CN110489918B - Method for processing elastic displacement of ultra-large floating body in anchoring analysis - Google Patents
Method for processing elastic displacement of ultra-large floating body in anchoring analysis Download PDFInfo
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Abstract
The invention relates to a method for processing elastic displacement of an ultra-large floating body in anchoring analysis, which realizes real-time calculation of the elastic displacement at a mooring point of the ultra-large floating body based on a principal coordinate response and a finite element analysis mode shape result obtained by calculating a three-dimensional water elastic frequency domain of the ultra-large floating body and can provide more accurate input data for the calculation of the tension characteristic of an anchoring system.
Description
Technical Field
The invention relates to the technical field of ocean engineering, in particular to a method for processing elastic displacement of an ultra-large floating body in anchoring analysis.
Background
The ultra-large floating body is widely concerned as an important ocean floating structure, two stages of ultra-large floating body research work are carried out in the last 90 th century in Japan, and related ultra-large floating body design technical research is also carried out in the United states in the same time period. In the 21 st century, a series of research works on ultra-large floating bodies were also carried out in china.
An important aspect of the research of the ultra-large floating body is the design and analysis of a positioning system of the floating body, the main positioning modes comprise two basic modes of dynamic positioning and anchoring positioning, and if the anchoring positioning is adopted, the dynamic characteristics of the anchoring system need to be analyzed in detail in the design process. Due to the large-scale and low-rigidity characteristics of the ultra-large floating body, the floating body can move elastically while doing rigid displacement motion, and the additionally generated elastic displacement motion is very important for accurately analyzing the dynamic characteristics of the anchoring system.
Disclosure of Invention
The applicant aims at the defects in the prior art and provides a method for processing the elastic displacement of the ultra-large floating body in the anchoring analysis, the principle is clear, the quick calculation of the elastic displacement can be realized, and the method is suitable for quickly evaluating the anchoring performance of the ultra-large floating body.
The technical scheme adopted by the invention is as follows:
a method for processing elastic displacement of an ultra-large floating body in anchoring analysis is characterized in that: the method comprises the following operation steps:
the method comprises the following steps: establishing a floating body three-dimensional finite element model, and obtaining the modal shape of the ultra-large floating body through modal analysis, wherein the calculation of the modal shape can be realized through solving a dynamic integral equation of the structure;
step two: selecting proper modal shape quantity as input shape of three-dimensional hydro-elastic calculation by taking the elastic shape obtained by calculation in the step one as an input condition, and calculating the main coordinate response of the ultra-large floating body by combining a three-dimensional hydro-elastic structure kinetic equation;
step three: the elastic modal shape is obtained in the step one, the elastic modal principal coordinate response of the ultra-large floating body is obtained in the step two, the elastic displacement of the ultra-large floating body at the position of the mooring point is obtained through calculation by a modal superposition method, and the elastic displacement expression is an important basis for displacement time domain expression;
step four: establishing and solving a motion equation of the ultra-large floating body and the anchoring system, adding tension of the mooring cable into a right-end term of the motion equation, and performing real-time coupling solution on the motion of the floating body and the tension of the mooring cable;
step five: calculating real-time displacement change data at the mooring point position of the ultra-large floating body, which is caused by the elastic displacement of the floating body, by taking the elastic displacement expression obtained in the third step as input;
step six: and on the basis of the six-degree-of-freedom rigid body motion of the ultra-large floating body obtained in the fourth step, the elastic displacement data are superposed, so that the overall displacement of the mooring point position of the floating body is obtained, and the real-time dynamic characteristic analysis of the anchoring system is realized.
The further technical scheme is as follows:
in the first step, the dynamic integral equation of the structure is involved in solving the elastic mode shape, and the expression is as follows:
wherein [ M ] is a total mass array, [ C ] is a total damping array, [ K ] is a total rigidity array, { U } is a total node displacement array after the object is dispersed, and { F } represents the external force applied to the object.
In the second step, the structural dynamics equation with the generalized principal coordinates as unknowns is described as follows:
wherein [ a ] is a structure generalized mass array; [b] is a generalized damping array; [c] is a generalized stiffness matrix; the corresponding expression of Z, delta and Q represents generalized surface distribution force, generalized concentration force and generalized volume force matrix. { p } is the principal coordinate response obtained by the calculation.
In the third step, the first step is that,
the expression of elastic displacement in the frequency domain is represented by:
Ai(ω) represents the contribution of the elastic mode shape to the displacement of the ith mooring point; m represents the total number of modes including rigid body modes; dji(ω) represents the jth order mode shape of the ith mooring point; p is a radical ofjRe(ω) represents the real part of the fundamental modal response of the j-th order, pjImAnd (ω) represents the imaginary part of the principal mode response of the j-th order.
In the fourth step, the real-time motion condition of the floating body is obtained by solving the coupled motion equation of the floating body and the anchoring system, and the six-degree-of-freedom time domain motion equation is as follows:
wherein [ M ]]Representing a generalized mass array; [ mu ] of]、[m]Representing an additional mass array; [ lambda ]]Representing an additional damping matrix; [ K (t- τ)]Representing an array of delay functions; [ C ]]Representing an array of hydrostatic recovery forces; { f (t) } denotes the generalized fluid force matrix; { Fmoor(t) represents the mooring force array of the mooring system.
In the fifth step and the sixth step, the elastic displacement time history description at the position of the mooring point on the ultra-large floating body can be expressed as:
FRi(t) shows the results of the ith mooring point taking into account the displacement of the buoyant body due to its elastic mode shape. ZetalIs the amplitude corresponding to the first wave frequency component; epsilonlRepresenting the random phase angle of the ith component regular wave;
the initial phase angle of displacement on six rigid body degrees of freedom of the ith mooring point caused by elastic deformation is shown, and N represents the number of waves.
The invention has the following beneficial effects:
the method has the advantages of compact and reasonable structure and convenient operation, and the established elastic displacement processing method can quickly evaluate the contribution of the elastic displacement of the ultra-large floating body to the integral displacement at the mooring point. The elastic displacement can be rapidly calculated based on the finite element modal shape and the water elasticity principal coordinate response of the ultra-large floating body.
The method established by the invention can enable the dynamic characteristics of the mooring cable to be more accurate. In the dynamic characteristic analysis process of the mooring cable, the elastic displacement of the floating body is superposed on the basis of the six-degree-of-freedom motion of the floating body rigid body, so that the motion condition of the floating body is simulated more truly, and the accurate simulation of the characteristics of the mooring cable is facilitated.
The method of the invention is based on the main coordinate response obtained by calculating the three-dimensional hydro-elastic frequency domain of the ultra-large floating body, and the additional influence caused by elastic displacement is added in the anchoring analysis process, so that the time domain analysis of the dynamic characteristic of the anchoring system can be realized.
The method has clear principle, can realize the quick calculation of the elastic displacement, and is suitable for the quick evaluation of the anchoring and mooring performance of the ultra-large floating body.
The invention can be applied to an elastic displacement and anchoring analysis system of an ultra-large floating body arranged in the sea.
Drawings
FIG. 1 is a wet surface mesh model of the ultra-large floating body of the invention.
Fig. 2 shows the mode shape (torsional mode) of the ultra-large floating body according to the present invention.
Fig. 3 is a calculation flow of the elastic displacement at the mooring point of the ultra-large floating body.
FIG. 4 is a schematic diagram of the calculation of the coupling between the ultra-large floating body and the mooring system.
Fig. 5 is a diagram showing the change of the tension of the mooring lines under the action of the elastic displacement of the ultra-large floating body.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
As shown in fig. 3, the method for processing elastic displacement of an ultra-large floating body in the mooring analysis of the embodiment is characterized in that: the method comprises the following operation steps:
the method comprises the following steps: establishing a floating body three-dimensional finite element model, and obtaining the modal shape of the ultra-large floating body through modal analysis, wherein the calculation of the modal shape can be realized through solving a dynamic integral equation of the structure;
step two: selecting proper modal shape quantity as input shape of three-dimensional hydro-elastic calculation by taking the elastic shape obtained by calculation in the step one as an input condition, and calculating the main coordinate response of the ultra-large floating body by combining a three-dimensional hydro-elastic structure kinetic equation;
step three: the elastic modal shape is obtained in the step one, the elastic modal principal coordinate response of the ultra-large floating body is obtained in the step two, the elastic displacement of the ultra-large floating body at the position of the mooring point is obtained through calculation by a modal superposition method, and the elastic displacement expression is an important basis for displacement time domain expression;
step four: establishing and solving a motion equation of the ultra-large floating body and the anchoring system, adding tension of the mooring cable into a right-end term of the motion equation, and performing real-time coupling solution on the motion of the floating body and the tension of the mooring cable;
step five: calculating real-time displacement change data at the mooring point position of the ultra-large floating body, which is caused by the elastic displacement of the floating body, by taking the elastic displacement expression obtained in the third step as input;
step six: and on the basis of the six-degree-of-freedom rigid body motion of the ultra-large floating body obtained in the fourth step, the elastic displacement data are superposed, so that the overall displacement of the mooring point position of the floating body is obtained, and the real-time dynamic characteristic analysis of the anchoring system is realized.
In the first step, the dynamic integral equation of the structure is involved in solving the elastic mode shape, and the expression is as follows:
wherein [ M ] is a total mass array, [ C ] is a total damping array, [ K ] is a total rigidity array, { U } is a total node displacement array after the object is dispersed, and { F } represents the external force applied to the object.
In the second step, the structural dynamics equation with the generalized principal coordinates as unknowns is described as follows:
wherein [ a ] is a structure generalized mass array; [b] is a generalized damping array; [c] is a generalized stiffness matrix; the corresponding expression of Z, delta and Q represents generalized surface distribution force, generalized concentration force and generalized volume force matrix. { p } is the principal coordinate response obtained by the calculation.
In the third step, the first step is that,
the expression of elastic displacement in the frequency domain is represented by:
Ai(ω) represents the contribution of the elastic mode shape to the displacement of the ith mooring point; m represents the total number of modes including rigid body modes; dji(ω) represents the jth order mode shape of the ith mooring point; p is a radical ofjRe(ω) represents the real part of the fundamental modal response of the j-th order, pjImAnd (ω) represents the imaginary part of the principal mode response of the j-th order.
In the fourth step, the real-time motion condition of the floating body is obtained by solving the coupled motion equation of the floating body and the anchoring system, and the six-degree-of-freedom time domain motion equation is as follows:
wherein [ M ]]Representing a generalized mass array; [ mu ] of]、[m]Representing an additional mass array; [ lambda ]]Representing an additional damping matrix; [ K (t- τ)]Representing an array of delay functions; [ C ]]Representing an array of hydrostatic recovery forces; { f (t) } denotes the generalized fluid force matrix; { Fmoor(t) represents the mooring force array of the mooring system.
In the fifth step and the sixth step, the elastic displacement time history description at the position of the mooring point on the ultra-large floating body can be expressed as:
FRi(t) shows the results of the ith mooring point taking into account the displacement of the buoyant body due to its elastic mode shape. ZetalIs the amplitude corresponding to the first wave frequency component; epsilonlRepresenting the random phase angle of the ith component regular wave;
the initial phase angle of displacement on six rigid body degrees of freedom of the ith mooring point caused by elastic deformation is shown, and N represents the number of waves.
The first embodiment is as follows:
in the step of fig. 3, a finite element model of the ultra-large floating body is established, and the elastic mode shape of the floating body is solved. When the elastic mode shape is solved, the integral equation of the dynamics of the structure is involved, and the expression is as follows:
wherein [ M ] is a total mass array, [ C ] is a total damping array, [ K ] is a total rigidity array, { U } is a total node displacement array after the object is dispersed, and { F } represents the external force applied to the object.
Assuming that the right-end term of the equation is zero, the structural object can be subjected to characteristic analysis, the natural frequency and the vibration mode of the structural object are solved, and the node displacement vibration mode of the discrete system is expressed as follows:
[D]＝[{D1},{D2},…,{Dr},…,{Dm}]
wherein, { DrWhere (r is 1, …, m) denotes an r-th order mode node displacement array, corresponding to a natural frequency ωr。
In fig. 3, the elastic modal shape calculated in the step one is provided as an input parameter to the step two, and the principal coordinate response, the hydrodynamic coefficient, the wave excitation force and the like of the ultra-large floating body are calculated. The structural dynamics equation with the generalized principal coordinates as unknowns is described as follows:
wherein [ a ] is a structure generalized mass array; [b] is a generalized damping array; [c] is a generalized stiffness matrix; and the { Z }, {. DELTA }, and { Q } correspond to generalized surface distribution force, generalized concentration force, and generalized volume force matrix. { p } is the principal coordinate response obtained by the calculation.
Step three in fig. 3 calculates the elastic displacement at the location of the mooring point. The expression of elastic displacement in the frequency domain is represented by:
Ai(ω) represents the contribution of the elastic mode shape to the displacement of the ith mooring point; m represents the total number of modes including rigid body modes; dji(ω) represents the jth order mode shape of the ith mooring point; p is a radical ofjRe(ω) represents the real part of the fundamental modal response of the j-th order, pjImAnd (ω) represents the imaginary part of the principal mode response of the j-th order.
Step four in fig. 3 is to obtain the real-time motion condition of the floating body by solving the coupled motion equation of the floating body and the mooring system. The six-degree-of-freedom time domain motion equation is as follows:
wherein [ M ]]Representing a generalized mass array; [ mu ] of]、[m]Representing an additional mass array; [ lambda ]]Representing an additional damping matrix; [ K (t- τ)]Representing an array of delay functions; [ C ]]Representing an array of hydrostatic recovery forces; { f (t) } denotes the generalized fluid force matrix; { Fmoor(t) represents the mooring force array of the mooring system.
Step five in fig. 3 enables a real-time description of the elastic displacement at the mooring point location. The elastic displacement time history description at the mooring point position on the very large buoy can be expressed as:
FRi(t) shows the results of the ith mooring point taking into account the displacement of the buoyant body due to its elastic mode shape. ZetalIs the amplitude corresponding to the first wave frequency component; epsilonlRepresenting the random phase angle of the ith component regular wave;
the initial phase angle of displacement on six rigid body degrees of freedom of the ith mooring point caused by elastic deformation is shown, and N represents the number of waves.
The specific parameters are as follows:
table 1 shows the main parameters of the ultra-large floating body, including total length, total width, draft, displacement, center of gravity position, moment of inertia, etc.
Table 2 shows the parameters of two mooring materials in a mooring system in a very large buoy configuration.
TABLE 1 ultra-large floater main parameters
TABLE 2 catenary parameters
Finally, through the operation steps of the method, the tension change of the mooring cable under the action of the elastic displacement of the floating body shown in the figure 5 is obtained, the real-time calculation of the elastic displacement at the mooring point of the ultra-large floating body is realized, and more accurate input data can be provided for the calculation of the tension characteristic of the anchoring system.
The above description is intended to be illustrative and not restrictive, and the scope of the invention is defined by the appended claims, which may be modified in any manner within the scope of the invention.
Claims (4)
1. A method for processing elastic displacement of an ultra-large floating body in anchoring analysis is characterized in that: the method comprises the following operation steps:
the method comprises the following steps: establishing a floating body three-dimensional finite element model, and obtaining the modal shape of the ultra-large floating body through modal analysis, wherein the calculation of the modal shape can be realized through solving a dynamic integral equation of the structure;
step two: selecting proper modal shape quantity as input shape of three-dimensional hydro-elastic calculation by taking modal shape obtained by calculation in the first step as input condition, and calculating main coordinate response of the ultra-large floating body by combining three-dimensional hydro-elastic structure kinetic equation;
step three: obtaining a modal shape in the step one, obtaining an elastic modal principal coordinate response of the ultra-large floating body in the step two, and calculating and obtaining the elastic displacement of the ultra-large floating body at the position of a mooring point by a modal superposition method, wherein the elastic displacement expression is an important basis for displacement time domain expression;
step four: establishing and solving a motion equation of the ultra-large floating body and the anchoring system, adding tension of the mooring cable into a right-end term of the motion equation, and performing real-time coupling solution on the motion of the floating body and the tension of the mooring cable;
step five: calculating real-time displacement change data at the mooring point position of the ultra-large floating body, which is caused by the elastic displacement of the floating body, by taking the elastic displacement expression obtained in the third step as input;
step six: on the basis of the six-degree-of-freedom rigid body motion of the ultra-large floating body obtained in the fourth step, elastic displacement data are superposed, so that the overall displacement of the mooring point position of the floating body is obtained, and the real-time dynamic characteristic analysis of the anchoring system is realized;
in the third step, the first step is that,
the expression of elastic displacement in the frequency domain is represented by:
Ai(ω) represents the contribution of the elastic mode shape to the displacement of the ith mooring point; m represents the total number of modes including rigid body modes; p is a radical ofjRe(ω) represents the real part of the fundamental modal response of the j-th order, pjIm(ω) represents the response of the dominant mode of the j-th orderAn imaginary part; ω represents the wave frequency; djiRepresenting the magnitude of a j-th order mode shape at an i-th mooring point;
in the fifth step and the sixth step, the elastic displacement time history description at the position of the mooring point on the ultra-large floating body can be expressed as:
FRi(t) represents the result of the ith mooring point in consideration of the displacement of the floating body due to the elastic mode shape of the floating body; zetalIs the amplitude corresponding to the first wave frequency component; epsilonlRepresenting the random phase angle of the ith component regular wave;
representing an initial phase angle of displacement of an ith mooring point on six rigid body degrees of freedom caused by elastic deformation, wherein N represents the number of waves; hRi(ωl) Representing the wave frequency omegalThe contribution value of the elastic modal deformation of the floating body to the displacement of the ith mooring point; k is a radical oflExpressing the wave number of the first component regular wave, x, y expressing the coordinates of the center of gravity of the floating body in a fixed coordinate system, and thetalWave angle, ω, representing the first component regular wavelRepresents the wave frequency of the i-th component regular wave, and t represents the current time.
2. The method for processing the elastic displacement of the ultra-large floating body in the anchoring analysis according to claim 1,
the method is characterized in that: in the first step, the dynamic integral equation of the structure is involved in solving the elastic mode shape, and the expression is as follows:
wherein [ M ] is a total mass array, [ C ] is a total damping array, [ K ] is a total rigidity array, { U } is a total node displacement array after the object is dispersed, and { F } represents the external force applied to the object.
3. The method for processing the elastic displacement of the ultra-large floating body in the anchoring analysis according to claim 1,
the method is characterized in that: in the second step, the structural dynamics equation with the generalized principal coordinates as unknowns is described as follows:
wherein [ a ] is a structure generalized mass array; [b] is a generalized damping array; [c] is a generalized stiffness matrix; the { Z }, { delta }, and { Q } correspondingly represent generalized surface distribution force, generalized concentration force, and generalized volume force arrays; { p } is the principal coordinate response obtained by the calculation.
4. The method for processing the elastic displacement of the ultra-large floating body in the anchoring analysis according to claim 1,
the method is characterized in that: in the fourth step, the real-time motion condition of the floating body is obtained by solving the coupled motion equation of the floating body and the anchoring system, and the six-degree-of-freedom time domain motion equation is as follows:
wherein [ M ]]Representing a generalized mass array; [ mu ] of]、[m]Representing an additional mass array;
representing an array of delay functions; [ C ]]Representing an array of hydrostatic recovery forces; { f (t) } denotes the generalized fluid force matrix; { Fmoor(t) represents a mooring force array of the mooring system;
x (t) represents the displacement variable of the float at time t,
representing the speed variation of the float at time τ, t-tableShowing the current time instant and tau the time instant at which the previous excitation occurred.
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