Based on mechanical characteristics such as large vertical load, large horizontal load, large bending moment and complex geological conditions, a large scale composite bucket foundation (CBF) is put forward. Both th...Based on mechanical characteristics such as large vertical load, large horizontal load, large bending moment and complex geological conditions, a large scale composite bucket foundation (CBF) is put forward. Both the theoretical analysis and numerical simulation are employed to study the bearing capacity of CBF and the relationship between loads and ground deformation. Furthermore, monopile, high-rise pile cap, tripod and CBF designs are compared to analyze the bearing capacity and ground deformation, with a 3-MW wind generator as an example. The resuits indicate that CBF can effectively bear horizontal load and large bending moment resulting from upper structures and environmental load.展开更多
Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model, three-dimensional turbulent flow in four low-specific-speed centrifugal impellers are simulated numerically and analyzed. The relativ...Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model, three-dimensional turbulent flow in four low-specific-speed centrifugal impellers are simulated numerically and analyzed. The relative velocity distribution, pressure distribution and static pressure rise at the design point are obtained for the regular impeller with only long blades and three complex impellers with long, mid or short blades. It is found that the back flow region between long-blade pressure side and mid-blade suction side is diminished and is pushed to pressure side of short blades near the outlet of impeller at suction side by the introduction of mid, short blades, and the size of back flow becomes smaller in a multi-blade complex impeller. And the pressure rises uniformly from inlet to outlet in all the impellers. The simulated results show that the complex impeller with long, mid and short blades can improve the velocity distribution and reduce the back flow in the impeller channel. The experimental results show that the back flow in the impeller has an important influence on the performance of pump and a more-blade complex impeller with long, mid and short blades can effectively solve low flow rate instability of the low-specific-speed centrifugal pump.展开更多
The objective of this work was to investigate the possibility of taper angle correction in cutting of complex micro-mechanical contours using a TruMicro ultra-short pulse laser in combination with the SCANLAB precSYS ...The objective of this work was to investigate the possibility of taper angle correction in cutting of complex micro-mechanical contours using a TruMicro ultra-short pulse laser in combination with the SCANLAB precSYS micro machining sub system. In a first step, the influence of the process parameters on the kerftaper angle of metallic alloys was systematically investigated without beam inclination. A set of base parameters was derived for the subsequent investigations. In a second step, the kerftaper angle was controlled by static beam inclination. In a third step, the same optics was used in its dynamic precession mode to fabricate micro-mechanical components of complex contours with perpendicular 0~ taper angles. It was found that taper angle adjustments of up to 7.5~ are possible with the used setup for cutting applications. Taper angle control is possible both in the static beam inclination mode and in the dynamic precession mode. The static mode could be interesting for contours with sharp inner radii and for achieving faster cutting times similar to results with fixed optics, but would require excellent synchronization of beam inclination and axis motion. The dynamic precession mode would allow an easier integration of the optics into a laser machine but will result in longer cutting times and limitations with respect to achievable inner radii.展开更多
Aiming at the shortcomings of traditional contact measurement methods such as low measurement efficiency,high cost and low accuracy,a non-contact optical measurement method based on the laser displacement sensor is pr...Aiming at the shortcomings of traditional contact measurement methods such as low measurement efficiency,high cost and low accuracy,a non-contact optical measurement method based on the laser displacement sensor is proposed.According to the relevant regulations of the coaxiality error evaluation standard and the structural characteristics of the compound gear shaft,we have designed and built a set of supporting software system as well as a hardware test platform.In this paper,the distance difference threshold and scale threshold methods are used to eliminate outlier data.The least squares circle is selected to calculate the center of the circle and the minimum containment cylinder axis method is used as the reference axis of the composite gear shaft.Compensated by the standard step shaft calibration,the coaxiality error of the composite gear shaft can be measured to be within 0.01 mm in less than two minutes.The range value of the multi-section measurement test is 0.065 mm.The average coaxiality error is∅0.476 mm.展开更多
A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate...A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.展开更多
Aimed at the problem that Fourier decomposition method(FDM)is sensitive to noise and existing mode mixing cannot accurately extract gearbox fault features,a gear fault feature extraction method combining compound dict...Aimed at the problem that Fourier decomposition method(FDM)is sensitive to noise and existing mode mixing cannot accurately extract gearbox fault features,a gear fault feature extraction method combining compound dictionary noise reduction and optimized FDM(OFDM)is proposed.Firstly,the characteristics of the gear signals are used to construct a compound dictionary,and the orthogonal matching pursuit algorithm(OMP)is combined to reduce the noise of the vibration signal.Secondly,in order to overcome the mode mixing phenomenon occuring during the decomposition of FDM,a method of frequency band division based on the extremum of the spectrum is proposed to optimize the decomposition quality.Then,the OFDM is used to decompose the signal into several analytic Fourier intrinsic band functions(AFIBFs).Finally,the AFIBF with the largest correlation coefficient is selected for Hilbert envelope spectrum analysis.The fault feature frequencies of the vibration signal can be accurately extracted.The proposed method is validated through analyzing the gearbox fault simulation signal and the real vibration signals collected from an experimental gearbox.展开更多
The study, conducted in the Canton Erd6-Pala Chad, aims to i) list the different cultural practices, ii) study their impact on the vegetation and iii) determine the methods of co-management of these cultural practi...The study, conducted in the Canton Erd6-Pala Chad, aims to i) list the different cultural practices, ii) study their impact on the vegetation and iii) determine the methods of co-management of these cultural practices. The surveys were realized on 50 households in the village and phytosociological plants in corn, millet, cotton and peanuts cultures. The data analysis by statgraphic and Excel and Principal Component Analysis (PCA) showed that maize production (1,200 kg/ha) ranked first at the expense of cotton (640 kg/ha). They negatively affect climate change (temperature increase (26%), rain drop (20%), land reclamation (18%) and flooding (12%)). Surveys of vegetation on three acres cotton fields (76.17%), millet (81.06%), corn (80.32%) and groundnut (83.56%) showed that there is no significant difference (P = 0.05) on the specific contribution of wood of different types of farming practices. Adventists species herbacious like Thelepogon elegans (27.84%), Hyptis spicigera (19.31%), Teramnus labialis (15.86%) have most important contributions in specific cultures. Methods of crop treatments have a destructive impact on the environment and the loss of biodiversity and the invasion of crops by adventists. Co-management, crop rotation, association of cultures, community forest management, agroforestry and training farmers in the use of inputs will reduce the potential risks of farming practices.展开更多
Design of composites and usage of new polymer materials allows for improvement of constructional properties of belts. Different applications: transmission, conveying or controlling have different meshing in gear. The...Design of composites and usage of new polymer materials allows for improvement of constructional properties of belts. Different applications: transmission, conveying or controlling have different meshing in gear. The work presents meshing model between timing belt and pulley and constructional features of transmission timing belts depending on materials used for their production. While designing timing belt, much attention should be paid to selection of materials, which has significant influence on mechanical properties of belts. This paper attempts to identify the model material and the nature of cooperation of timing belt-pulley; this is basic knowledge for the development of timing belt gear.展开更多
Due to the unique environment of karst landscapes, there are many uncertainties regarding the recovery of vegetation following human disturbance. Through standard wood parsing and growth ring investigation in Puding c...Due to the unique environment of karst landscapes, there are many uncertainties regarding the recovery of vegetation following human disturbance. Through standard wood parsing and growth ring investigation in Puding county in Guizhou province, China, we studied the process of vegetation restoration in karst areas. According to our results, during the recovery of karst vegetation height increases and ground diameter enlargement of tree layers occurred. Increases in the height and ground diameter followed logarithmic and growth curves, respectively. The development time of trees showed continuity, and growth points were randomly distributed. However, with large propagule quantities, vegetation can be directly restored and developed into a secondary high forest without a grass filling stage, and the recovery time is shortened.展开更多
Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model,three dimensional turbulent flow fields in centrifugal pump with long-mid-short blade complex impeller are calculated and analyzed numeric...Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model,three dimensional turbulent flow fields in centrifugal pump with long-mid-short blade complex impeller are calculated and analyzed numerically.The relative velocity and pressure distributions in the flowpart are obtained.It is found that the flow in the passage of the complex impeller is unsymmetrical due to the joint action between volute and impeller.The back-flow region is at inlet of long-blade suction side,near middle part of long-blade pressure side and outlet of short-blade suction side.The flow near volute throat is affected greatly by volute.The relative velocity is large and it is easy to bring back flow at outlet of the complex impeller near volute throat.The static and total pressure rise uniformly from inlet to outlet in the impeller.At impeller outlet,the pressure periodically decreases from pressure side to suction side,and then the static pressure sharply rise near the throat.The experimental results show that the back flow in the impeller has an important influence on the performance of pump.展开更多
A controllable mechanical turbo-compounding(CMTC) system including continuously variable transmission(CVT) and power turbine bypass valve is proposed to recover waste heat from engine exhaust. The combined matching pr...A controllable mechanical turbo-compounding(CMTC) system including continuously variable transmission(CVT) and power turbine bypass valve is proposed to recover waste heat from engine exhaust. The combined matching principle considering swallowing capacity of both charging turbine and power turbine, main gear ratio is investigated at first based on the analysis of individual influence. Then the effects and strategies of CVT and power turbine bypass valve are studied for better performance under off-design conditions. At last, the transient response of intake pressure of engine with CMTC system is researched and the fuel saving potential is tested under driving cycle conditions. The results indicate that the overall fuel efficiency elevates at the off-design conditions if CVT is adopted due to the improvement of power turbine operating efficiency by speed modulation. The diversion of exhaust through power turbine bypass valve under the low load condition is necessary. The back pressure of the charging turbine infuences the transient response of intake pressure for a fixed CMTC configuration. A method featured by the assistance of power turbine bypass valve is tested to improve the transient response of the intake pressure. The fuel consumption reduces by 2% and 3.4% under highway fuel economy test(HWFET) and Tianjin 503(TJ503) driving cycles respectively.展开更多
This article discusses the development of the numerical methods of gas flow coupled with heat transfer,and introduces the fluid net-works method for rapid prediction of the performance of the composite cooling structu...This article discusses the development of the numerical methods of gas flow coupled with heat transfer,and introduces the fluid net-works method for rapid prediction of the performance of the composite cooling structures in turbine blade.The reliability of these methods is verified by comparing experimental data.For a HPT rotor blade,a rapid prediction on the internal cooling structures is first made by using the fluid network analysis,then an assessment of aerodynamic and heat transfer characteristics is conducted.Based on the network analysis results,three ways to improve the design of the cooling structures are tested,i.e.,adjusting the cooling gas flow mass ratios for different inner cooling cavities,reducing the flow resistances of the channel turning structures,and improving the local internal cooling structure geometries with high temperature distribution.Through the verification of full three-dimensional gas/solid/coolant conjugate heat transfer calculation,we conclude that the modified design can make the overall temperature distribution more even by significantly reducing the highest temperature of the blade surface,and reasonably matching the parameters of different coolant inlets.The results show that the proposed calculation methods can remarkably reduce the design cycle of complex turbine blade cooling structure.展开更多
By using Schwarz alternating method, this paper presents asimplified alternating algorithm for the problems of two holes having arbitrary shapes and arrangements in an isotropic homogeneous linear elastic infinite reg...By using Schwarz alternating method, this paper presents asimplified alternating algorithm for the problems of two holes having arbitrary shapes and arrangements in an isotropic homogeneous linear elastic infinite region, and obtains stress and displacement fields for random times of iteration. After precision analysis it is found that the results for twenty times of iteration are of very high precision, and those with higher precision can be acquired if the iteration solving is further conducted. The comparison of the results from FEM further proves the reliability of the simplified alternating algorithm presented by this paper.展开更多
文摘Based on mechanical characteristics such as large vertical load, large horizontal load, large bending moment and complex geological conditions, a large scale composite bucket foundation (CBF) is put forward. Both the theoretical analysis and numerical simulation are employed to study the bearing capacity of CBF and the relationship between loads and ground deformation. Furthermore, monopile, high-rise pile cap, tripod and CBF designs are compared to analyze the bearing capacity and ground deformation, with a 3-MW wind generator as an example. The resuits indicate that CBF can effectively bear horizontal load and large bending moment resulting from upper structures and environmental load.
基金the National Natural Science Foundation of China (No.50576088), the Natural Science Foundation of Zhejiang Province (No.R503170) and the Doctoral Program Foundation of Ministry of Education (No.20030335009).
文摘Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model, three-dimensional turbulent flow in four low-specific-speed centrifugal impellers are simulated numerically and analyzed. The relative velocity distribution, pressure distribution and static pressure rise at the design point are obtained for the regular impeller with only long blades and three complex impellers with long, mid or short blades. It is found that the back flow region between long-blade pressure side and mid-blade suction side is diminished and is pushed to pressure side of short blades near the outlet of impeller at suction side by the introduction of mid, short blades, and the size of back flow becomes smaller in a multi-blade complex impeller. And the pressure rises uniformly from inlet to outlet in all the impellers. The simulated results show that the complex impeller with long, mid and short blades can improve the velocity distribution and reduce the back flow in the impeller channel. The experimental results show that the back flow in the impeller has an important influence on the performance of pump and a more-blade complex impeller with long, mid and short blades can effectively solve low flow rate instability of the low-specific-speed centrifugal pump.
文摘The objective of this work was to investigate the possibility of taper angle correction in cutting of complex micro-mechanical contours using a TruMicro ultra-short pulse laser in combination with the SCANLAB precSYS micro machining sub system. In a first step, the influence of the process parameters on the kerftaper angle of metallic alloys was systematically investigated without beam inclination. A set of base parameters was derived for the subsequent investigations. In a second step, the kerftaper angle was controlled by static beam inclination. In a third step, the same optics was used in its dynamic precession mode to fabricate micro-mechanical components of complex contours with perpendicular 0~ taper angles. It was found that taper angle adjustments of up to 7.5~ are possible with the used setup for cutting applications. Taper angle control is possible both in the static beam inclination mode and in the dynamic precession mode. The static mode could be interesting for contours with sharp inner radii and for achieving faster cutting times similar to results with fixed optics, but would require excellent synchronization of beam inclination and axis motion. The dynamic precession mode would allow an easier integration of the optics into a laser machine but will result in longer cutting times and limitations with respect to achievable inner radii.
基金supported by the National Natural Science Foundation of China(No.51975293)Aeronautical Science Foundation of China (No. 2019ZD052010)
文摘Aiming at the shortcomings of traditional contact measurement methods such as low measurement efficiency,high cost and low accuracy,a non-contact optical measurement method based on the laser displacement sensor is proposed.According to the relevant regulations of the coaxiality error evaluation standard and the structural characteristics of the compound gear shaft,we have designed and built a set of supporting software system as well as a hardware test platform.In this paper,the distance difference threshold and scale threshold methods are used to eliminate outlier data.The least squares circle is selected to calculate the center of the circle and the minimum containment cylinder axis method is used as the reference axis of the composite gear shaft.Compensated by the standard step shaft calibration,the coaxiality error of the composite gear shaft can be measured to be within 0.01 mm in less than two minutes.The range value of the multi-section measurement test is 0.065 mm.The average coaxiality error is∅0.476 mm.
基金Project(51805368)supported by the National Natural Science Foundation of ChinaProject(2018QNRC001)supported by the Young Elite Scientists Sponsorship Program,China+1 种基金Project(DMETKF2021017)supported by the Fund of State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science and Technology,ChinaProject(HTL-0-21G07)supported by the National key Laboratory of Science and Technology on Heicopter Transmission,China。
文摘A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.
基金The National Natural Science Foundation of China(No.51975117)the Key Research&Development Program of Jiangsu Province(No.BE2019086).
文摘Aimed at the problem that Fourier decomposition method(FDM)is sensitive to noise and existing mode mixing cannot accurately extract gearbox fault features,a gear fault feature extraction method combining compound dictionary noise reduction and optimized FDM(OFDM)is proposed.Firstly,the characteristics of the gear signals are used to construct a compound dictionary,and the orthogonal matching pursuit algorithm(OMP)is combined to reduce the noise of the vibration signal.Secondly,in order to overcome the mode mixing phenomenon occuring during the decomposition of FDM,a method of frequency band division based on the extremum of the spectrum is proposed to optimize the decomposition quality.Then,the OFDM is used to decompose the signal into several analytic Fourier intrinsic band functions(AFIBFs).Finally,the AFIBF with the largest correlation coefficient is selected for Hilbert envelope spectrum analysis.The fault feature frequencies of the vibration signal can be accurately extracted.The proposed method is validated through analyzing the gearbox fault simulation signal and the real vibration signals collected from an experimental gearbox.
文摘The study, conducted in the Canton Erd6-Pala Chad, aims to i) list the different cultural practices, ii) study their impact on the vegetation and iii) determine the methods of co-management of these cultural practices. The surveys were realized on 50 households in the village and phytosociological plants in corn, millet, cotton and peanuts cultures. The data analysis by statgraphic and Excel and Principal Component Analysis (PCA) showed that maize production (1,200 kg/ha) ranked first at the expense of cotton (640 kg/ha). They negatively affect climate change (temperature increase (26%), rain drop (20%), land reclamation (18%) and flooding (12%)). Surveys of vegetation on three acres cotton fields (76.17%), millet (81.06%), corn (80.32%) and groundnut (83.56%) showed that there is no significant difference (P = 0.05) on the specific contribution of wood of different types of farming practices. Adventists species herbacious like Thelepogon elegans (27.84%), Hyptis spicigera (19.31%), Teramnus labialis (15.86%) have most important contributions in specific cultures. Methods of crop treatments have a destructive impact on the environment and the loss of biodiversity and the invasion of crops by adventists. Co-management, crop rotation, association of cultures, community forest management, agroforestry and training farmers in the use of inputs will reduce the potential risks of farming practices.
文摘Design of composites and usage of new polymer materials allows for improvement of constructional properties of belts. Different applications: transmission, conveying or controlling have different meshing in gear. The work presents meshing model between timing belt and pulley and constructional features of transmission timing belts depending on materials used for their production. While designing timing belt, much attention should be paid to selection of materials, which has significant influence on mechanical properties of belts. This paper attempts to identify the model material and the nature of cooperation of timing belt-pulley; this is basic knowledge for the development of timing belt gear.
基金the National Key Basic Research Development Program(2013CB956702)Great Basic Research Fund of the Chinese Academy of Sciences(XDA05070405)+1 种基金Great Basic Research Fund of Guizhou Province(QKH-JZ-2014-200203)100 High Level Innovating Project(QKHRC-2015-4022)
文摘Due to the unique environment of karst landscapes, there are many uncertainties regarding the recovery of vegetation following human disturbance. Through standard wood parsing and growth ring investigation in Puding county in Guizhou province, China, we studied the process of vegetation restoration in karst areas. According to our results, during the recovery of karst vegetation height increases and ground diameter enlargement of tree layers occurred. Increases in the height and ground diameter followed logarithmic and growth curves, respectively. The development time of trees showed continuity, and growth points were randomly distributed. However, with large propagule quantities, vegetation can be directly restored and developed into a secondary high forest without a grass filling stage, and the recovery time is shortened.
基金supported by National Natural Science Foundation of China granted No.20706049 and No.50976105Zhejiang Provincial Natural Science Foundation Granted No.R1100530 and No.R107635
文摘Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model,three dimensional turbulent flow fields in centrifugal pump with long-mid-short blade complex impeller are calculated and analyzed numerically.The relative velocity and pressure distributions in the flowpart are obtained.It is found that the flow in the passage of the complex impeller is unsymmetrical due to the joint action between volute and impeller.The back-flow region is at inlet of long-blade suction side,near middle part of long-blade pressure side and outlet of short-blade suction side.The flow near volute throat is affected greatly by volute.The relative velocity is large and it is easy to bring back flow at outlet of the complex impeller near volute throat.The static and total pressure rise uniformly from inlet to outlet in the impeller.At impeller outlet,the pressure periodically decreases from pressure side to suction side,and then the static pressure sharply rise near the throat.The experimental results show that the back flow in the impeller has an important influence on the performance of pump.
基金supported by the National Basic Research Program of China(Grant No.2011CB707206)
文摘A controllable mechanical turbo-compounding(CMTC) system including continuously variable transmission(CVT) and power turbine bypass valve is proposed to recover waste heat from engine exhaust. The combined matching principle considering swallowing capacity of both charging turbine and power turbine, main gear ratio is investigated at first based on the analysis of individual influence. Then the effects and strategies of CVT and power turbine bypass valve are studied for better performance under off-design conditions. At last, the transient response of intake pressure of engine with CMTC system is researched and the fuel saving potential is tested under driving cycle conditions. The results indicate that the overall fuel efficiency elevates at the off-design conditions if CVT is adopted due to the improvement of power turbine operating efficiency by speed modulation. The diversion of exhaust through power turbine bypass valve under the low load condition is necessary. The back pressure of the charging turbine infuences the transient response of intake pressure for a fixed CMTC configuration. A method featured by the assistance of power turbine bypass valve is tested to improve the transient response of the intake pressure. The fuel consumption reduces by 2% and 3.4% under highway fuel economy test(HWFET) and Tianjin 503(TJ503) driving cycles respectively.
基金supported by the National Natural Science Foundation of the innovative group of China(Grant No.51121004)the National Natural Science Foundation of China(Grant No.50706009)
文摘This article discusses the development of the numerical methods of gas flow coupled with heat transfer,and introduces the fluid net-works method for rapid prediction of the performance of the composite cooling structures in turbine blade.The reliability of these methods is verified by comparing experimental data.For a HPT rotor blade,a rapid prediction on the internal cooling structures is first made by using the fluid network analysis,then an assessment of aerodynamic and heat transfer characteristics is conducted.Based on the network analysis results,three ways to improve the design of the cooling structures are tested,i.e.,adjusting the cooling gas flow mass ratios for different inner cooling cavities,reducing the flow resistances of the channel turning structures,and improving the local internal cooling structure geometries with high temperature distribution.Through the verification of full three-dimensional gas/solid/coolant conjugate heat transfer calculation,we conclude that the modified design can make the overall temperature distribution more even by significantly reducing the highest temperature of the blade surface,and reasonably matching the parameters of different coolant inlets.The results show that the proposed calculation methods can remarkably reduce the design cycle of complex turbine blade cooling structure.
基金the National Natural Science Foundation of China (Grant No. 49772166).
文摘By using Schwarz alternating method, this paper presents asimplified alternating algorithm for the problems of two holes having arbitrary shapes and arrangements in an isotropic homogeneous linear elastic infinite region, and obtains stress and displacement fields for random times of iteration. After precision analysis it is found that the results for twenty times of iteration are of very high precision, and those with higher precision can be acquired if the iteration solving is further conducted. The comparison of the results from FEM further proves the reliability of the simplified alternating algorithm presented by this paper.