A load-mapping-based fine analysis method and system for a three-dimensional floating tunnel structure, and a medium

Abstract

The application discloses a kind of three-dimensional suspended tunnel structure refinement analysis method, system and medium based on load mapping.The method, on the one hand, considering that suspended tunnel is slender structure, can simplify the calculation of hydrodynamic load using Morison equation;On the other hand, the internal force obtained by simulating the suspended tunnel beam model is dynamically mapped to a series of nodes of the three-dimensional suspended tunnel shell finite element model at each time step, realizing the dynamic coupling between the deformation of the suspended tunnel and the load applied in the time domain.The present application inversely calculates the resultant force of complex dynamic load through the response of beam finite element model, and maps the resultant force to the nodal force of each node on the shell finite element model through the load mapping method, greatly reducing the calculation time and improving the calculation efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of three-dimensional suspended tunnel structure analysis, and relates to a load dynamic response mapping and structure refinement analysis method applicable to the field of suspended tunnels, and in particular to a three-dimensional suspended tunnel structure refinement analysis method, system and medium based on load mapping. Background Art

[0002] As a new type of structure that solves traffic problems in long and deep straits, floating tunnels have been a research hotspot in recent years. They consist of a pipe body, anchor cables, a deep-water foundation, and structures connecting the two banks. Floating tunnels are located in a complex marine environment and are subject to multiple loads, such as waves, tidal currents, and earthquakes. In order to assess the safety of floating tunnels under these multiple loads, a detailed three-dimensional stress analysis is essential. This analysis can identify critical areas that may exceed strength standards, thereby guiding the modification and reinforcement of the floating tunnel cross-section design and ensuring the integrity and durability of the tunnel. Furthermore, detailed stress analysis of floating tunnel structures can play a positive role in revising the construction specifications for floating tunnels and revealing how dynamic loads affect the vibration behavior and fatigue life of the tunnel.

[0003] Existing structural analysis and simulation methods for suspended tunnels mostly use traditional beam models. These models simplify the complex three-dimensional suspended tunnel into a simple beam model for calculation. While this simplification helps to shorten calculation time to a certain extent, it ignores the lateral stresses in the tunnel cross-section and fails to provide sufficient information to predict the detailed stress distribution of the structure under actual operating conditions, which may pose certain risks during the design and assessment process. More refined three-dimensional stress analysis can reveal these critical details and provide more comprehensive protection for structural safety. Therefore, it is necessary to develop and implement more advanced analysis methods to deeply explore the stress distribution in the suspended tunnel cross-section and ensure the stability and durability of the entire structure.

[0004] To address the problem of detailed stress analysis of three-dimensional floating tunnel structures, some researchers have attempted to use CFD methods. However, these methods suffer from numerous issues, including slow computational speed, complex calculations, and difficulty handling complex load distributions. Alternatively, some researchers have proposed three-dimensional static analysis methods to address this issue. Based on diffraction theory and the hydraulic engineering software WAMIT, they calculate wave inertia forces and, using the Morison equation and the commercial software ORCAFLEX, wave drag and added mass forces. These forces are then applied to the three-dimensional floating tunnel finite element model in the form of pressure distribution, initial displacement, or maximum acceleration. This entire process involves at least four programs (WAMIT, ORCAFLEX, ABAQUS, and an in-house program). Furthermore, these four programs are not fully coupled, requiring highly skilled researchers and high operational requirements, making them difficult to generalize. Furthermore, this method lacks rigorous three-dimensional time-history analysis of the entire structure. Therefore, to improve computational efficiency and reduce computational complexity, a fast and reliable method for detailed analysis of three-dimensional floating tunnel structures is needed that accurately and reliably reflects the effects of actual loads on structural details in the time domain, thereby enabling preliminary assessment of the strength design of the floating tunnel under various operating conditions. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention provides a load-mapping-based three-dimensional suspended tunnel structure refinement analysis method, system, and medium. This method can map the dynamic response of a suspended tunnel beam model to the surface nodes of a three-dimensional shell model in the time domain, thereby performing a refined analysis of the stress and strain of the local structure of the suspended tunnel. This method involves a set of theoretical formulas for solving the equivalent loads of suspended tunnel segments and a theoretical formula for equivalent external load mapping, which are computationally efficient and simple. Furthermore, by comparing the magnitude of the end reaction forces of the suspended tunnel beam model and the shell model, the load mapping method verifies the structural equivalence of the structure, further ensuring the accuracy of the final structural analysis. In summary, the load-mapping-based three-dimensional structural analysis method of the present invention has a simple model and rapid analysis, which can improve the speed of existing suspended tunnel three-dimensional structural analysis. Furthermore, this method can compensate for the deficiency of existing methods in not performing rigorous three-dimensional time-history analysis of the three-dimensional suspended tunnel cross-section. Therefore, this load mapping analysis method has significant practical significance in the field of suspended tunnels.

[0006] The technical solutions adopted in the present invention are as follows:

[0007] A load mapping-based refined analysis method for a three-dimensional suspended tunnel structure includes the following steps:

[0008] Create two finite element models: a beam model and a shell model, ensuring that the structural parameters of the two are consistent and only using different element types; calculate the wave load based on the Morison equation, calculate the net buoyancy based on the gravity and buoyancy formula, and apply the wave load and net buoyancy to the beam model; perform dynamic response analysis of the beam model using finite element analysis software, and record the internal force, displacement, rotation, anchor reaction force and other responses of each analysis node of the beam model.

[0009] According to the coordinate transformation formula, the response of each analysis node in the deformed beam coordinate system is transformed into the shell coordinate system. Then, according to the principle of force balance, the equivalent load on each segment is obtained;

[0010] The equivalent external loads on each analysis segment are distributed to each node of the shell model, and the finite element analysis of the shell model is performed. The response data of the equivalent position points are recorded. The accuracy and similarity of the mapping algorithm can then be evaluated by comparing the response results of the two models, such as internal forces and displacements.

[0011] According to the stress results calculated by the shell finite element model, a three-dimensional refined stress analysis is performed on the roadbed and main beam structure of the shell finite element model section.

[0012] In the above technical solution, it is further required that the two established finite element models are completely consistent in terms of cross-sectional area, moment of inertia, material elastic modulus, Poisson's ratio, anchor cable inclination angle, etc. Among them, the beam model is usually simulated using a two-node three-dimensional beam unit, which is defined by two nodes and has 6 degrees of freedom: 3 displacements and 3 rotations. This unit is based on the Timoshenko beam theory, assuming that the transverse shear behavior of the beam is linear elastic with a fixed modulus. At the same time, the strain caused by the torsion of the beam is very small and can withstand large axial strains. The advantage of this unit is that its calculation is simple and efficient, and the consumption of computing resources is relatively small. The shell model usually uses a four-node shell unit, assuming that its one-dimensional thickness is significantly smaller than other dimensions. It is suitable for simulating plane or curved thin-walled structures and can simulate the membrane effect and shear stress distribution under external forces.

[0013] Regular wave force loading is performed on the beam finite element model based on the Morison equation. The Morison equation is a fundamental theoretical model for describing hydrodynamic loads under wave action. It divides the hydrodynamic load into two components: inertial force and drag. The fluid is assumed to be homogeneous, incompressible, and its motion is continuous. The structure is also assumed to be small compared to the wavelength. For a suspended tunnel, the structural dimensions generally meet the requirements of the Morison equation.

[0014] The process of using finite element analysis software to analyze the dynamic response of a beam model subjected to regular waves. The analysis time, time step, output step, and boundary conditions are appropriately set, and a dynamic implicit solver is used. After the solution is complete, the internal forces, displacements, rotations, and anchor cable reactions at each analysis node of the beam model are extracted and entered into a text file.

[0015] Furthermore, since the internal force and other responses obtained from the beam model are based on the local coordinate system of the deformed beam, while the coordinates of the loading node forces are based on the initial shell coordinate system, it is necessary to first rotate the deformed beam coordinates to the pre-deformed beam coordinate system, and then rotate and translate the pre-deformed beam coordinate system to the initial shell coordinate system.

[0016] The rotation matrix that rotates the deformed beam coordinates to the undeformed beam coordinate system is as follows:

[0017]

[0018] in, θ1, θ2, and θ3 represent the rotation angles of the deformed coordinates around the x, y, and z axes, respectively.

[0019] V' xB ,V' yB ,V' zB With M' xB ,M' xB ,M' xB is the internal force of each analysis node after the beam is deformed by finite element analysis. xB ,V' yB ,V' zB Respectively represent the forces in the x, y, and z directions of each analysis node of the beam after deformation, M' xB ,M' xB ,M' xB Respectively represent the moments of each analysis node of the beam in the x, y, and z directions after deformation. xB ,V yB ,V zB They represent the forces in the x, y, and z directions of each analysis node of the beam before deformation. xB ,M yB ,M zB They represent the moments in the x, y, and z directions of each analysis node of the beam before deformation.

[0020] The rotation formula for rotating the beam coordinate system before deformation to the initial shell coordinate system direction is as follows:

[0021]

[0022] Among them, V' xS ,V' yS ,V'zS They represent the forces in the x, y, and z directions of each analysis node of the shell before translation.

[0023] M' xS ,M' yS ,M' zS They represent the moments in the x, y, and z directions of the analysis nodes of the shell before translation.

[0024] The formula for translating the beam coordinate system position before deformation to the initial shell coordinate system position is as follows:

[0025]

[0026] Where x, y, and z represent the displacement of each analysis node in the shell coordinate system in the x, y, and z directions respectively. For analysis node j, (V xs ) j ,(V ys ) j ,(V zs ) j and (M xs ) j ,(M ys ) j ,(M zs ) j is the internal force of the analysis node in the shell coordinate system. xs ) j ,(V ys ) j ,(V zs ) j Analyze the forces on the nodes in the x, y, and z directions respectively. (M xs ) j ,(M ys ) j ,(M zs ) j To analyze the moments of the nodes in the x, y, and z directions.

[0027] It should be noted that since the coordinate system of the anchor point is the global coordinate system and it is fixed to the ground and will not move, only the following coordinate transformation is required:

[0028]

[0029] Among them, for the anchor cable numbered m, (R xS ) m ,(R yS ) m ,(R zS ) m is the anchor cable reaction force in the x, y, and z directions in the shell coordinate system, (R xB ) m ,(RyB ) m ,(R zB ) m is the anchor cable reaction in the x, y, and z directions in the beam coordinate system.

[0030] After completing the above coordinate transformation, all components have been successfully transformed into the shell coordinate system to be loaded.

[0031] Furthermore, to address the complex external responses of the corresponding segments of the suspended tunnel, this paper proposes for the first time a mathematical expression for calculating the equivalent load on each segment of the suspended tunnel. This expression can convert the internal forces at both ends of each segment of the suspended tunnel into the equivalent external load on the segment.

[0032] It should be noted that the selection of analysis nodes is arbitrary, and the area between two analysis nodes is an analysis segment. However, in order to facilitate the consideration of the role of anchor cables, for segments with anchor cables, we will consider placing the anchor cables at the center of the two analysis nodes. For segments without anchor cables, (R xS ) m ,(R yS ) m ,(R zS ) m Both are equal to 0.

[0033] Applying the principle of force balance, we establish force balance equations in the horizontal and vertical directions. The balance method is shown below.

[0034]

[0035] Among them, for a given analysis node j of the beam model at a certain moment, l j+1 is the distance between the j+1th analysis node and the segment resultant center. j is the distance between the jth analysis node and the center of the segment resultant force. For a given analysis segment i of the beam model at a certain moment, F x,i ,F y,i ,F z,i Its equivalent force in the x, y, and z directions.

[0036] M x,i ,M y,i ,M z,i is its equivalent moment in the x, y, and z directions.

[0037] Furthermore, to map the forces and moments on the analysis segment to each three-dimensional node within the corresponding segment of the shell model, this paper proposes a theoretical formula for beam-to-shell load mapping, applicable to the field of suspended tunnels. This formula ensures that the net force acting on the segment center from each node equals the equivalent load calculated above, thereby ensuring overall structural balance during the mapping process.

[0038] Given a suspended tunnel segment i, assume that it has N nodes in a certain time step, and the coordinates of the segment center are (x i ,y i ,z i ). For any point in the segment, the coordinates are (x r ,y r ,z r ) node r, considering the unevenness of the wave action on the suspended tunnel in space and the simplicity of numerical solution, the lateral node force f x,r and vertical nodal force f y,r Assuming that it obeys a linear distribution related to its coordinates, the axial nodal force f z,r It is assumed to be evenly distributed. r ,y r ,z r ) and the resultant force of segment i, the formula is as follows.

[0039]

[0040] In the formula, for any node r on the shell model at a certain moment, f x,r ,f y,r ,f z,r is the horizontal, vertical and longitudinal nodal force; x0, y0, z0 are the distances from the segment center, where x0 = x r -x i ,y0=y r -y i ,z0=z r -z i It is worth noting that considering the influence of depth on wave and current, assuming that only the lateral force f x,i To M z,i k1, k2, k3, k4, k5, k6, k7 are the parameters to be solved for the equation.

[0041] Comparing the support reaction results for the suspended tunnel beam finite element model and the plate-shell finite element model is an effective way to evaluate whether the load mapping algorithm accurately maps external forces to the shell model. The comparison data typically includes the time-domain responses of internal forces and displacements at the same or corresponding locations on the two models. This comparison can be used to assess the accuracy and reliability of the mapping algorithm in converting dynamic loads into equivalent static loads. If the results of the two models are in good agreement, it means that the load mapping algorithm is successful and can be used for further analysis and design. If the results differ significantly, it is necessary to review the assumptions and calculation steps in the mapping process and make necessary adjustments to improve accuracy.

[0042] Furthermore, based on the load mapping of the aforementioned steps, the present invention can complete the loading of the three-dimensional plate-shell finite element model of the suspended tunnel under the action of waves, thereby performing a fast and efficient finite element analysis on it. After the simulation is completed, the present invention focuses on the strength analysis of the key internal components of the suspended tunnel (such as the roadbed and main beam). By analyzing the stress distribution of the suspended tunnel roadbed and main beam structure in various directions, the specific location where the maximum stress occurs is determined, and the possible failure mechanism is further explored, providing a scientific basis for tunnel design optimization, the formulation of strength improvement measures, and the effective identification and prevention of potential risks.

[0043] A load-mapping-based refined analysis system for a three-dimensional suspended tunnel structure, for implementing the load-mapping-based refined analysis method for a three-dimensional suspended tunnel structure as described above, the system comprising: an equivalent load calculation module for converting the responses of each analysis node in the deformed beam coordinate system to the shell coordinate system, and calculating the equivalent load on each segment based on the principle of force balance;

[0044] The load mapping module is used to distribute the equivalent load on each analysis segment to each node of the shell model.

[0045] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the load mapping-based refined analysis method for a three-dimensional suspended tunnel structure as described above.

[0046] An electronic device, comprising:

[0047] one or more processors;

[0048] a memory for storing one or more programs;

[0049] When the one or more programs are executed by the one or more processors, the one or more processors implement the three-dimensional floating tunnel structure refinement analysis method based on load mapping as described in any one of the above items.

[0050] Beneficial effects:

[0051] This paper proposes a simple load mapping algorithm for detailed analysis of suspended tunnel structures under regular waves in the time domain. This algorithm uses the Morison equation to provide a simple evaluation of the hydrodynamic loads acting on the suspended tunnel structure. The algorithm converts the internal forces and anchor cable reactions of the suspended tunnel beam model into equivalent loads for the corresponding tunnel segments. The equivalent loads are then converted into nodal forces acting on the plate and shell model, completing the loading and analysis of the suspended tunnel. Finally, the accuracy of the load mapping algorithm was verified by comparing the reaction forces and displacements at the end sections of two suspended tunnel models.

[0052] This load mapping method provides a simple approach to time-domain analysis of three-dimensional suspended tunnels, eliminating the need for complex hydrodynamic calculations or the coupling of multiple software programs. At the same time, compared to traditional mapping methods, this method considers the effects of six components, including shear force and bending moment. Furthermore, due to the prior analysis of the suspended tunnel beam model, the present invention can subsequently analyze suspended tunnel segments with greater stress or stable time periods separately based on the operating results of the beam model. For large-scale suspended tunnel models, this will significantly reduce calculation time and improve computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Flowchart for detailed analysis of the three-dimensional structure of the suspended tunnel;

[0054] Figure 2 Schematic diagram of the suspended tunnel beam finite element model and the plate-shell finite element model;

[0055] Figure 3 Coordinate transformation diagram for suspended tunnel beam finite element model and plate-shell finite element;

[0056] Figure 4 Schematic diagram of equivalent load solution for real suspended tunnel;

[0057] Figure 5 Schematic diagram of the suspended tunnel load mapping method;

[0058] Figure 6 The force, moment and displacement verification diagrams for the suspended tunnel beam finite element model and the plate-shell finite element model;

[0059] Figure 7 The von Mises cloud diagram of the subgrade and main beam structure of the suspended tunnel plate-shell finite element model along the tunnel length direction;

[0060] Figure 8 This is the von Mises cloud diagram of the cross section at the shore connection (fixed end) of the suspended tunnel plate and shell finite element model;

[0061] Figure 9 This is the circumferential stress cloud diagram of the subgrade and main beam structure of the suspended tunnel plate shell finite element model;

[0062] Figure 10 This is the tangential stress cloud diagram of the subgrade and main beam structure of the suspended tunnel plate shell finite element model;

[0063] Figure 11 This is the axial stress cloud diagram of the roadbed and main beam structure of the suspended tunnel plate shell finite element model. DETAILED DESCRIPTION

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] like Figure 1 FIG. 1 is a flow chart of the method of the present invention. According to a specific embodiment of the present invention, the load mapping-based refined analysis method for a three-dimensional suspended tunnel structure includes the following steps:

[0066] Step 1: If Figure 2 As shown, a beam finite element model and a three-dimensional refined shell finite element model were created in the finite element software. The basic parameters of the suspended tunnel, such as the pipe area, moment of inertia, density, centroid, elastic modulus, anchor cable density, elastic modulus, spacing, angle, water depth, and suspension depth, were defined as shown in Table 1.

[0067] Taking a regular wave with a height of 5m and a period of 12s as an example, this invention completes the loading of wave added mass force and resistance during dynamic analysis by programming a command stream. This includes the definition of fluid properties, such as fluid density, wave height, wavelength, wave period, and wave direction, as well as structural parameters such as structure diameter, resistance coefficient, and mass coefficient.

[0068] The process of performing a dynamic response analysis of a beam model subjected to regular waves using finite element analysis software. Set the output time step to 1 second and the total analysis time to 150 seconds.

[0069] In the beam coordinate system, the x, y, and z directions are defined as the axial, transverse, and vertical directions. In the shell coordinate system, the z, x, and y directions are defined as the axial, transverse, and vertical directions. Boundary conditions restrict translational and rotational freedom in six directions at one end (i.e., the fixed end), while the other end restricts axial displacement and transverse and vertical rotations. A dynamic implicit solver is used. After the solution is complete, the internal forces, displacements, rotations, and anchor cable reactions at each analysis node of the beam model are extracted and entered into a text file.

[0070] Table 1 Basic parameters of suspended tunnel

[0071]

[0072]

[0073] Step 2: Considering that the subsequent loading process of nodal forces is based on the initial undeformed three-dimensional plate-shell finite element model, while the internal force and other response results are based on the beam finite element model after displacement and rotation, this patent uses a coordinate transformation method to achieve the conversion of loads from the beam coordinate system to the shell coordinate system.

[0074] Specifically, first Figure 3 The internal forces of different analysis nodes shown in (a) in the deformed beam coordinate system are rotated to Figure 3 (b) The direction of the beam coordinate system before deformation is calculated as follows:

[0075]

[0076] in, θ1, θ2, and θ3 represent the rotation angles of the deformed coordinates around the x, y, and z axes, respectively.

[0077] V' xB ,V' yB ,V' zB With M' xB ,M' xB ,M' xB is the internal force of each analysis node after the beam is deformed by finite element analysis. xB ,V' yB ,V' zB Respectively represent the forces in the x, y, and z directions of each analysis node of the beam after deformation, M' xB ,M' xB ,M' xB Respectively represent the moments of each analysis node of the beam in the x, y, and z directions after deformation. xB ,V yB ,V zB They represent the forces in the x, y, and z directions of each analysis node of the beam before deformation. xB ,M yB ,M zB They represent the moments in the x, y, and z directions of each analysis node of the beam before deformation.

[0078] Secondly, in Figure 3 In the beam coordinate system of (b), the direction of the regular wave is consistent with the positive direction of the y-axis, the axis of the tube is parallel to the x-axis, and the direction of gravity is parallel to the z-axis. Figure 3 (c) In the shell coordinate system, the direction of the regular wave is consistent with the positive direction of the x-axis, the axis of the tube is parallel to the z-axis, and the direction of gravity is parallel to the y-axis. Therefore, to facilitate the subsequent solution and application of loads, the present invention needs to rotate the internal force of the analysis node again from the direction of the pre-deformation beam coordinate system to the direction of the shell coordinate system. The rotation matrix can be expressed by the following equation:

[0079]

[0080] Among them, V' xS ,V' yS ,V' zS They represent the forces in the x, y, and z directions of each analysis node of the shell before translation.

[0081] M' xS ,M' yS ,M' zS They represent the moments in the x, y, and z directions of the analysis nodes of the shell before translation.

[0082] In this method, the influence of torque change caused by displacement is further considered. The calculation process can be implemented by applying the following equation:

[0083]

[0084] Among them, x, y, z represent the displacement of each analysis node in the three directions in the shell coordinate system. For analysis node j, (V xs ) j ,(V ys ) j ,(V zs ) j and (M xs ) j ,(M ys ) j ,(M zs ) j is the internal force of the analysis node in the shell coordinate system. xs ) j ,(V ys ) j ,(V zs ) j Analyze the forces on the nodes in the x, y, and z directions respectively. (M xs ) j ,(M ys ) j ,(M zs ) j To analyze the moments of the nodes in the x, y, and z directions.

[0085] It should be noted that since the coordinate system of the anchor point is the global coordinate system and it is fixed to the ground and will not move, only the following coordinate transformation is required:

[0086]

[0087] Among them, for the anchor cable numbered m, (R xS ) m ,(R yS ) m ,(R zS ) m is the anchor cable reaction force in the x, y, and z directions in the shell coordinate system, (R xB ) m ,(R yB ) m ,(R zB ) m is the anchor cable reaction in the x, y, and z directions in the beam coordinate system.

[0088] Afterwards, based on the principle of force and moment balance, the present invention converts the internal force of the beam model into an external equivalent load that is easy to handle for each segment of the suspended tunnel. It should be noted that the selection of analysis nodes is arbitrary, and the area between two analysis nodes is an analysis segment. However, in order to facilitate the consideration of the role of anchor cables, for segments with anchor cables, we will consider placing the anchor cables at the center of the two analysis nodes. For segments without anchor cables, (R xS ) m ,(R yS ) m ,(R zS ) m Both are equal to 0.

[0089] Reference Figure 4 , the present invention constructs a force balance equation in three directions. The equation is as follows:

[0090]

[0091] Among them, for a given analysis node j of the beam model at a certain moment, l j+1 is the distance between the j+1th analysis node and the segment resultant center. j is the distance between the jth analysis node and the center of the segment resultant force. For a given analysis segment i of the beam model at a certain moment, F x,i ,F y,i ,F z,i Its equivalent force in the x, y, and z directions.

[0092] M x,i ,M y,i ,M z,i is its equivalent moment in the x, y, and z directions.

[0093] Step 3: If Figure 5 As shown, to map the forces and moments on the analysis segment to each 3D node within the corresponding segment of the shell model, this paper innovatively proposes a load mapping theory formula applicable to the field of suspended tunnels, enabling load conversion from beam models to shell models. Specifically, this theory ensures that the net force exerted by each node on the segment center is consistent with the equivalent load calculated above, thereby ensuring the stability and equilibrium of the entire structure.

[0094] At any time step, for a given floating tunnel segment i, it is assumed that it has N nodes, and the center coordinates of the segment are (x i ,y i ,z i For any node r in the segment, assume its coordinates are (x r ,y r ,z r). In view of the spatial non-uniformity of the wave action on the suspended tunnel and for the convenience of numerical solution, we assume that the x-direction node force f x,r and the y-direction nodal force f y,r follows a distribution linearly related to its coordinates, while the z-direction node force is assumed to be uniformly distributed. Based on this, we establish the node r(x r ,y r ,z r ) and the equivalent load of segment i, the formula is as follows:

[0095]

[0096] In the formula, for any node r on the shell model at a certain moment, f x,r ,f y,r ,f z,r is the nodal force in the x, y, and z directions; x0, y0, and z0 are the distances from the segment center, where x0 = x r -x i ,y0=y r -y i ,z0=z r -z i It is worth noting that considering the influence of depth on wave and current, assuming that only the lateral force f x,i To M z,i k1, k2, k3, k4, k5, k6, k7 are the parameters to be solved for the equation.

[0097] Step 4: Apply the obtained nodal force to each node of the shell model and perform finite element calculation. To verify the equivalence of the mapping algorithm, in the beam coordinate system, the y and z directions are the horizontal and vertical directions. In the shell coordinate system, the x and y directions are the horizontal and vertical directions. Figure 6 As shown in the figure, the horizontal and vertical reaction forces at the fixed ends and the horizontal and vertical displacements at the center of the beam model under wave action are represented by black dotted lines. The horizontal and vertical reaction forces at the fixed ends and the horizontal and vertical displacements at the center of the shell model under nodal force action are represented by red short dotted lines to observe whether the curves fit.

[0098] In addition, the correlation coefficient is used to represent the correlation between the response of the beam model under the action of regular waves and the response of the shell model under the action of nodal forces. The results of the correlation coefficient calculation are shown in Table 2. The correlation coefficients are close to 1. The calculation results in Table 2 show that the support reaction and displacement of the beam model under the action of regular waves and the shell model under the action of load mapping are almost completely positively correlated. Figure 6 , we can see that the curves of the beam model and the shell model are also consistent. In summary, the force, moment and displacement of the beam model and the shell model in the time domain are consistent well, which shows that the mapping algorithm is accurate.

[0099] Table 2 Correlation coefficients of internal forces and displacements

[0100]

[0101] Step 5: After completing the finite element analysis, conduct a detailed strength analysis of the internal components of the suspended tunnel body, such as the roadbed and main beam. Figure 7 As shown in Figure 2, at the moment of maximum displacement, the von Mises stress value of the roadbed and main beam structure at the shore connection is the largest. Figure 8 The stress cloud diagram of the shore connection section is analyzed.

[0102] Since the elastic modulus of the material used in the present invention is close to that of C40 concrete, the allowable tensile, compressive, and shear values ​​of the material can be calculated according to the specifications. The calculation formula is as follows:

[0103] f c ' k =40.000MPa

[0104]

[0105]

[0106]

[0107] According to the above formula, the stress of the roadbed and main beam structure at the shore connection of the floating tunnel in this example can be evaluated. Figure 9 In the study, when subjected to regular waves with a wave height of 5m and a period of 12s, the maximum circumferential tensile stress in the roadbed and main beam structure reached 7.934MPa, exceeding the allowable tensile stress value of 4.450MPa. However, in the assessment of circumferential compressive stress, the roadbed and main beam structures did not have any circumferential compressive elements. Figure 10 In the test, the maximum shear stress of the roadbed and main beam structure is 1.895MPa, which is less than the allowable value of 3.75MPa. Figure 11 The maximum axial tensile stress in the roadbed and main beam structure was 7.491 MPa, exceeding the permissible tensile value of 4.450 MPa. The maximum axial compressive stress in the roadbed and main beam structure was -3.857 MPa, less than the permissible value of 16.000 MPa.

[0108] Based on these results, the tensile strength of the roadbed and main beam components of a suspended tunnel should be strengthened when designing them. This can be achieved by equipping them with an appropriate amount of tensile reinforcement or adopting other structural measures. Furthermore, existing designs do not require additional design measures for shear and compression resistance, aside from strengthening tensile strength.

[0109] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0110] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0111] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0112] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0113] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A three-dimensional floating tunnel structure refinement analysis method based on load mapping, characterized in that: include: Create two finite element models: a beam model and a shell model, ensuring that the structural parameters of the two are consistent and only using different element types; Calculate the wave load and net buoyancy, and apply them to the beam model. Perform dynamic response analysis of the beam model using finite element analysis software, and record the internal force, displacement, rotation, and anchor cable reaction response of each analysis node of the beam model. The responses of each analysis node in the deformed beam coordinate system are converted to the shell coordinate system, and then the equivalent load on each segment is obtained based on the principle of force balance. Distribute the equivalent load on each analysis segment to each node of the shell model, perform finite element analysis of the shell model, and record the response data of the equivalent position points; According to the stress results calculated by the shell model finite element, a three-dimensional refined stress analysis is performed on the roadbed and main beam structure of the shell finite element model section.

2. The three-dimensional floating tunnel structure refinement analysis method based on load mapping according to claim 1 is characterized in that: The structural parameters of the two established finite element models include cross-sectional area, moment of inertia, material elastic modulus, Poisson's ratio, and anchor cable inclination angle; among them, the beam model is simulated using a two-node three-dimensional beam element, and the shell model is simulated using a four-node shell element.

3. The load mapping-based refined analysis method for three-dimensional suspended tunnel structures according to claim 1 is characterized in that: The responses of each analysis node in the deformed beam coordinate system are converted to the shell coordinate system, specifically including the following steps: first, the deformed beam coordinate system is rotated to the undeformed beam coordinate system, and then the undeformed beam coordinate system is rotated and translated to the initial shell coordinate system.

4. The load mapping-based refined analysis method for three-dimensional suspended tunnel structures according to claim 3 is characterized in that: The coordinates of the deformed beam are rotated to the coordinate system of the beam before deformation. The rotation matrix is ​​as follows: ， in, , Respectively represent the coordinates after deformation around The rotation angle of the axis, and is the internal force of each analysis node after the beam is deformed by finite element analysis, where Respectively represent the analysis nodes of the beam after deformation Directional force, Respectively represent the analysis nodes of the beam after deformation The torque in the direction of They represent the analysis nodes of the beam before deformation Directional force, Represents the analysis nodes of the beam before deformation Directional torque; Then rotate the direction of the beam coordinate system before deformation to the direction of the initial shell coordinate system. The rotation formula is as follows: ， in, They represent the analysis nodes of the shell before translation Directional force, Represents the analysis nodes of the shell before translation Directional torque; Finally, the beam coordinate system position before deformation is translated to the initial shell coordinate system position. The formula is as follows: ， in, Respectively represent the analysis nodes in the shell coordinate system The displacement in the direction of the analysis node j is and is the internal force of the analysis node in the shell coordinate system, where The forces acting on the analysis nodes in the x, y, and z directions are respectively, To analyze the moments of the nodes in the x, y, and z directions.

5. The method for fine-grained analysis of three-dimensional suspended tunnel structures based on load mapping according to claim 3 is characterized in that: The coordinate system of the anchor point is the global coordinate system, and it is fixed to the ground and will not move. The following coordinate transformation is performed: ， Among them, for the anchor cable numbered m, are the anchor cable reactions in the x, y, and z directions in the shell coordinate system, is the anchor cable reaction in the x, y, and z directions in the beam coordinate system.

6. The load mapping-based refined analysis method for three-dimensional suspended tunnel structures according to claim 1 is characterized in that: The internal forces at both ends of each segment of the suspended tunnel are converted into equivalent external loads on the segment, including: Apply the principle of force balance to establish the force balance equation in the horizontal and vertical directions. The balance method is as follows: ， Among them, for a given analysis node of the beam model at a certain moment , For the The distance between the analysis node and the segment resultant center, For the The distance between an analysis node and the center of the segment resultant force, for a given analysis segment of the beam model at a certain moment , For its equivalent force in the x, y, and z directions, Its equivalent moment in the x, y, and z directions; Analyze the forces at node j in the x, y, and z directions respectively. To analyze the moment of node j in the x, y, and z directions, Analyze the forces at node j+1 in the x, y, and z directions respectively. To analyze the moments of node j+1 in the x, y, and z directions; They are located in 、 Analysis segment between two analysis nodes The anchor reaction forces of the anchor cable with internal number m in the x, y, and z directions in the shell coordinate system are all taken as 0 if there is no anchor cable in the segment.

7. The load mapping-based refined analysis method for three-dimensional suspended tunnel structures according to claim 1 is characterized in that: Use the beam model to shell model load mapping to map the forces and moments on the analysis segment to each 3D node in the corresponding segment of the shell model, and ensure that the net force of each node on the segment center is equal to the equivalent load. Specifically, it includes: Given a suspended tunnel segment , assuming that there is a total of nodes, and the coordinates of the segment center are ; For any point in the segment, the coordinates are Node , the lateral nodal force and vertical nodal forces Assuming that it follows a linear distribution with respect to its coordinates, the axial nodal forces It is assumed to be evenly distributed; thus, the node The relationship with the resultant force of segment i is as follows: ， Where, is the equivalent force of segment i in the x, y, and z directions, is the equivalent moment of segment i in the x, y, and z directions; for any node on the shell model at a certain moment , are the horizontal, vertical and longitudinal nodal forces; x0, y0, z0 are the distances from the segment center, where ; k1, k2, k3, k4, k5, k6, k7 are the parameters required to solve the equation.

8. A three-dimensional floating tunnel structure refinement analysis system based on load mapping, characterized in that: A system for implementing a load mapping-based refined analysis method for a three-dimensional suspended tunnel structure according to any one of claims 1 to 7, comprising: The equivalent load calculation module is used to convert the response of each analysis node in the deformed beam coordinate system to the shell coordinate system, and calculate the equivalent load on each segment based on the force balance principle; The load mapping module is used to distribute the equivalent load on each analysis segment to each node of the shell model.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the load mapping-based refined analysis method for a three-dimensional suspended tunnel structure according to any one of claims 1 to 7 is implemented.

10. An electronic device, characterized in that: The device comprises: one or more processors; a memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the three-dimensional floating tunnel structure refinement analysis method based on load mapping as described in any one of claims 1 to 7.

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