2 Structural Model

2.1 Members to be modelled

2.1.1 All main longitudinal and transverse structural elements are to be modelled. These include:

Inner and outer shell,
Deck,
Double bottom floors and girders,
Transverse and vertical web frames,
Hatch coamings,
Stringers,
Transverse and longitudinal bulkhead structures,
Other primary supporting members,
Other structural members which contribute to hull girder strength.

All plates and stiffeners on the structure, including web stiffeners, are to be modelled. Brackets which contribute to primary supporting member strength and the size of which is not less than the typical mesh size (s-by-s) described in [2.4.2], are to be modelled.

2.2 Extent of model

2.2.1 Longitudinal extent

Except the foremost and aftermost cargo hold models, the longitudinal extent of the cargo hold FE model is to cover three cargo hold lengths. The transverse bulkheads at the ends of the model are to be modelled. Where corrugated transverse bulkheads are fitted, the model is to include the extent of the bulkhead stool structure forward and aft of the tanks/holds at the model ends. The web frames at the ends of the model are to be modelled. Typical finite element models representing the midship cargo hold region of different ship type configurations are shown in Figure 3 and Figure 4.

The foremost and the aftmost cargo holds are located at the middle of the FE models as follows:

Foremost cargo hold: from the after bulkhead of the cargo hold no. 2 to the ship’s foremost cross section where the reinforced ring or web frame remains continuous from the base line to the strength deck.
Aftermost cargo hold: from the after bulkhead of the engine room to the forward bulkhead of no. N-1 cargo hold, where N is the number of holds or sets of holds numbered from forward to aft.

Examples of finite element models representing the foremost and aftermost cargo holds of different ship type configurations are shown in Figure 5 and Figure 6.

2.2.2 Hull form modelling

In general, the finite element model is to represent the geometry of the hull form. In the midship cargo hold region, the finite element model may be prismatic provided the mid-hold has a prismatic shape.

In the foremost cargo hold model, the hull form forward of the transverse section at the middle of the fore part up to the model end as defined in [2.2.1] may be modelled with a simplified geometry. The transverse section at the middle of the fore part up to the model end may be extruded out to the fore model end, as shown in Figure 2.

In the aftmost cargo hold model, the hull form aft of the middle of the machinery space may be modelled with a simplified geometry. The section at the middle of the machinery space may be extruded out to its aft bulkhead, as shown in Figure 2.

When the hull form is modelled by extrusion, the geometrical properties of the transverse section located at the middle of the considered space (fore or machinery space) are copied along the simplified model. The transverse web frames are to be considered along this extruded part with the same properties as the ones in the fore part or in the machinery space.

Figure 2 : Hull form simplification for foremost and aftmost cargo hold model

2.2.3 Transverse extent

Both port and starboard sides of the ship are to be modelled.

2.2.4 Vertical extent

The full depth of the ship is to be modelled including primary supporting members above the upper deck, trunks, forecastle and/or cargo hatch coaming, if any.

The superstructure or deck house in way of the machinery space and the bulwark are not required to be included in the model.

2.3 Finite element types

2.3.1 Shell elements are to be used to represent plates.

2.3.2 All stiffeners are to be modelled with beam elements having axial, torsional, bi-directional shear and bending stiffness. The eccentricity of the neutral axis is to be modelled.

2.3.3 Face plates of primary supporting members and brackets are to be modelled using rod or beam elements.

Figure 3 : Example of 3 cargo hold model within midship region of oil tankers

Figure 4 : Example of 3 cargo hold model within midship region of a bulk carrier

Example of cargo hold model of a bulk carrier (shows only port side of the full breadth model)

Figure 5 : Example of FE model for the foremost cargo hold structure of an oil tanker

Figure 6 : Example of FE model for the aftermost cargo hold structure of a bulk carrier

Figure 7 : Typical finite element mesh on web frame

Figure 8 : Typical finite element mesh on transverse bulkhead

s = Stiffener spacing

2.4 Structural modelling

2.4.1 Aspect ratio

The aspect ratio of the shell elements is in general not to exceed 3. The use of triangular shell elements is to be kept to a minimum. Where possible, the aspect ratio of shell elements in areas where there are likely to be high stresses or a high stress gradient is to be kept close to 1 and the use of triangular elements is to be avoided.

2.4.2 Mesh

The shell element mesh is to follow the stiffening system as far as practicable, hence representing the actual plate panels between stiffeners. In general, the shell element mesh is to satisfy the following requirements:

a) One element between every longitudinal stiffener, see Figure 7. Longitudinally, the element length is not to be greater than 2 longitudinal spaces with a minimum of three elements between primary supporting members.
b) One element between every stiffener on transverse bulkheads, see Figure 8.
c) One element between every web stiffener on transverse and vertical web frames, cross ties and stringers, see Figure 7 and Figure 9.
d) At least 3 elements over the depth of double bottom girders, floors, transverse web frames, vertical web frames and horizontal stringers on transverse bulkheads. For cross ties, deck transverse and horizontal stringers on transverse wash bulkheads and longitudinal bulkheads with a smaller web depth, modelling using 2 elements over the depth is acceptable provided that there is at least 1 element between every web stiffener. For a single side bulk carrier, 1 element over the depth of side frames is acceptable. The mesh size of adjacent structure is to be adjusted accordingly.
e) The mesh on the hopper tank web frame and the topside web frame is to be fine enough to represent the shape of the web ring opening, as shown in Figure 7.
f) The curvature of the free edge on large brackets of primary supporting members is to be modelled to avoid unrealistic high stress due to geometry discontinuities. In general, a mesh size equal to the stiffener spacing is acceptable. The bracket toe may be terminated at the nearest nodal point provided that the modelled length of the bracket arm does not exceed the actual bracket arm length. The bracket flange is not to be connected to the plating, as shown in Figure 10. The modelling of the tapering part of the flange is to be in accordance with [2.4.8]. An example of acceptable mesh is shown in Figure 10. A finer mesh is to be used for the determination of detailed stress at the bracket toe, as given in Ch 7, Sec 3.

Figure 9 : Typical finite element mesh on horizontal transverse stringer on transverse bulkhead

s = Stiffener spacing

Figure 10 : Typical finite element mesh on transverse web frame main bracket

2.4.3 Finer mesh

Where the geometry cannot be adequately represented in the cargo hold model and the stress exceeds the cargo hold mesh acceptance criteria, a finer mesh may be used for such geometry to demonstrate satisfactory scantlings. The mesh size required for such analysis can be governed by the geometry. In such cases, the average stress within an area equivalent to that specified in [2.4] is to comply with the requirements given in [5.2].

2.4.4 Corrugated bulkhead

Diaphragms in the stools, supporting structure of corrugated bulkheads and internal longitudinal and vertical stiffeners on the stool plating are to be included in the model. Modelling is to be carried out as follows:

a) The corrugation is to be modelled with its geometric shape.
b) The mesh on the flange and web of the corrugation is in general to follow the stiffener spacing inside the bulkhead stool.
c) The mesh on the longitudinal corrugated bulkhead is to follow longitudinal positions of transverse web frames, where the corrections to hull girder vertical shear forces are applied in accordance with [4.4.7].
d) The aspect ratio of the mesh in the corrugation is not to exceed 2 with a minimum of 2 elements for the flange breadth and the web height.
e) Where difficulty occurs in matching the mesh on the corrugations directly with the mesh on the stool, it is acceptable to adjust the mesh on the stool in way of the corrugations.
f) For a corrugated bulkhead without an upper stool and/or lower stool, it may be necessary to adjust the geometry in the model. The adjustment is to be made such that the shape and position of the corrugations and primary supporting members are retained. Hence, the adjustment is to be made on stiffeners and plate seams if necessary.
g) When corrugated bulkhead is subjected to liquid cargo or ballast, dummy rod elements with a cross sectional area of 1 mm² are to be modelled at the corrugation knuckle between the flange and the web. Dummy rod elements are to be used as minimum at the two corrugation knuckles closest to the intersection between:

Transverse and longitudinal bulkheads,
Transverse bulkhead and inner hull,
Transverse bulkhead and side shell.

h) Manholes in diaphragms are to be modelled according to [2.4.9].

2.4.5 Example of mesh arrangements of the cargo hold structure are shown in Figure 11 to Figure 14.

Figure 11 : Example of FE mesh arrangements of cargo hold structure for a bulk carrier

Figure 12 : Example of FE mesh on transverse corrugated bulkhead structure for a product tanker

Figure 13 : Example of FE mesh arrangements of cargo tank structure for an aframax tanker

Figure 14 : Examples of FE mesh arrangements of cargo tank structure for VLCC and product tanker

2.4.6 Sniped stiffener

Non continuous stiffeners are to be modelled as continuous stiffeners, i.e. the height web reduction in way of the snip ends are not to be modelled.

2.4.7 Web stiffeners of primary supporting members

Web stiffeners of primary supporting members are to be modelled. Where these stiffeners are not in line with the primary FE mesh, it is sufficient to place the line element along the nearby nodal points provided that the adjusted distance does not exceed 0.2 times the stiffener spacing under consideration. The stresses and buckling utilisation factors obtained need not be corrected for the adjustment. Buckling stiffeners on large brackets, deck transverses and stringers parallel to the flange are to be modelled. These stiffeners may be modelled using rod elements.

2.4.8 Face plate of primary supporting member

The effective cross sectional area at the curved part of the face plate of primary supporting members and brackets is to be calculated in accordance with Ch 3, Sec 7. The cross sectional area of a rod or beam element representing the tapering part of the face plate is to be based on the average cross sectional area of the face plate in way of the element length.

2.4.9 Openings

Methods of representing openings and manholes in webs of primary supporting members are to be in accordance with Table 1. Regardless of size, manholes are to be modelled by removing the appropriate elements.

Table 1 : Representation of openings in primary supporting member webs

Criteria	Modelling decision	Analysis
h_o/h < 0.5 and g_o < 2.0	Openings do not need to be modelled	To be evaluated by the screening procedure as given in Ch 7, Sec 3, [3.1.1]
Manholes	The geometry of the opening is to be modelled by removing the adequate elements	To be evaluated by the screening procedure as given in Ch 7, Sec 3, [3.1.1]
h_o/h ≥ 0.5 or g_o ≥ 2.0	The geometry of the opening is to be modelled	To be evaluated by fine mesh as given in Ch 7, Sec 3, [2.1.1]
where: : Length of opening parallel to primary supporting member web direction, in m, see Figure 15. For sequential openings where the distance, d_o between openings is less than 0.25 h, the length is to be taken as the length across openings as shown in Figure 16. h_o : Height of opening parallel to depth of web, in m, see Figure 15 and Figure 16. h : Height of web of primary supporting member in way of opening, in m, see Figure 15 and Figure 16.

Figure 15 : Openings in web

Figure 16 : Length lo for sequential openings with d_o < h/4

2.5 Boundary conditions

2.5.1 General

All boundary conditions described in this section are in accordance with the global coordinate system defined in Ch 4, Sec 1.

2.5.2 Application

The boundary conditions given [2.5.3] are applicable to cargo hold finite element model analyses in cargo hold region.

2.5.3 Boundary conditions

The boundary conditions consist of the rigid links at model ends, point constraints and end-beams. The rigid links connect the nodes on the longitudinal members at the model ends to an independent point at neutral axis in centreline. The boundary conditions to be applied at the ends of the cargo hold FE model, except for the foremost cargo hold, are given in Table 2. For the foremost cargo hold analysis, the boundary conditions to be applied at the ends of the cargo hold FE model are given in Table 3.

Table 2 : Boundary constraints at model ends except the foremost cargo hold models

Location	Translation			Rotation
Location	δ_x	δ_y	δ_z	θ_x	θ_y	θ_z
Aft End
Independent point	-	Fix	Fix	M_T-end	-	-
Cross section	-	Rigid link	Rigid link	Rigid link	-	-
Cross section	End beam, see [2.5.4]
Fore End
Independent point	-	Fix	Fix	Fix	-	-
Intersection of centreline and inner bottom	Fix	-	-	-	-	-
Cross section	-	Rigid link	Rigid link	Rigid link	-	-
Cross section	End beam, see [2.5.4]
Note 1: [-] means no constraint applied (free). Note 2: See Figure 17.

Table 3 : Boundary constraints at model ends of the foremost cargo hold model

Location	Translation			Rotation
Location	δ_x	δ_y	δ_z	θ_x	θ_y	θ_z
Aft End
Independent point	-	Fix	Fix	Fix	-	-
Intersection of centreline and inner bottom	Fix	-	-	-	-	-
Cross section	-	Rigid link	Rigid link	Rigid link	-	-
Cross section	End beam, see [2.5.4]
Fore End
Independent point	-	Fix	Fix	M_T-end	-	-
Cross section	-	Rigid link	Rigid link	Rigid link	-	-
Cross section	Endbeam, see [2.5.4]
Note 1: [-] means no constraint applied (free). Note 2: See Figure 17. Note 3: Boundary constraints in fore end are to be located at the most forward reinforced ring or web frame which remains continuous from the base line to the strength deck.

Figure 17 : Boundary conditions applied at the model end sections

2.5.4 End constraint beams

End constraint beams are to be modelled at the both end sections of the model along all longitudinally continuous structural members and along the cross deck plating of bulk carriers. An example of end beams at one end for a double hull bulk carrier is shown in Figure 18.

Figure 18 : End constraint beams for a bulk carrier

The properties of beams are calculated at fore and after sections separately and all beams at each end section have identical properties as follows:

Net moment of inertia: I_yy-n50 = I_zz-n50 = I_xx-n50 (J) = 1/25 of the vertical hull girder moment of inertia of fore/aft end cross sections based on the net FE model.
Net cross sectional area: A_y-n50 and A_z-n50 = 1/80 of the fore/aft end cross sectional areas based on the net FE model.

where:

I_yy-n50 : Moment of inertia about local beam Y axial, in m⁴.

I_zz-n50 : Moment of inertia about local beam Z axial, in m⁴.

I_xx-n50 (J) : Torsional inertia, in m⁴.

A_y-n50 : Shear area in local beam Y direction, in m².

A_z-n50 : Shear area in local beam Z direction, in m².