Full-size mechanical analysis method for flexible offshore floating photovoltaic structure

Abstract

The invention relates to the technical field of photovoltaic equipment, and discloses a full-size mechanical analysis method for a flexible offshore floating photovoltaic structure, which comprises the following steps: establishing a floating photovoltaic geometric model, carrying out multi-scale structural discretization based on stress characteristics, and calculating local adaptive time step lengths and global time step lengths of various components; for all the units of the component type i, the repeated displacement vectors, the internal force and the external force are solved respectively; synchronizing the particles in global time; calculating and integrating the sum of external force and internal force vectors of the particles; and judging whether the Z coordinate of the central point of the cable net structure meets an iteration stopping condition or not to obtain the geometric configuration of the structure under the steady-state effect. According to the scheme, multi-scale structural discretization is carried out based on the stress characteristics of all the components, a self-adaptive time step mechanism and an asynchronous calculation mechanism are introduced, and efficient structural full-size mechanical response calculation is achieved.

Description

Technical Field

[0001] This invention relates to the field of photovoltaic equipment technology, and specifically to a full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea. Background Technology

[0002] Currently, in order to build a new power system with new energy as the mainstay, the new energy industry urgently needs rapid development, and photovoltaic power generation has become a key growth point. Traditional land-based photovoltaic power generation faces core challenges: large-scale land use intensifies land competition and drives up costs, especially in the western region where resources are abundant but insufficient local consumption leads to serious curtailment of solar power; while the eastern region, with its strong electricity demand, is constrained by the high losses and difficulties of long-distance power transmission.

[0003] Therefore, land-intensive floating photovoltaic (PV) systems have attracted attention. While this technology once developed rapidly in inland waters, its development has become relatively limited due to strict ecological protection policies in recent years. Meanwhile, the vast ocean areas, with their abundant wind and solar resources, have become a new focus for new energy development, and the commercialization prospects of offshore floating PV are very broad. However, offshore floating PV is still in its early stages of development. One of the main technical challenges is the need for in-depth research into the complex nonlinear interaction mechanisms between the harsh wind, wave, and current environment and floating structures, especially flexible structures. Existing analytical methods for flexible offshore PV structures face higher requirements.

[0004] As a novel form of marine photovoltaic structure, the mechanical behavior of flexible floating photovoltaic structures under environmental loads exhibits the following characteristics: First, it involves the coupling of multiple components. The entire force transmission path includes various components such as floating units, flexible connecting ropes, longitudinal and transverse cable nets, rigid outer frames, and mooring cables. Rigid and flexible components alternate; the floating units and outer frames are rigid components, while the flexible connecting ropes, longitudinal and transverse cable nets, and mooring cables are flexible components, with loads being transferred alternately between rigid and flexible components. Third, it exhibits a high degree of nonlinearity. The characteristics of the mooring cables determine their large deformation and the large displacement of the surface structure. At the same time, the mechanical behavior of the flexible cable net structure and flexible connecting ropes also exhibits significant geometric nonlinearity. The complex force transmission path involving multiple components and rigid-flexible coupling, as well as the highly nonlinear mechanical behavior during the force transmission process, determines the complexity of the full-scale mechanical analysis of flexible floating photovoltaic structures. Traditional finite element methods suffer from computational convergence issues when dealing with the above problems. Summary of the Invention

[0005] The present invention aims to provide a full-scale mechanical analysis method for flexible floating photovoltaic structures at sea, in order to solve the problems of the complexity and non-convergence of traditional finite element methods in performing full-scale analysis of flexible floating photovoltaic structures.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a full-scale mechanical analysis method for flexible floating photovoltaic structures at sea, comprising: Step 1: Establish the geometric model of the floating photovoltaic system; Step 2: Discretize the scale structure based on the force characteristics to form particles and connecting elements; use rod elements to simulate the photovoltaic pontoon, use cable elements to simulate the longitudinal and transverse cable nets and mooring cables, use relaxed cable element models to simulate flexible connecting ropes, and use beam elements to simulate the rigid outer frame; wherein, the modeling geometric length of the relaxed cable element model is the geometric straight line length between the corner point of the photovoltaic pontoon and the cable net node; Step 3: Assign material properties to each type of component; Step 4: Calculate the local adaptive time step and global time step for various components; Step 5: Apply boundary conditions and loads to distribute the loads equally to the relevant particles; Step 6: Calculate the displacement vector of each particle within each component type i; Step 7: Calculate and integrate the unit internal and external forces of the particles in each component; Step 8: Repeat for each component type i. Next step 6~7; Step 9: Execute Step 6 again, at which point all particles are synchronized in global time; Step 10: Coordinate the positions of particles at the joints of different components; Step 11: Calculate and integrate the unit internal forces and external forces of the particles of each component. In this step, the internal force of the particle at the connection is the sum of the internal force vectors of the units of different component types acting on the particle. Step 12: Determine whether the difference between the Z coordinates of the center point of the cable net structure and the two adjacent global time steps ΔT is less than the preset value. If this stopping iteration condition is not met, repeat steps 5 to 11 above until the stopping iteration condition is met, and complete the geometric configuration of the structure under steady-state action.

[0007] The flexible offshore floating photovoltaic structure consists of five types of components: photovoltaic floating boxes, cable-net structures, soft connection ropes, rigid outer frames, and mooring cables. Among them, the photovoltaic floating boxes in the distributed array are the main load-bearing components, with relatively small deformation under the action of wind, waves, and currents, and can be regarded as rigid components, which are simulated using rod elements. The longitudinal and transverse cable-nets and mooring cables are force-transmitting components that can only withstand tension and not compression, and have the characteristics of large displacement and large deformation during force application, which are simulated using cable elements. For the soft connection ropes, according to the aforementioned characteristics, a new type of cable element model - the slack cable element model is established: the geometric length of the model is the geometric straight-line length between the corner points of the photovoltaic floating box and the nodes of the cable-net (this length is called the 1-fold length). The two ends of the longitudinal and transverse cable-nets are connected to the rigid outer frame, and the rigid outer frame needs to ensure sufficient rigidity to ensure the stability of the cable-net grid, which is simulated using beam elements. This solution conducts multi-scale structural discretization based on the force characteristics of each component, establishes a finite particle model of the flexible offshore floating photovoltaic structure, and introduces an adaptive time step mechanism and an asynchronous calculation mechanism to achieve efficient calculation of the full-scale mechanical response of the structure.

[0008] Preferably, the calculation method for the internal force of the slack element model is as follows: set the stress-free length L0 of the slack cable element to be λ times the length. Whenever calculating the internal force of the element, first determine the relationship between the length L of the element and L0. If the element length L < L0, the internal force is forcibly set to 0, indicating that the soft connection rope is still in a slack state at this time; when L > L0, the internal force is calculated according to the elongation L - L0 of the slack cable element. Due to the slack characteristic of the soft connection rope, a slack element model is established in this solution in combination with its force characteristics to better simulate the actual soft connection rope structure, making the final force analysis result more accurate.

[0009] Preferably, step 4 specifically includes: for each type of component, based on the length, material density, and Young's modulus of its discrete elements, sequentially determine a minimum stable time step shared by all elements within each type of component , as their respective local adaptive step sizes; based on the local adaptive time step Δt i of each type of component, calculate the global time step ΔT, , and find the ratio of the global time step ΔT to each local time step Δt i . .

[0010] Preferably, the local adaptive step sizes of each type of component in step 4 need to meet the following conditions: In the formula, ρ i is the material density of the i-type component, E i is the Young's modulus of the material, and l i is the element length.

[0011] Preferably, step 6 specifically includes: Step 61: For each particle within each component type i, use the central difference method, with its local time step... The particle displacement vector is calculated explicitly in steps over time, as shown in the following formula: In the formula, This indicates that particle J is in time + Δt i The displacement vector at time t, F J Let C1 and C2 be the resultant force vector acting on particle J, and C1 and C2 be the calculated coefficients related to damping. It is a unit The equivalent mass assigned to point J; Step 62: For particles connected to the rigid outer frame element, further calculate the particle's angular displacement using the following formula: In the formula, This indicates that particle J is in time + Δt i The angular displacement at time M J Let J be the net torque acting on particle J. It is a unit The equivalent rotational inertia assigned to point J.

[0012] Preferably, step 7 includes: Step 71: Calculate the element internal force increment based on the element's pure deformation and material constitutive relation, then superimpose it with the element's initial internal force to obtain the element's internal force. The specific formula is as follows: In the formula, K is the stiffness matrix of the element, and Δ is the pure deformation of the element; the internal forces of the rigid outer frame element also include the bending moment internal forces of the element, as shown in the following formula: In the formula This represents the internal force vector of the element at time time t. This represents the bending moment of the element at time time; Step 72: Add all the internal and external forces of all units to the particle. The net force on the particle is: In the formula P J Let J be the vector of the external force acting on particle J. Let α be the internal force vector of the unit α connected to particle J; The resultant force of the rigid outer frame element also includes the resultant moment it experiences, as shown in the following formula: In the formula, Q J Let J be the bending moment caused by the external force. Let be the internal bending moment of unit α connected to particle J.

[0013] Preferably, in step 7, when performing a local time step for a particle within a global time step for a particle of type i, the element internal forces of other types of components acting on the particle at the connection point are directly calculated using the element internal forces obtained from the previous integer multiple of the global time step node. k is an integer and , where time represents the current time point of the particle.

[0014] Preferably, in step 7, the unit deformation of the photovoltaic pontoon, flexible connecting rope, longitudinal and transverse cable net, and mooring cable is the unit's expansion and contraction, calculated using the following formula: In the formula, l time Indicates the length of the unit at time point 'time'; The pure deformation of the rigid frame element is calculated using the following formula: In the formula, A and B represent the two endpoints of the rigid outer frame element, β is the angular deformation of the element endpoint, Δθ is the sum of the rigid body rotation and angular deformation of the element endpoint in a local time step, and γ is the rigid body rotation of the element in a local time step.

[0015] Preferably, in step 2, the mass of the unit is concentrated onto the particle, and the formula for calculating the particle mass is: In the formula, J is the particle number; n is the total number of units connected to particle J. It is a unit The equivalent mass assigned to point J; where, for particles connected to rigid outer frame elements, the particle mass also includes its rotational inertia, as shown in the formula: In the formula, It is a unit The equivalent rotational inertia is assigned to point J. In this scheme, all the mass of the element is concentrated on the particle; the element only serves as a connector, and the particle's mass comes from all the elements connected to it.

[0016] The preferred step 10 specifically includes: when multiple displacement vector calculation results exist for particles at the connection points of different types of components, the displacement vector of such particles is uniformly taken as the result calculated using the larger local time step. Since particles at the connection points belong to units of different types of components, and these units use different local time steps, the particles at the connection points may have results calculated using different local time steps. This can lead to multiple displacement vector calculation results. In this solution, the displacement vector of such particles is uniformly taken as the result calculated using the larger local time step.

[0017] Advantages of this solution: 1. In view of the unique initial relaxation characteristics of flexible connecting ropes, this invention innovatively proposes and establishes a "relaxed rope unit" model, which accurately characterizes the relaxation characteristics of flexible connections, solves the difficulties of traditional methods in directly simulating connectors with specific pre-relaxed lengths, and significantly improves the accuracy of stress state analysis of the connection parts.

[0018] 2. This innovative method integrates cable elements, rod elements, rigid beam elements, and custom relaxed cable elements to accurately match the stress characteristics of various components. It solves the problem that the traditional finite mass method cannot accurately simulate the complex rigid-flexible coupled dynamic characteristics, which leads to difficulties in large-scale full-size analysis.

[0019] 3. An internal force coupling mechanism based on global time step nodes was established, realizing multi-scale rigid-flexible coupling analysis, and providing a reliable method for full-scale mechanical analysis of flexible floating photovoltaic structures at sea.

[0020] 4. The differences in the properties of multi-scale structural components lead to significant variations in their critical stability time steps. Traditional finite-mass methods, to meet the most stringent constraints, employ a globally uniform minimum time step, resulting in low computational efficiency, particularly in large-scale structures. This method innovatively calculates a local adaptive time step for each component type, allowing components of the same type to operate according to their respective Δt values. i The method employs a step-by-step approach and constructs an asynchronous computation mechanism. This approach effectively avoids the computational efficiency bottleneck of a globally unified minimum time step, significantly improving computational efficiency (especially for large structures containing a large number of low-critical-step components), making large-scale full-size simulation analysis of flexible floating photovoltaic structures practical for engineering applications. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating an embodiment of the present invention.

[0022] Figure 2 This is a schematic diagram of a flexible floating photovoltaic structure for marine applications according to an embodiment of the present invention.

[0023] Figure 3 Embodiments of the present invention Figure 2 A schematic diagram of the structure at point A.

[0024] Figure 4 This is a diagram of a flexible floating photovoltaic structure for an analytical example of an embodiment of the present invention.

[0025] Figure 5 This is a time history curve of the displacement of the center point of the cable net structure according to an embodiment of the present invention.

[0026] Figure 6 This is a comparison diagram of the morphology of the structure before and after deformation in an embodiment of the present invention.

[0027] Figure 7 This is a diagram showing the distribution of longitudinal cable internal forces in a cable net structure according to an embodiment of the present invention.

[0028] Figure 8 This is a diagram showing the distribution of transverse cable internal forces in a cable net structure according to an embodiment of the present invention.

[0029] Figure 9 This is a tension cloud diagram of the cable net structure according to an embodiment of the present invention. Detailed Implementation

[0030] The following detailed description illustrates the specific implementation method: The reference numerals in the accompanying drawings include: 1. Photovoltaic pontoon; 2. Cable net structure; 3. Flexible connecting rope; 4. Rigid outer frame; 5. Mooring system.

[0031] Example: A full-scale mechanical analysis method for flexible floating photovoltaic structures at sea, such as Figure 1 As shown, it includes the following steps: Step 1: Establish the geometric model of the floating photovoltaic system.

[0032] Flexible floating photovoltaic structures at sea, such as Figure 2 As shown, the system consists of a photovoltaic pontoon 1, a cable net structure 2, flexible connecting ropes 3 connecting the photovoltaic pontoon 1 and the cable net structure 2, a rigid outer frame 4, and a mooring system 5. The ends of the longitudinal and transverse cable nets are connected to the rigid outer frame 4. The longitudinal and transverse cables are arranged at equal intervals and staggered. The photovoltaic modules are independent photovoltaic pontoons 1, arranged within the cable net mesh. Photovoltaic modules are installed on the photovoltaic pontoons 1, and the four corners are fixed to the cable net nodes by flexible connecting ropes 3. The outer frame is anchored by the mooring system 5, forming a large floating photovoltaic array.

[0033] Among them, such as Figure 3 As shown, the photovoltaic floating box 1 and the longitudinal and transverse cable nets adopt a flexible connection form, that is, four soft connecting ropes 3 are used to connect the four corner points of the photovoltaic floating box 1 and the four cable net nodes of the corresponding cable net grid.

[0034] Step 2: Perform multi-scale structural discretization based on stress characteristics.

[0035] Flexible floating photovoltaic structures comprise components of various dimensions and characteristics, including poles (floating boxes), cables (cable nets, mooring), slack cables (connecting ropes), and beams (outer frame). Traditional finite mass methods cannot accurately simulate their complex rigid-flexible coupled dynamic characteristics, leading to difficulties in large-scale full-size analysis. This scheme classifies the flexible offshore floating photovoltaic structure into five types of components: photovoltaic floating boxes (1), cable net structures (2), flexible connecting ropes (3), rigid outer frame (4), and mooring cables. Based on the characteristics of these components, different unit structures are used for simulation to conduct stress analysis, as detailed below: 1. The photovoltaic floating box 1 of the distributed array, as the main stress-bearing member, has relatively small deformation under the action of wind, waves and currents and can be regarded as a rigid member, which is simulated by rod elements.

[0036] 2. The longitudinal and transverse cable nets and mooring cables are force-transmitting members, which can only bear tension and not compression, and have the characteristics of large displacement and large deformation during force application, and are simulated by cable elements.

[0037] 3. In the photovoltaic structure, in order to ensure that the soft connection rope 3 only transmits the load on the photovoltaic floating box 1 and does not participate in the force transmission of the overall structure, it is usually necessary to lengthen the length of the soft connection rope 3 so that its initial length is λ times (λ>1) of the geometric straight-line distance between the corner point of the photovoltaic floating box 1 and the cable net node. For example, λ = 1.2. Therefore, the soft connection rope 3 has a relaxation characteristic.

[0038] For the soft connection rope 3, the traditional finite particle method lacks an effective element model to directly simulate its mechanical behavior. In this solution, a new type of cable element model - the relaxed cable element model is established: the modeled geometric length is the geometric straight-line length between the corner point of the photovoltaic floating box 1 and the cable net node (this length is called 1-fold length); its internal force calculation rule is: set the stress-free length L0 of the relaxed cable element to be λ times the length. Whenever calculating the internal force of the element, first determine the relationship between the length L of the element and L0. If the element length L < L0, the internal force is forced to be set to 0, indicating that the soft connection rope 3 is still in a relaxed state at this time. When L > L0, the internal force is calculated according to the elongation L - L0 of the relaxed cable element.

[0039] In view of the unique initial relaxation characteristic of the flexible connection rope, the traditional finite particle method lacks an effective element model to directly simulate its mechanical behavior. The present invention innovatively proposes and establishes a "relaxed cable element" model, which accurately characterizes the relaxation characteristic of the flexible connection, solves the difficulties existing in the traditional method when directly simulating the connector with a specific pre-relaxed length, and significantly improves the accuracy of the stress state analysis of the connection part.

[0040] 4. The two ends of the longitudinal and transverse cable nets are connected to the rigid outer frame 4. The rigid outer frame 4 needs to ensure sufficient rigidity to ensure the stability of the cable net grid, and is simulated by beam elements.

[0041] In this step, the structure can be discretized into a finite number of particles, and the particles are connected by various elements. All the mass of the element is concentrated on the particle, and the element only plays a connecting role. The mass of the particle comes from all the elements connected to it. The mass of the particle is calculated according to the following formula: (1) In the formula, J is the number of the particle; n is the total number of elements connected to the particle J; is the element The equivalent mass assigned to point J. For the particle connected to the rigid outer frame 4 element, its moment of inertia also needs to be calculated: (2) In the formula, It is a unit The equivalent rotational inertia assigned to point J.

[0042] Step 3: Assign material properties to each type of component.

[0043] The material properties obtained in this step include Young's modulus, element density, Poisson's ratio, and shear modulus.

[0044] Step 4: Calculate the local adaptive time step and global time step for various components.

[0045] In this step, for each type of component among the aforementioned photovoltaic pontoon 1, cable net structure 2, flexible connecting rope 3, rigid outer frame 4, and mooring cable, based on the length, material density, and Young's modulus of its discrete elements, a minimum stable time step shared by all elements within each type of component is determined sequentially. , which serves as their respective local adaptive step size.

[0046] The differences in the properties of multi-scale structural components lead to significant variations in their critical stability time steps. Traditional finite-mass methods, to satisfy the most stringent constraints, employ a globally uniform minimum time step, resulting in low computational efficiency, particularly in large-scale structures. This method innovatively calculates a local adaptive time step (Δt) for each component type. i ), allowing components of the same type to be internally arranged according to their respective Δt i The algorithm steps forward and constructs an asynchronous computing mechanism, which effectively avoids the computational efficiency bottleneck of a globally unified minimum time step and significantly improves computational efficiency. This is especially true for large structures containing a large number of low-critical-step components, making large-scale full-size simulation analysis of flexible floating photovoltaic structures practical for engineering projects.

[0047] The local adaptive step size for each type of component must meet the following conditions: (3) In the formula, ρ i For the material density of type i component, E i For the Young's modulus of the material, l i The unit length is denoted as .

[0048] Based on the local adaptive time step Δt of each type of component i Calculate the global time step ΔT. And calculate the global time step ΔT and the local time step Δt. i ratio .

[0049] Step 5: Apply boundary conditions and loads.

[0050] In this step, the seabed anchor point of the mooring cable is set as the displacement boundary constraint point, and the wind, wave and current loads are applied to the structure, distributing the loads equally to the relevant particles.

[0051] Step 6: Local parallel time-step computation.

[0052] For each particle within each component type i, the central difference method is used, with its local time step... The particle displacement vector is calculated explicitly by stepping over time increments.

[0053] (4) In the formula, This indicates that particle J is in time + Δt i The displacement vector at time t, F J The net force vector acting on particle J is calculated by the following formula: (5) In the formula, P J Let J be the vector of the external force acting on particle J. Let α be the internal force vector of the unit α connected to particle J. The internal force of the unit acting on the particle must be negative.

[0054] C1 and C2 are damping-related calculation coefficients, calculated using the following formula: (6) In the formula, ζ is the damping factor.

[0055] For particles connected to the rigid outer frame element 4, the angular displacement of the particles also needs to be calculated: (7) In the formula, This indicates that particle J is in time + Δt i The angular displacement at time M J Let J be the net torque acting on particle J.

[0056] (8) In the formula, Q J Let J be the bending moment caused by the external force. Let α be the internal bending moment of the unit α connected to particle J.

[0057] Step 7: Integration of internal and external forces of particles.

[0058] In this step, the internal and external forces of each component's particles are integrated. The internal force calculation is divided into two parts: pure deformation calculation and internal force solution. The concept of reverse motion is introduced. Through virtual reverse motion, the element shape at the end of each iteration time step is translated or rotated in reverse to the initial moment of each iteration time step, thereby decoupling element displacement and deformation. By comparing the element shape at the initial moment and the end moment, the pure deformation of the element at each iteration time step is obtained.

[0059] Among them, the pure deformation of the photovoltaic pontoon 1, the flexible connecting rope 3, the longitudinal and transverse cable nets, and the mooring cable is the unit's expansion and contraction: (9) In the formula, l time This indicates the length of the unit at time point 'time'.

[0060] The pure deformation of the rigid outer frame 4 is calculated using the following formula: (10) In the formula, A and B represent the two endpoints of the rigid outer frame element 4, β is the angular deformation of the element endpoint, Δθ is the sum of the rigid body rotation and angular deformation of the element endpoint within a local time step, and γ is the rigid body rotation of the element within a local time step. The formulas for calculating Δθ and γ are as follows: (11) (12) in, Let be the unit direction vector of the rigid outer frame element 4 at time t.

[0061] The internal force increment of the element is calculated based on the pure deformation of the element and the constitutive relation of the material, and then superimposed with the initial internal force of the element to obtain the internal force of the element.

[0062] (13) In the formula, K is the stiffness matrix of the element, which is calculated in the same way as the traditional finite element method; Δ is the pure deformation of the element.

[0063] For the rigid outer frame element 4, it is also necessary to calculate the bending moment and internal forces of the element: (14) This represents the internal force vector of the element at time time t. This represents the bending moment of the element at time t.

[0064] By summing the internal and external forces of all units onto the particles, we obtain the force situation of each particle. The net force on the particle is: (15) For particles connected to the rigid outer frame element 4, the net torque they experience must also be calculated: (16) In this scheme, for particles at the connection points of different types of components, the internal forces from other types of components acting on them during asynchronous calculations of different types of components exhibit a time lag. When a particle within a type i component (including particles at its connection points with other types of components) is localized within a global time step, the internal forces from other types of components acting on the particles at the connection points are directly calculated using the internal forces obtained from the previous integer multiple of the global time step node. k is an integer and `time` represents the current time point of the particle. At the connection point, the particle is subjected to internal forces from different units. However, within a global time step, because different unit particles use different local time steps, the internal forces of different units are not unified at the time points, and the internal force data is not synchronized. Therefore, the internal forces calculated using synchronized time points are used.

[0065] Step 8: Repeat for each component type i. Steps 6-7 .

[0066] Step 9: Execute Step 6 again, at which point all particles are synchronized in global time.

[0067] In this step, all particles of all components (i.e., all particles) have completed n. i The calculation is performed in n iterations, meaning it has gone through n iterations. i *Δt i =ΔT time, therefore they are synchronized in time.

[0068] Step 10: Coordinate the positions of particles at the connection points of different components.

[0069] Particles at the connection points of different types of components, because they belong to the units of different types of components, use different local time steps. That is, the particles at the connection points may have results calculated by different local time steps, which may result in multiple displacement vector calculation results. When multiple displacement vector calculation results occur, the displacement vector of this type of particle is uniformly taken as the result calculated by the larger local time step.

[0070] Step 11: Integration of internal and external forces of particles.

[0071] This step is used to integrate the sum of the external forces acting on the particle and the internal forces acting on the particle by all the different types of components connected to the particle. The meaning of the integrated internal forces in this step is different from that in step 7.

[0072] In this step, the internal forces of each element are first solved, and the process for solving the internal forces of each element is the same as that in step 7. Then, the internal forces of all elements are accumulated onto the particle, the external load is updated, and the forces of the external load acting on the particle are superimposed to obtain the final force situation of the particle. This scheme integrates the resultant internal forces of particles at the connection points of different types of components, that is, the sum of the internal force vectors of all different types of components connected to the particle acting on it, realizing multi-scale coupling of the structure.

[0073] Step 12: Determine if the iteration terminates.

[0074] The iteration termination condition in this step is as follows: the difference between the Z coordinates of the center point of cable net structure 2 and the difference between two adjacent global time steps ΔT is less than 10. -4 m. If not satisfied, repeat steps 6-11. If satisfied, terminate the iteration.

[0075] Step 13: Calculation complete. The final positions of all particles constitute the geometric configuration of the structure in steady state.

[0076] In this scheme, the structural analysis method uses an explicit algorithm to solve the mechanical equilibrium equations, so each iteration has a result output. The calculation results of each global iteration step are recorded, time-history curves are plotted, and the dynamic response process of the structure is visualized and monitored. The positional information of all particles before and after deformation can be extracted, and the initial and final steady-state configurations of the structure can be plotted, intuitively describing the morphological changes of the structure. The internal force data of various types of structural components at steady state or specified times can be extracted, and the internal force distribution diagram of the structure can be plotted. All element internal forces are sorted and high-force elements are selected, and specified elements are highlighted in the overall structural morphology diagram, clearly and intuitively showing which parts are under stress concentration, facilitating subsequent local component reinforcement and structural optimization.

[0077] The following is a detailed example using the above analysis. The structural form of the structural scheme is as follows Figure 4 As shown, the structure consists of a photovoltaic pontoon 1, flexible connecting ropes 3, longitudinal and transverse cable nets, rigid outer buoys, and mooring cables, conforming to the characteristics of multi-component rigid-flexible coupling and strongly nonlinear mechanical behavior. The loads on the structure were calculated using AQWA software and applied to the structure. The structural mechanical behavior was then simulated using the aforementioned structural analysis methods.

[0078] The displacement-time history curve of the center point of the cable net structure 2 is as follows: Figure 5 As shown in the figure, the simulation results of the proposed structural analysis method for the complex mechanical behavior of flexible floating photovoltaic cells converge.

[0079] Figure 6 shows a comparison of the structure's morphology before and after deformation. As can be seen from the figure, the proposed structural analysis method can effectively simulate the complex mechanical behavior of flexible floating photovoltaic structures at sea, and the calculation results converge.

[0080] The force distribution diagram of the longitudinal and transverse cables of cable net structure 2 is as follows: Figure 7 and Figure 8 As shown. Extract the tension of all elements in the longitudinal and transverse cable nets and plot the tension contour map, as shown in the figure. Figure 9 As shown, the stress state is distinguished by color, and the area where the stress is most concentrated can be seen. Designers can use this information to optimize the internal force distribution of the structure and strengthen local components.

[0081] This invention innovatively proposes and establishes a "relaxed cable element" model, accurately characterizing the relaxation characteristics of flexible connections. This overcomes the difficulties of traditional methods in directly simulating connectors with specific pre-relaxation lengths, significantly improving the accuracy of stress state analysis at connection points. This method innovatively integrates cable elements, rod elements, rigid beam elements, and a custom-defined relaxed cable element, accurately matching the stress characteristics of various components. An internal force coupling mechanism based on global time step nodes is established, enabling multi-scale rigid-flexible coupling analysis and providing a reliable method for full-scale mechanical analysis of flexible floating photovoltaic structures. This method innovatively calculates the local adaptive time step for each component type, allowing components of the same type to operate according to their respective Δt values. i The method employs a step-by-step approach and constructs an asynchronous computation mechanism. This approach effectively avoids the computational efficiency bottleneck of a globally unified minimum time step, significantly improving computational efficiency and enabling practical large-scale full-size simulation analysis of flexible marine floating photovoltaic structures.

[0082] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention. In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea, characterized in that, Including: Step 1: Establish a floating photovoltaic geometric model; Step 2: Discretize the scale structure based on the force characteristics to form particles and units connecting the particles; use rod units to simulate photovoltaic floating boxes, cable units to simulate horizontal and vertical cable meshes and mooring cables, a relaxed cable unit model to simulate soft connection ropes, and beam units to simulate rigid outer frames; among them, the modeling geometric length of the relaxed cable unit model is the geometric straight-line length between the corner points of the photovoltaic floating box and the nodes of the cable mesh; Step 3: Assign material properties to various types of components; Step 4: Calculate the local adaptive time step and global time step for each type of component; Step 5: Apply boundary conditions and loads, and equivalently distribute the loads to the relevant particles; Step 6: Calculate the displacement vector of each particle within each component type i; Step 7: Calculate and integrate the internal and external forces of the particles of each component; Step 8: Repeat for each component type i. Next step 6~7; Step 9: Execute Step 6 again, at this time all particles are synchronized in global time; Step 10: Coordinate the positions of the particles at the joints of different components; Step 11: Calculate and integrate the internal and external forces of the particles of each component. In this step, the internal force of the particle at the joint is the sum of the internal force vectors of the units of different component types acting on this particle; Step 12: Determine whether the difference in the Z coordinate of the center point of the cable mesh structure between two adjacent global time steps ΔT is less than a preset value. If this stop iteration condition is not met, repeat the above Steps 5 to Step 11 until the stop iteration condition is met to complete the geometric configuration of the structure under steady-state action.

2. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 1, characterized in that: The calculation method for the internal force of the relaxed cable unit model is: set the stress-free length L0 of this relaxed cable unit as λ times the length. Whenever calculating the internal force of the unit, first determine the relationship between the length L of the unit and L0. If the unit length L < L0, the internal force is forcibly set to 0, indicating that the soft connection rope is still in a relaxed state at this time; when L > L0, the internal force is calculated according to the elongation amount L - L0 of the relaxed cable unit.

3. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 1, characterized in that: Step 4 specifically includes: for each type of component, based on the length of its discrete element, material density, and Young's modulus, sequentially determining a minimum stable time step shared by all elements within each type of component. , as their respective local adaptive step size; based on the local adaptive time step Δt of each type of component. i Calculate the global time step ΔT. And calculate the global time step ΔT and the local time step Δt. i ratio .

4. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 3, characterized in that: In Step 4, the local adaptive step lengths of each type of component need to meet the following conditions: In the formula, ρ i For component type i, E is the material density. i For the Young's modulus of the material, l i The unit length is denoted as .

5. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 1, characterized in that: Step 6 specifically includes: Step 61: For each particle within each component type i, use the central difference method, with its local time step... The particle displacement vector is calculated explicitly in steps over time, as shown in the following formula: In the formula, This indicates that particle J is in time + Δt i The displacement vector at time t, F J Let C1 and C2 be the resultant force vector acting on particle J, and C1 and C2 be the calculated coefficients related to damping. It is a unit The equivalent mass assigned to point J; Step 62: For the particles connected to the rigid outer frame unit, further calculate the angular displacement of the particles, and the formula is as follows: In the formula, This indicates that particle J is in time + Δt i The angular displacement at time M J Let J be the net torque acting on particle J. It is a unit The equivalent rotational inertia assigned to point J.

6. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 5, characterized in that: Step 7 includes: Step 71: Calculate the element internal force increment based on the element's pure deformation and material constitutive relation, then superimpose it with the element's initial internal force to obtain the element's internal force. The specific formula is as follows: In the formula, K is the stiffness matrix of the element, and Δ is the pure deformation of the element; the internal forces of the rigid outer frame element also include the bending moment internal forces of the element, as shown in the following formula: In the formula This represents the internal force vector of the element at time time t. This represents the bending moment of the element at time time; Step 72: Accumulate the internal and external forces of all units onto the particles, and the resultant force received by the particles is: In the formula P J Let J be the vector of the external force acting on particle J. Let α be the internal force vector of the unit α connected to particle J; Among them, the resultant force of the rigid outer frame unit also includes the resultant torque it receives, and the specific formula is: In the formula, Q J Let J be the bending moment caused by the external force. Let be the internal bending moment of unit α connected to particle J.

7. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 6, characterized in that: In step 7, when a particle within a type i component performs a local time step within a global time step, the element internal forces of other types of components acting on the particle at the connection point are directly calculated using the element internal forces obtained from the previous integer multiple of the global time step node. k is an integer and , where time represents the current time point of the particle.

8. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 5, characterized in that: In Step 7, the pure deformation of the units of the photovoltaic floating box, soft connection rope, horizontal and vertical cable meshes, and mooring cables is the elongation amount of the unit, and the calculation formula is as follows: In the formula, l time Indicates the length of the unit at time point 'time'; The pure deformation of the rigid outer frame is calculated according to the following formula: [[ID=2l]]In the formula, A and B respectively represent the two end points of the rigid outer frame unit, β is the angular deformation amount of the unit end point, Δθ is the sum of the rigid rotation amount and the angular deformation amount of the unit end point within one local time step, and γ is the rigid rotation amount of the unit within one local time step.

9. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 1, characterized in that: In Step 2, the mass of the unit is concentrated on the particles, and the calculation formula for the particle mass is: In the formula, J is the particle number; n is the total number of units connected to particle J. It is a unit The equivalent mass assigned to point J; where, for particles connected to rigid outer frame elements, the particle mass also includes its rotational inertia, as shown in the formula: In the formula, It is a unit The equivalent rotational inertia assigned to point J.

10. The full-scale mechanical analysis method for a flexible floating photovoltaic structure at sea according to claim 1, characterized in that: Step 10 specifically includes: When there are multiple calculation results of displacement vectors for the particles at the joints of different types of components, the displacement vector of this type of particle is uniformly taken as the result calculated according to the larger local time step.

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