The dynamic behavior of floating offshore wind turbine (FOWT) is crucial for its design and optimization. A novel dynamics analysis method for the spar-type FOWT system is proposed in this paper based on the theorem o...The dynamic behavior of floating offshore wind turbine (FOWT) is crucial for its design and optimization. A novel dynamics analysis method for the spar-type FOWT system is proposed in this paper based on the theorem of moment of momentum and the Newton’s second law. The full nonlinearity of the equations of motion (EOMs) and the full nonlinear coupling between external loads and the motions are preserved in this method. Compared with the conventional methods, this method is more transparent and it can be applied directly to the large-amplitude rotation cases. An in-house code is developed to implement this method. The capability of in-house code is verified by comparing its simulation results with those predicted by FAST. Based on the in-house code, the dynamic responses of a spar-type FOWT system are investigated under various conditions.展开更多
The problem of hydrodynamics of the three-leaf dislocated floating-ring bearing was studied by means of boundary element method.The law including the distribution of pressure on boundary surface(axial,bearing and floa...The problem of hydrodynamics of the three-leaf dislocated floating-ring bearing was studied by means of boundary element method.The law including the distribution of pressure on boundary surface(axial,bearing and floating-ring)and its friction loss in different eccentricities was obtained.The results show that the inner friction of three-leaf dislocated bearing increases from 390.875to 1 091.65,and the inner friction of three-leaf dislocated floating-ring bearing increases from 94.2523to 114.5069with eccentricity varying from 0to 0.075in nondimensional.So changing the pressure and flow field of bearing by adding floating-ring is more stability and less wasted work of friction than three-leaf dislocated bearing.展开更多
With the rapid increase of the number and influence of floating population in China,it is urgently needed to understand the regional types of China＇s floating population and their spatial characteristics. After revie...With the rapid increase of the number and influence of floating population in China,it is urgently needed to understand the regional types of China＇s floating population and their spatial characteristics. After reviewing the current methods for identifying regional types of floating population,this paper puts forward a new composite-index identification method and its modification version which is consisted of two indexes of the net migration rate and gross migration rate. Then,the traditional single-index and the new composite-index identification methods are empirically tested to explore their spatial patterns and characteristics by using China＇s 2000 census data at county level. The results show：（1） The composite-index identification method is much better than traditional single-index method because it can measure the migration direction and scale of floating simultaneously,and in particular it can identify the unique regional types of floating population with large scale of immigration and emigration. （2） The modified composite-index identification method,by using the share of a region＇s certain type of floating population to the total in China as weights,can effectively correct the over-or under-estimated errors due to the rather large or small total population of a region. （3） The spatial patterns of different regional types of China＇s floating population are closely related to the regional differentiation of their natural environment,population density and socio-economic development level. The three active regional types of floating population are mainly located in the eastern part of China with lower elevation,more than 800 mm precipitation,rather higher population densities and economic development levels.展开更多
An integrated structural strength analysis method for a Spar type floating wind turbine is proposed in this paper,and technical issues related to turbine structure modeling and stress combination are also addressed.Th...An integrated structural strength analysis method for a Spar type floating wind turbine is proposed in this paper,and technical issues related to turbine structure modeling and stress combination are also addressed.The NREL-5MW ＂Hywind＂ Spar type wind turbine is adopted as study object.Time-domain dynamic coupled simulations are performed by a fully-coupled aero-hydro-servo-elastic tool,FAST,on the purpose of obtaining the dynamic characteristics of the floating wind turbine,and determining parameters for design load cases of finite element calculation.Then design load cases are identified,and finite element analyses are performed for these design load cases.The structural stresses due to wave-induced loads and wind-induced loads are calculated,and then combined to assess the structural strength of the floating wind turbine.The feasibility of the proposed structural strength analysis method for floating wind turbines is then validated.展开更多
A numerical model is developed by use of the boundary integral equation method to investigate the responses of a two-dimensional floating structure. The structure under consideration consisting of two pontoons, is con...A numerical model is developed by use of the boundary integral equation method to investigate the responses of a two-dimensional floating structure. The structure under consideration consisting of two pontoons, is connected by a rigid framework, and linked to the sea floor by a mooring system. The theoretical conception is based on potential theory with hnear external forces, and applied to an arbitrarily shaped body and water depth. The discussion includes the influence of draft and space between pontoons on the responses of the floating structure. Finally, the validity of the method is adequately verified by experimental results.展开更多
A Constrained Interpolation Profile （CIP）-based model is developed to predict the mooring force of a two-dimensional floating oil storage tank under wave conditions, which is validated against to a newly performed e...A Constrained Interpolation Profile （CIP）-based model is developed to predict the mooring force of a two-dimensional floating oil storage tank under wave conditions, which is validated against to a newly performed experiment. In the experiment, a box-shaped floating oil storage apparatus is used. Computations are performed by an improved CIP-based Cartesian grid model, in which the THINC/SW scheme （THINC： tangent of hyperbola for interface capturing; SW： Slope Weighting）, is used for interface capturing. A multiphase flow solver is adopted to treat the water-air-body interactions. The Immersed Boundary Method （IBM） is implemented to treat the body surface. Main attention is paid to the sum force of mooring line and velocity field around the body. It is found that the sum force of the mooring line increases with increasing wave amplitude. The body suffers from water wave impact and large body motions occur near the free surface. The vortex occurs near the sharp edge, i.e., the sharp bottom comers of the float- ing oil storage tank and the vortex shedding can be captured by the present numerical model. The present model could be further improved by including turbulence model which is currently under development. Comparison between the computational mooring forces and the measured mooring forces is presented with a reasonable agreement. The developed numerical model can predict the mooring line forces very well.展开更多
Very Large Floating Structures (VLFS) have received considerable attention recently. Efficient and accurate estimation of their hydroelastic responses in waves is very important for the design. The most efficient appr...Very Large Floating Structures (VLFS) have received considerable attention recently. Efficient and accurate estimation of their hydroelastic responses in waves is very important for the design. The most efficient approach would obviously be the analytical one, Within the category of analytical approaches, the simplified method proposed by Ohkusu and his colleague are of special characteristics. However, when one studies their methods, several questions arise. The purpose of this paper is to critically study the simplified methods proposed by Ohkusu and his colleague in order to answer these questions. Some problems in their original methods have been found and possible improvements are suggested. It is concluded that the improved simplified method using the same idea of Ohkusu and his colleague could provide a reasonable estimate of the hydroelastic response of mat-like VLFS in a certain range of incident angles of waves.展开更多
Single crystals of La0.67Ca0.33MnO3 and La0.67Ca0.33Mn0.96Fe0.04O3 were obtained by floating zone method. Laue diffraction pattern and rocking curve of the single crystals show that their quality is good. The magnetic...Single crystals of La0.67Ca0.33MnO3 and La0.67Ca0.33Mn0.96Fe0.04O3 were obtained by floating zone method. Laue diffraction pattern and rocking curve of the single crystals show that their quality is good. The magnetic behaviours of these compounds have been studied. Fe doping significantly depresses the magnetic contribution to the total specific heat Cp, but slightly influences the lattice contribution at temperatures above 50K. The peak of Cp shifts towards high temperatures with increasing magnetic field. Both single crystals exhibit the first-order magnetic transition around the Curie temperature.展开更多
A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fo...A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.展开更多
Vertical axis wind turbines(VAWTs) are advantageous for the development of large-scale offshore wind power because the drive system is located at the bottom of the turbine. This study investigates the structural stren...Vertical axis wind turbines(VAWTs) are advantageous for the development of large-scale offshore wind power because the drive system is located at the bottom of the turbine. This study investigates the structural strength of a tri-floater floating foundation supporting a 2.6 MW Darrieus VAWT. Finite element models of the floating foundation were developed using space plate-beam elements. The environmental loads, such as the aerodynamic loads, static wind loads, and wave-current loads, were considered. The general strengths of the floating foundation were calculated for the normal operating case(a cut-out wind speed of 25 m s^(-1) and blade rotation of 12 r min^(-1) were used to analyze the most unfavorable loads) and an extreme case(wind speed of 40 m s^(-1) and parked blades), and the weak components of the structure were analyzed. The results show that the floating foundation meets the strength requirements and the structural stress is highest when the wave, wind, and current are in a collinear direction. The main and secondary supporting bars transmit the loads between the stand columns and the tower foundation, and their stresses are higher than those in the other components. In the actual design, these supporting bars should be strengthened. The aerodynamic loads are very important and should be considered in the structural strength analysis of the floating foundation and the floating wind turbine system.展开更多
The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory...The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.展开更多
Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular w...Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.展开更多
Critical Path Method (CPM) Scheduling has proven to be an effective project management tool. However, teaching the topic has proven difficult to include all elements of CPM yet keep it simple enough for students to un...Critical Path Method (CPM) Scheduling has proven to be an effective project management tool. However, teaching the topic has proven difficult to include all elements of CPM yet keep it simple enough for students to understand. In an effort to simplify the teaching of critical path method scheduling, the issue of two total floats in an activity does not get the attention necessary to address its occurrence. The objective of this paper is to present a mathematical method to show multiple total floats are possible for an activity. Also presented are suggestions for schedule crashing when multiple total floats are found. Two totals floats can be found if constraints (Lag or Lead) or non-Finish-to-Start (FS) relationships, or both are used in a network diagram. Situations are possible where an activity may have a start total float (STF) of zero but have a finish total float (FTF) greater than zero, or vice versa. Because the critical path generally follows the zero total float, these situations, where either the STF or the FTF is critical while the other is not, determines how the critical path activity must be controlled and crashed. This paper will present approaches of how to crash the schedule when a portion of the activity, either start or finish, is critical. Also presented will be methods to teach the subject matter with or without the use of scheduling software. Critical Path Method was revisited to see what the minimal conditions are needed to have activities with two total float. Generalized crashing methods were studied to see if the methods can be used when two total floats exist.展开更多
The free-surface wave interaction with a pontoon-type very large floating structure(VLFS) is analyzed by utilizing a modal expansion method. The modal expansion method consists of separating the hydrodynamic analysis ...The free-surface wave interaction with a pontoon-type very large floating structure(VLFS) is analyzed by utilizing a modal expansion method. The modal expansion method consists of separating the hydrodynamic analysis and the dynamic response analysis of the structure. In the dynamic response analysis of the structure,the deflection of the structure with various edge conditions is decomposed into vibration modes that can be arbitrarily chosen. Free-free beam model, pinned-free beam model and fixed-free beam model are three different types of edge conditions considered in this study. For each of these beam models, the detailed mathematical formulations for calculating the corresponding eigenvalues and eigenmodes have been given, and the mathematical formulations corresponding to the beam models of pinned-free beam and fixed-free beam are novel. For the hydrodynamic analysis of the structure, the boundary value problem(BVP) equations in terms of plate modes have been established, and the BVP equations corresponding to the beam models of pinned-free beam and fixedfree beam are also novel. When these BVP equations are solved numerically, the structure deflections and the wave reflection and transmission coefficients can be obtained. These calculation results point out some findings valuable for engineering design.展开更多
Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwat...Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant No.11632011)
文摘The dynamic behavior of floating offshore wind turbine (FOWT) is crucial for its design and optimization. A novel dynamics analysis method for the spar-type FOWT system is proposed in this paper based on the theorem of moment of momentum and the Newton’s second law. The full nonlinearity of the equations of motion (EOMs) and the full nonlinear coupling between external loads and the motions are preserved in this method. Compared with the conventional methods, this method is more transparent and it can be applied directly to the large-amplitude rotation cases. An in-house code is developed to implement this method. The capability of in-house code is verified by comparing its simulation results with those predicted by FAST. Based on the in-house code, the dynamic responses of a spar-type FOWT system are investigated under various conditions.
基金National Natural Science Foundation of China(11362015)
文摘The problem of hydrodynamics of the three-leaf dislocated floating-ring bearing was studied by means of boundary element method.The law including the distribution of pressure on boundary surface(axial,bearing and floating-ring)and its friction loss in different eccentricities was obtained.The results show that the inner friction of three-leaf dislocated bearing increases from 390.875to 1 091.65,and the inner friction of three-leaf dislocated floating-ring bearing increases from 94.2523to 114.5069with eccentricity varying from 0to 0.075in nondimensional.So changing the pressure and flow field of bearing by adding floating-ring is more stability and less wasted work of friction than three-leaf dislocated bearing.
基金Foundation： Knowledge Innovation Program of the Chinese Academy of Sciences, No.KZCX2-YW-322, National Natural Science Foundation of China, No.40971102 The National Science and Technology Support Plan, No.2006BAJ11B02-04
文摘With the rapid increase of the number and influence of floating population in China,it is urgently needed to understand the regional types of China＇s floating population and their spatial characteristics. After reviewing the current methods for identifying regional types of floating population,this paper puts forward a new composite-index identification method and its modification version which is consisted of two indexes of the net migration rate and gross migration rate. Then,the traditional single-index and the new composite-index identification methods are empirically tested to explore their spatial patterns and characteristics by using China＇s 2000 census data at county level. The results show：（1） The composite-index identification method is much better than traditional single-index method because it can measure the migration direction and scale of floating simultaneously,and in particular it can identify the unique regional types of floating population with large scale of immigration and emigration. （2） The modified composite-index identification method,by using the share of a region＇s certain type of floating population to the total in China as weights,can effectively correct the over-or under-estimated errors due to the rather large or small total population of a region. （3） The spatial patterns of different regional types of China＇s floating population are closely related to the regional differentiation of their natural environment,population density and socio-economic development level. The three active regional types of floating population are mainly located in the eastern part of China with lower elevation,more than 800 mm precipitation,rather higher population densities and economic development levels.
基金financially supported by the National Natural Science Foundation of China(Grant No.51239007)
文摘An integrated structural strength analysis method for a Spar type floating wind turbine is proposed in this paper,and technical issues related to turbine structure modeling and stress combination are also addressed.The NREL-5MW ＂Hywind＂ Spar type wind turbine is adopted as study object.Time-domain dynamic coupled simulations are performed by a fully-coupled aero-hydro-servo-elastic tool,FAST,on the purpose of obtaining the dynamic characteristics of the floating wind turbine,and determining parameters for design load cases of finite element calculation.Then design load cases are identified,and finite element analyses are performed for these design load cases.The structural stresses due to wave-induced loads and wind-induced loads are calculated,and then combined to assess the structural strength of the floating wind turbine.The feasibility of the proposed structural strength analysis method for floating wind turbines is then validated.
文摘A numerical model is developed by use of the boundary integral equation method to investigate the responses of a two-dimensional floating structure. The structure under consideration consisting of two pontoons, is connected by a rigid framework, and linked to the sea floor by a mooring system. The theoretical conception is based on potential theory with hnear external forces, and applied to an arbitrarily shaped body and water depth. The discussion includes the influence of draft and space between pontoons on the responses of the floating structure. Finally, the validity of the method is adequately verified by experimental results.
基金supported by the National Natural Science Foundation of China (51209184,51279186,51479175)
文摘A Constrained Interpolation Profile （CIP）-based model is developed to predict the mooring force of a two-dimensional floating oil storage tank under wave conditions, which is validated against to a newly performed experiment. In the experiment, a box-shaped floating oil storage apparatus is used. Computations are performed by an improved CIP-based Cartesian grid model, in which the THINC/SW scheme （THINC： tangent of hyperbola for interface capturing; SW： Slope Weighting）, is used for interface capturing. A multiphase flow solver is adopted to treat the water-air-body interactions. The Immersed Boundary Method （IBM） is implemented to treat the body surface. Main attention is paid to the sum force of mooring line and velocity field around the body. It is found that the sum force of the mooring line increases with increasing wave amplitude. The body suffers from water wave impact and large body motions occur near the free surface. The vortex occurs near the sharp edge, i.e., the sharp bottom comers of the float- ing oil storage tank and the vortex shedding can be captured by the present numerical model. The present model could be further improved by including turbulence model which is currently under development. Comparison between the computational mooring forces and the measured mooring forces is presented with a reasonable agreement. The developed numerical model can predict the mooring line forces very well.
基金The project was supported by the National Natural Science Foundation of China (Grant No. 50039010) the Science and Technology Development Foundation of Shanghai Municipal Government (Grant No. 00XD14015).
文摘Very Large Floating Structures (VLFS) have received considerable attention recently. Efficient and accurate estimation of their hydroelastic responses in waves is very important for the design. The most efficient approach would obviously be the analytical one, Within the category of analytical approaches, the simplified method proposed by Ohkusu and his colleague are of special characteristics. However, when one studies their methods, several questions arise. The purpose of this paper is to critically study the simplified methods proposed by Ohkusu and his colleague in order to answer these questions. Some problems in their original methods have been found and possible improvements are suggested. It is concluded that the improved simplified method using the same idea of Ohkusu and his colleague could provide a reasonable estimate of the hydroelastic response of mat-like VLFS in a certain range of incident angles of waves.
文摘Single crystals of La0.67Ca0.33MnO3 and La0.67Ca0.33Mn0.96Fe0.04O3 were obtained by floating zone method. Laue diffraction pattern and rocking curve of the single crystals show that their quality is good. The magnetic behaviours of these compounds have been studied. Fe doping significantly depresses the magnetic contribution to the total specific heat Cp, but slightly influences the lattice contribution at temperatures above 50K. The peak of Cp shifts towards high temperatures with increasing magnetic field. Both single crystals exhibit the first-order magnetic transition around the Curie temperature.
基金supported by the National Natural Science Foundation of China (Grant No. 51108224)the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (Grant No. BS2010HZ005)
文摘A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.
基金supported by the National Natural Science Foundation of China(No.51579176)the Natural Science Foundation of Tianjin(No.16JCYBJC21200)the Research Fund of the State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University(No.1501)
文摘Vertical axis wind turbines(VAWTs) are advantageous for the development of large-scale offshore wind power because the drive system is located at the bottom of the turbine. This study investigates the structural strength of a tri-floater floating foundation supporting a 2.6 MW Darrieus VAWT. Finite element models of the floating foundation were developed using space plate-beam elements. The environmental loads, such as the aerodynamic loads, static wind loads, and wave-current loads, were considered. The general strengths of the floating foundation were calculated for the normal operating case(a cut-out wind speed of 25 m s^(-1) and blade rotation of 12 r min^(-1) were used to analyze the most unfavorable loads) and an extreme case(wind speed of 40 m s^(-1) and parked blades), and the weak components of the structure were analyzed. The results show that the floating foundation meets the strength requirements and the structural stress is highest when the wave, wind, and current are in a collinear direction. The main and secondary supporting bars transmit the loads between the stand columns and the tower foundation, and their stresses are higher than those in the other components. In the actual design, these supporting bars should be strengthened. The aerodynamic loads are very important and should be considered in the structural strength analysis of the floating foundation and the floating wind turbine system.
基金supported by the Lloyd's Register Educational Trust (The LRET) through the joint centre involving University College London, Shanghai Jiao Tong University and Harbin Engineering University
文摘The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.
基金the National Key R&D Program of China (Grant No.2016YFE0200100)the National Natural Science Foundation of China (Grant Nos.51490672 and 51479026).
文摘Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions(QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong(2017) proposed a method to divide the QTFs into different components,which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.
文摘Critical Path Method (CPM) Scheduling has proven to be an effective project management tool. However, teaching the topic has proven difficult to include all elements of CPM yet keep it simple enough for students to understand. In an effort to simplify the teaching of critical path method scheduling, the issue of two total floats in an activity does not get the attention necessary to address its occurrence. The objective of this paper is to present a mathematical method to show multiple total floats are possible for an activity. Also presented are suggestions for schedule crashing when multiple total floats are found. Two totals floats can be found if constraints (Lag or Lead) or non-Finish-to-Start (FS) relationships, or both are used in a network diagram. Situations are possible where an activity may have a start total float (STF) of zero but have a finish total float (FTF) greater than zero, or vice versa. Because the critical path generally follows the zero total float, these situations, where either the STF or the FTF is critical while the other is not, determines how the critical path activity must be controlled and crashed. This paper will present approaches of how to crash the schedule when a portion of the activity, either start or finish, is critical. Also presented will be methods to teach the subject matter with or without the use of scheduling software. Critical Path Method was revisited to see what the minimal conditions are needed to have activities with two total float. Generalized crashing methods were studied to see if the methods can be used when two total floats exist.
基金the Research Project from the Chinese State Key Laboratory of Ocean Engineering of Shanghai Jiao Tong University(No.GKZD010038)
文摘The free-surface wave interaction with a pontoon-type very large floating structure(VLFS) is analyzed by utilizing a modal expansion method. The modal expansion method consists of separating the hydrodynamic analysis and the dynamic response analysis of the structure. In the dynamic response analysis of the structure,the deflection of the structure with various edge conditions is decomposed into vibration modes that can be arbitrarily chosen. Free-free beam model, pinned-free beam model and fixed-free beam model are three different types of edge conditions considered in this study. For each of these beam models, the detailed mathematical formulations for calculating the corresponding eigenvalues and eigenmodes have been given, and the mathematical formulations corresponding to the beam models of pinned-free beam and fixed-free beam are novel. For the hydrodynamic analysis of the structure, the boundary value problem(BVP) equations in terms of plate modes have been established, and the BVP equations corresponding to the beam models of pinned-free beam and fixedfree beam are also novel. When these BVP equations are solved numerically, the structure deflections and the wave reflection and transmission coefficients can be obtained. These calculation results point out some findings valuable for engineering design.
基金supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant no.51021004)the Research Fund of State Key Laboratory in Ocean Engineering of Shanghai Jiaotong University(Grant no.1104)the Scientific Research Foundation of Civil Aviation University of China(Grant no.09QD08X)
文摘Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.
