Fluid-Structural Interaction Study of the Structural Arrangement of a Riverine Low-Draft Combat Boat for Coastal Transit Conditions

The Riverine low draft combat boats are aluminium-built crafts designed to operate exclusively in low-depth riverine environments. Given the Colombian geography, these operations might be extended to estuaries or coastal transit conditions. Consequently, there is a need of studying the structural integrity of the hull in the case of coastal transit. A fluid-structural interaction study was performed in which the hydrodynamic hull pressures are associated as an input in a static structural finite element analysis. The obtained hull pressures were compared with the values suggested by the classification rules. Los botes de combate fluvial de bajo calado son embarcaciones fluviales con un arreglo estructural en aluminio exclusivamente diseñado para operar en ríos de baja profundidad. No obstante, debido a la geografía nacional, estas operaciones pudieran extenderse a condiciones de estuario o tránsitos costeros. De esta manera, surge la necesidad de evaluar la resistencia estructural del casco en condiciones de tránsito costero. Para tal fin, se realizó un estudio de interacción fluido estructural en la que se enlaza las presiones hidrodinámicas en el casco como entrada para un análisis por elementos finitos. Las presiones en el casco fueron contrastadas con los valores obtenidos con el uso reglas de las Sociedades de Clasificación.

longitudinal stiffeners, and two side girders.The side hull structure consists of AW 6082-T6 flat-bar longitudinal stiffeners which purpose is to provide the required stiffness to the plates of the side.These side plates are to be vertically supported AW 5083 H321 frames [see Fig. 1].Four of these frames are watertight bulkheads [7].
The deck is composed of a AW 5083 H321 plate and seven flat-bar longitudinal stiffeners.This deck is transversally supported by profiles deck beams and bulkheads and longitudinally supported by two side girders.
The principal particulars of this combat boat are summarized in the next table [see table 1] [see Fig. 2].
Although the vessel was designed to operate in a riverine environment, it might occur the cases where the vessel is assigned to operate in estuaries or develop an occasional coastal transit between river mouths.
The riverine low draft combat boat designed with naval-grade aluminium and 10 m 2 polymeric ballistic protection panels on deck, can develop riverine patrolling and reconnaissance operations in low-depth waters.the technical feature of this boat includes a 24 knots maximum speed, an operative range of 300 km, and the capability to provide tactical fire support [1].
The structural arrangement of this boat was designed to maintain a low weight while the security of the crew, the structural integrity of the hull and the boat performance remain preserved at riverine conditions.To ensure the structural integrity of the hull, the scantling was performed according to recommendations and requirements of the classification societies ABS in "Rules for Building and Classing, High-Speed Craft; Hull Construction and Equipment" [2] and ISO 12215 "Small craft -Hull construction and scantlings -Part 5: Design pressures for monohulls, design stresses, scantlings determination" [3].Given the structural arrangement obtained, its structural integrity was evaluated and improved by direct analysis in a global model according to "Class Guideline-Finite Element Analysis" by DNV-GL [4].
The hull scantling refers to the assessment of selected plates and stiffeners' geometrical dimensions in accordance with their mechanical properties and section modulus.The strength of the hull to environmental and duty external loads depends largely on the structural arrangement and its capability to withstand bending and shear stresses [5].First, the hull girder strength was assessed according to cross-section inertial properties followed by local calculation of plates thickness and cross-section of primary and secondary stiffeners.In this way, the plates of the structure and the respective primary and secondary structural reinforcements are to be designed in such a way their mechanical strength is high enough to prevent crack initiation due to wave pressures on the hull [6].

Principal particulars Values
Length over all 8.68 m These natural frequencies depend on the mass and stiffness properties of the system [10].The interaction between the encounter frequency and the natural frequencies of the ship leads to a boat amplitude response.When the encounter and the natural frequencies present equal values might occur resonance phenomena.When the encounter frequency is very low, at head seas conditions, the dynamic effect associated with damping is virtually negligible and the boat motion amplitude is on the same order as the wave amplitudes.In the case of high wave frequencies, the boat responses are reduced because the short wavelength does not excite the hull motion [11].
Hence, the main aim of this work is to evaluate, by computational methods, the effects of hydrodynamic pressures on the hull's structural integrity at different headings and wave frequencies.The hydrodynamic behavior study was developed with the software Ansys Aqwa and the pressures were exported to the static structural model of Ansys Mechanical to evaluate the strength of the structural arrangement by the finite element method.
In the present methodology it was detailed the hydrodynamic diffraction computational model and the linked structural finite element development.

Geometry
Shell modeling was carried out by using ANSYS In those cases, the hull could be subject to loads or pressures that overcome the structural arrangement resistance even though the assessment from rules and guidelines of the classification societies, which calculations are generally of semi-empirical nature and also are calibrated to secure the lifespan expected, allow a simplified approach of complex structural problems with a wide safety factor [8].
For the scantling of small crafts under riverine conditions, classification societies' rules dictate a design wave height of 0.5 m [2].This wave height can be classified as a Beaufort sea state 2 scale but changes in wave frequency and direction will affect the level of pressure on the hull and hence, the stress levels along the structural arrangement [9].
Waves are an external agent with a considerable influence on the behavior of ships in a marine environment.The wave frequency is inversely proportional to the wavelength and celerity.The latter, given by the relation between wavelength and period, is a distinctive factor among surface waves and other types of wave motions [10].The relative boat speed in relation to the waves is defined as the encounter frequency.The encounter frequency is a function of boat speed (Vs) and the encounter angle (β).This frequency is only zero when the velocity of the observer in the direction of wave propagation and the wave velocity are equal.On the other hand, when the wave speed is lower than the parallel component to the wave direction of the boat speed, the encounter frequency is negative and the boat overtakes the waves [11].
In the boat, each degree of freedom that has a restoring force has an associated natural frequency.The worst frequency-heading combination at which the hull's response amplitude is a maximum, was evaluated by direct analysis to obtain the effect on the structural arrangement according to the next block diagram [see Fig. 5].

Direct Analysis
Global modeling of the boat and the subsequent finite element method analysis are explained in detail in this section.The analysis is subjected to plain stress and linear-elastic mechanics simplifications.
SpaceClaim 2022 software.Only external hull surfaces were included.These hull surfaces are divided by the waterline [see Fig. 3].

Meshing
The surfaces were meshed with 10029 elements and a defeaturing tolerance of 0.005 m.This element size allows a maximum frequency of 1.55 Hz for the analysis [see Fig. 4].

Hydrodynamic Response Analysis
The computations of the wave-induced motions were carried out by utilizing three-dimensional potential flow based in diffraction-radiation theory.
The computations of the hydrodynamic pressures took into account all six degree of freedom rigidbody motions of the full.The environmental constants and mass properties are detailed in the next table This analysis considers the operational profile at full load capacity.Wave headings (β) were evaluated with increments of 15°, the wave encounter frequencies (ω e ) covers a range from 0.015 Hz to 1.2 Hz with increments of 0.1 Hz [2].For this study the wave pattern was simplified with a regular wave with 0.5 m amplitude as a first approach [2].

Boundary Conditions
The boundary conditions for the global structural model should reflect simple supports that will

Load Conditions
Hydrodynamic pressure, imported from the Ansys Aqwa software, was applied on the hull below de waterline.Design pressure calculations from class requirements was assigned on the deck with a value of 5 kN/m2 [2] [3] [see Fig. 8].
In this section, the results of the hydrodynamic response analysis and the use of the obtained hull pressures results as an input of a structural analysis are detailed.
avoid built-in stresses so the reaction forces in the boundaries are to be minimized [4].ANSYS Inertia relief option allows to exactly balance the force differences on the supports creating a state of static equilibrium.Two of these fixation points were applied at transom intersecting the main deck at portside and starboard, and the last one, in the bow centerline intersecting waterline.

Hydrodynamic Pressures
Different wave frequencies and headings were tested in the proposed interval and it was found that the wave frequency of 0.44 Hz produces the highest pressure levels with a wave amplitude of 0.5 m [see Fig. 9].
Regarding the headings, the highest hull pressures were obtained with beam seas [see Fig. 10 & Fig. 11].The lowest hull pressures were reported with head seas [see Fig. 12 & Fig. 13].All with a wave height set in 0.5 m.The hydrodynamic pressure magnitude difference between both load cases is close to 7.5 times.
On the other hand, the obtained motions at different waves frequencies and headings showed that there are intervals in which the boat would present unsecure navigation and must be avoided.

Hydrostatic Results
From the hydrodynamic diffraction analysis, it was obtained the hydrostatic characterization of the boat.Some of these are summarized below [see table 6].In the case of incrementing the wave height from a typical sea state 2 with 0.5 m of wave height to a sea state 3 with 1.25 m of wave height, the hull presented an increase of 2.7 times in the hydrodynamic pressure from sea state 2 and 12.7 times higher from a sea state 1 at head seas conditions [see Fig. 15].Analyzing the motions of the hull under sea state 3 conditions it was found that the boat would present an unsafe navigation in a wide range of headings and frequencies [see Fig. 16].Table 7. Hydrodynamic pressures on the bottom.

Direct Analysis
Given the results of the hydrodynamic pressures on the hull as function of heading, frequency, and a wave amplitude of 0.5 m, critical direct analysis was carried out with a heading of 90° and a frequency of 0.44 Hz.At this load case, the highest pressures were found in the vicinity of the bottom -side connection.The side panels presented an equivalent maximum stress near to 84 MPa with a consequent 2.7 safety factor [see Fig. 17].
Frames and bulkheads showed stress values between 25 MPa to 45 MPa in the hull pressure influence zone.Nevertheless, there is a spot in the frame above deck in a bulkhead station where equivalent stresses close to 140 MPa are reported, but given        ANYFANTIS, K. «Ultimate strength of stiffened panels subjected to non-uniform thrust,» is 0.98 in the chine and 1.62 in the side plates.
Regarding profiles, the lowest safety factor is about 1.27 in non-affected zones.Higher stresses than the allowed are situated in heat-affected zones in one of the side frame stiffener; however, given the focused nature of these, their localized plastic deformation will not compromise overall strength.Nevertheless, the insufficient safety factor of a chine plate zone, the pressures exceed the strength of the structural arrangement [see Fig. 28].
The structural arrangement strength for a riverine low-draft combat boat was analyzed by a hydrodynamic response analysis and direct analysis.It can be concluded that the structure of the hull can withstand sea state 2 conditions.Nevertheless, the low draft of the vessel and its flat bottom might imply unsecure navigation specially under beam waves ± 60° conditions within frequencies from 0.44 Hz.to 0.55 Hz, thus the design performance will be drastically reduced at estuaries and coastal transit conditions.Further considerations, such as crew comfort standards, might reduce even more the coastal transit capabilities of the boat.
According to the obtained hydrodynamic pressures on the hull by this computational model, Classification Societies Rules apply safety factors up to 2, this without having into account slamming pressures components.Given the time-dependent loads and the hydro-elastic structural response characteristic of slamming, the calculation of this phenomenon outpaced the computational model used by the software.
Sea state 3 present unsafe navigating conditions in a wide range of frequencies and headings because the boat motions.Additionally, at 120° of heading at resonance frequency of 0.44 Hz the structural arrangement strength of the side-bottom assembly is not enough to withstand the imported hydrodynamic pressures.

Fig. 3 .
Fig. 3. Hull surface cut by the water surface.

Fig. 15 .
Fig. 15.Hydrodynamic pressure as a function of frequency and sea states.
Fig. 18.Stress distribution in the frames with beam seas.

Fig. 25 .
Fig. 25.Location of the maximum hydrodynamic pressure on the bottom with a 260° wave phase angle.

Fig. 9 .
Fig. 26.Stress levels at aft section of the boat.

Fig. 27 .
Fig. 27.Stress levels at aft section of the boat.

Table 2 .
Mass properties for the model.
Alvarado, Urango, Vásquez Ship Science & Technology -Vol.18 -n.°35 -(41-56) July 2024 -Cartagena (Colombia) Structural model Geometry Shell modeling was carried out by using ANSYS SpaceClaim 2022 software [see Fig. 6].Bonded contacts were used among structural elements given their welded connections.Meshing of the structural model SHELL181 elements were used for meshing.This four-node element with six degrees of freedom at each node is suitable for analyzing thin to moderately thick shell structures [see Fig. 7].After a convergence test, a 30 mm meshing element size was used.The shell geometry is represented by 4 Node Linear Quadrilateral elements; the degenerate 4 Node Linear Triangular option was only used as filler in mesh generation [4] [12].

Table 4 .
5083-H321 aluminum alloy mechanical properties were assigned to plates whereas aluminum alloy 6082 T6 properties were set to stiffeners.The mechanical properties of both aluminum alloys are detailed in the next table [see table 4].Aluminum alloys mechanical properties defined for the model [10].

Table 5 .
Allowable stresses on structural members.
At sea state 3, with a consequent wave amplitude of 1.25 m, a resonance frequency of 0.44 Hz, and a heading of 120°.Stress levels increase in such a way reach values up to 126 MPa in the chine and 115 MPa in the side plates.Given the allowable stresses stated in table 5, the lowest safety factor in plates At head seas conditions, the effect of hull's hydrodynamic pressures on the structural arrangement stress levels decreases in comparison with others load cases and this behavior is consistent with the pressure levels showed in The authors are very grateful for the constant support of The Science and Technology Corporation for Naval, Maritime and Riverine Industry Development (COTECMAR).