate Spline algorithm (CSTPS) is approached, analyzed and applied. Such new approach gains optimal mutual information, which shows its registration result satisfactory. The experiments also show it can apply in both local and global elastic registration.
文摘The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.
文摘In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.
基金Supported by New Technology Integration Project of Anhui Meteorological Bureau(AHXJ201704)Project for Masters and Doctors of Anhui Meteorological Bureau(RC201701)
文摘In order to achieve refined precipitation grid data with high accuracy and high spatial resolution,hourly precipitation grid dataset with 1 km spatial resolution in Anhui Province from May to September (in the rainy season) in 2016 and from August 2017 to July 2018 was established based on thin plate smoothing spline (TPS),which meets the needs of climate change research and meteorological disaster risk assessment.The interpolation errors were then analyzed.The grid precipitation product obtained based on thin plate smoothing spline,CLDAS-FAST and CLDAS-FRT were evaluated.The results show that the interpolated values of hourly precipitation by thin plate smoothing spline are close to the observed values in the rainy season of 2016.The errors are generally below 0.9 mm/h.However,the errors of precipitation in the mountainous areas of eastern Huaibei and western Anhui are above 1.2 mm/h.On monthly scale,the errors in June and July are the largest,and the proportion of absolute values of the errors ≥2 mm/h is up to 2.0% in June and 2.2% in July.The errors in September are the smallest,and the proportion of absolute values of the errors ≥2 mm/h is only 0.6%.The root mean square (RMSE) is only 0.37 mm/h,and the correlation coefficient (COR) is 0.93.The interpolation accuracy of CLDAS-FRT is the highest,with the smallest RMSE (0.65 mm/h) and mean error ( ME =0.01 mm/h),and the largest COR (0.81).The accuracy of the precipitation product obtained by thin plate smoothing spline interpolation is close to that of CLDAS-FAST.Its RMSE is up to 0.80 mm/h,and its ME is only -0.01 mm/h.Its COR is 0.73,but its bias (BIAS) is up to 1.06 mm/h.
基金supported by the National Natural Science Foundation of China(11001037,11102037,11290143)the Fundamental Research Funds for the Central Universities(DUT13LK07)
文摘The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.
文摘Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.
文摘In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.
文摘In this paper, Von Karman's set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point (SFP) method and by the spline finite element (SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.
基金Project supported by the Division Research Grant from City University of Hong Kong(No.DRG 13/08-09)
文摘The spline finite strip method (FSM) is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems. To date, no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such, in this paper, the mathematical exact solutions of spline finite strips in the plate analysis are derived using a unitary transformation approach (abbreviated as the U-transformation method herein). These exact solutions are presented for the first time in open literature. Unlike the conventional spline FSM which involves assembly of the global matrix equation and its numerical solution, the U-transformation method decouples the global matrix equation into the one involving only two unknowns, thus rendering the exact solutions of the spline finite strip to be derived explicitly. By taking Taylor's series expansion of the exact solution, error terms and convergence rates are also derived explicitly and compared directly with other numerical methods. In this regard, the spline FSM converges at the same rate as a non-conforming finite element, yet involving a smaller number of unknowns compared to the latter. The convergence rate is also found superior to the conventional finite difference method.