Joint stress of a hinged platform composed of eight boxes

The box-type hinged platform has important applications in ocean engineering. In this paper, a multi-module assembled box-type platform is described. The mid-section load of the platform is numerically simulated based on the three-dimensional velocity potential theory and the indirect time-domain method through the hydrodynamic module AQWA in ANSYS. The stress of the hinged joints of platforms was performed using finite element analysis software in ANSYS software. The results show that: (1) In irregular waves, the shear force and bending moment in the middle section of the platform increases with the increase of the significant wave height; (2) Under the same towing scheme, the stress of the hinged joints between box platforms shows an increasing trend with the increase of wave level. Under the same wave working condition, the stress at the uniaxial nut of the hinged joints is relatively high, which is prone to fracture.


Introduction
China's near-island reef natural geographic conditions are very complex [1][2][3].Most of the seabed geology is sandy.The underwater topography is relatively gentle, the draft is shallow, and the water depth changes drastically, which are docking difficulties [4].The box-type platform can be a good solution to this problem.The Box-type platform, using barges for towing, multi-module hinged whole group towing, can not only improve the stability of the box-type platform towing but also improve the platform installation efficiency.
Currently, most of the research on platforms focuses on the motion response.Newman [5] investigated the motion response characteristics of an articulated double-floating body based on the modal expansion method, which greatly reduces the system's degrees of freedom.Diamantoulaki and Angelide [6] used Newman's method to study the effect of the frequency of the incident wave and the number of floats on the kinematic response of an articulated multi-floating body system; it was found that the configuration of the articulated floats array has a significant effect on the kinematic response of the multibody system.Ding et al. [7] investigated the towing characteristics of a foundation platform in still water, downwash, and upwash.The experimental results showed that when the platform towing process encounters large waves, reducing the towing speed is an effective way to ensure the wave resistance and stability of the structure.Based on the linear potential flow theory, Wang et al. [8] investigated the motion response of an articulated multi-float structure under the action of regular waves in the frequency domain by using the modal method.They took three articulated box floats as an example and discussed the effects of water depth and articulation position on the motion response of the structure.Sun et al. [9] investigated the hydrodynamic response and bending moment distribution of a multi-module hinged floating bridge under the action of regular waves through hydrodynamic model tests.They analyzed the bending moment and motion response of the pontoon bridge based on hydrodynamic theory.Sun and Li [10] conducted an experimental study on the coupling response between an articulated floating platform with a side-by-side single-point mooring system and a cargo ship.They analyzed the relative motion characteristics of a multi-floating body parallel single-point mooring system under regular waves and irregular sea conditions.
The motion response of the platform has been systematically studied at home and abroad, but there is no in-depth understanding of the joint stress of a multi-module assembled box-type platform.Based on this, this paper adopts the AWQA hydrodynamic module in ANSYS software.Based on the threedimensional potential flow theory, it systematically carries out the response characteristic analysis of the middle profile load of the multi-module assembled box-type platform under three working conditions of the irregular wave.It then carries out the stress analysis of the articulated joints of the boxtype platform by using the finite element analysis software in ANSYS software.

Model and parameters of the box platform
The paper takes the multi-module assembled box-type platform under the overall towing mode as the research object.When establishing the model, the coordinate system is defined first: the X -axis is the direction of the ship's length, the Y -axis is the direction of the ship's width, and the Z -axis is vertically upward.The platform system consists of eight box-type protection platforms, from front to back, in order of No. 1 to No. 8 box-type platforms.The origin is located in the center of the No. 1 boxtype platform's waterline surface.The APDL module of ANSYS is utilized to establish the wet surface model of a single-box platform.After importing it into AQWA, the eight box platforms are duplicated, and the towing cable and the articulation between the platforms are established.On top of each platform can be placed a square cabin or hauling materials, and the spacing between adjacent safeguard platforms is 0.2 m .The hydrodynamic analysis model is shown in Figure 1, and the main parameters of the platform are shown in Table 1.

Parameters of hinged joint
Neighboring box safeguard platforms are connected to each other by means of hinged joints.There are six sets of hinged joints between each box platform, two in each set.The three-dimensional diagram of the joints and their connection to the neighboring box platforms is shown in Figure 2. The hinged joints are made of high-strength steel, and their main parameters and material properties are shown in Table 2.

Marine environmental conditions
The multi-module box-type platform is arranged in the reef area near the island, considering the role of wind and wave currents in the sea.According to the typical sea state, the wind speed is taken as the 1 minute average wind speed of 10 m above the sea level, which is 10 ms .Combined with the relevant data of the area where the box-type platform is arranged, the surface current speed of the water near the platform is 0.4 ms .After careful consideration, the Jonswap spectrum is used to fit the irregular wave condition, and the incidence angle of the wind, wave, and current is 0  .The environmental condition parameters for the irregular wave condition of the box-type platform are shown in Table 3.

Calculation results and analysis of mid-section load
The statistics of the maximum mid-section load of the box-type platform under operating conditions are shown in Table 4. From Table 4, it can be seen that the mid-section load z F is larger than x F and y F , and M is larger than x M and z M .In the irregular wave conditions, the force and bending moment of the mid-section load increase with the increase of the wave level.The maximum shear force of the mid-section load is 120.1 kN , and the maximum bending moment is 1752 kN m  .

Calculation results and analysis of structural strength of hinged joints
The hinged joint is modeled using solidwork 3D modeling software.The model is imported into ANSYS finite element analysis software (Mechanical) to mesh the joint, and the finite element model of the joint is shown in Figure 3.The strength analysis of the hinged joint is performed by applying the calculated stress amplitude of the mid-section load to the unit nodes on both sides of the finite element model.Figures 4 to 6 show the stress clouds of the joint under irregular wave conditions.From Figures 4 to 6, it can be seen that ( 1) under the same towing scheme, the joint stress of the box-type platform shows an increasing trend with the increase of the wave level.The joint stress is the largest when there is a meaningful wave height of 1.25 m and a spectral peak period of 6.00 s.The joint stress is up to 890 MPa.(2) Under the same wave condition, the single joint lug side stress of the hinged joint is larger and easy to fracture.

Conclusions
In this paper, for the multi-module assembled box-type platform under overall towing, the numerical simulation of the mid-section load of the platform is carried out by using the AQWA module in ANSYS software.The strength analysis of the hinged joints of the box-type platform is carried out by using the finite element analysis software in ANSYS software.The main conclusions are as follows:(1) In irregular wave conditions, the mid-section shear force and bending moment show an increasing trend with the increase of sea state class.This is because as the sea state level increases, the greater the wave impact on the floating bridge is, the greater the motion of the floating bridge is, and the greater the forces and bending moments that the center profile will be subjected.(2) Under the same towing scheme, the joint stresses between box-type platforms show an increasing trend with the increase of wave class.This is because as the sea state level increases, the movement of the floating bridge increases, and the stresses on the joints also increase.Under the same wave condition, the stresses on the side of the single joint lugs of the hinged joints are larger and prone to fracture.

Figure 1 .
Figure 1.Hydrodynamic analysis model of box platform.

Figure 2 .
Figure 2. Three-dimensional view of the model of the joints and its connection to the adjacent box platform section.

Figure 3 .
Figure 3. Finite element model of the hinged joint.

Figure 4 .
Figure 4. Stress cloud of the joint under A1 condition.

Figure 5 .
Figure 5. Stress cloud of the joint under A2 condition.

Figure 6 .
Figure 6.Stress cloud of the joint under A3 condition.

Table 1 .
Main parameters of individual platform.

Table 2 .
Material parameters of hinged joints.

Table 3 .
Environmental operating parameters for irregular wave conditions.

Table 4 .
Statistical results of the maximum mid-section load of box-type platform.