2 FE Modelling

2.1 General

2.1.1

Evaluation of hot spot stresses for fatigue assessment requires the use of very fine finite element meshes in way of areas of high stress concentration. These very fine mesh zones may be incorporated into the global model as shown in Figure 2. The coarse mesh model of the cargo holds is to be made according to Ch 7, Sec 2, [2.4]. Alternatively, this very fine mesh analysis can be carried out by means of separate local finite element models with very fine mesh zones in conjunction with the boundary conditions obtained from a global model of the cargo holds. Typical local finite element models of a hopper knuckle with very fine mesh are shown in Figure 3, Figure 4, and Figure 5.

2.1.2 Corrosion model

The very fine mesh finite element models used for fatigue assessment are to be made using net thickness, t_n50, in accordance with Ch 9, Sec 1, [5.1].

2.1.3 Separate local FE model

Where a separate local finite element model is used, the extent of the local model is to be such that the calculated stresses are not significantly affected by the imposed boundary conditions and application of loads. The boundary of the fine mesh model is to be taken at adjacent primary supporting members such as girders, stringers and floors in the cargo hold model as far as practicable. Transverse web frames, stringer plates and girders at the boundaries of the local model need not be represented in the local model.

2.1.4

The evaluation of hot spot stress for ‘a’ type hot spot is to be based on shell element of mesh size t_n50 × t_n50, where t_n50 is the net thickness of the plate in way of the considered hot spot. The evaluation of hot spot stress for a ‘b’ type hot spot is to be based on shell element of mesh size 10×10 mm. The aforementioned mesh size is to be maintained within the very fine mesh zone, extending over at least 10 elements in all directions from the fatigue hot spot position. The transition of element size between the coarser mesh and the very fine mesh zone is to be done gradually and an acceptable mesh quality is to be maintained. This transition mesh is to be such that a uniform mesh with regular shape gradually transitions from smaller elements to larger ones. An example of the mesh transition in way of the side frame bracket toe is shown in Figure 6.

2.1.5

Four-node shell elements with adequate bending and membrane properties are to be used inside the very fine mesh zone. The four node element is to have a complete linear field of in-plane stresses and hence pure inplane bending of the element can be exactly represented. In case of steep stress gradients, 8 node thin shell elements are to be used if deemed practical. The shell elements are to represent the mid plane of the plating. For practical purposes, adjoining plates of different thickness may be assumed to be median line aligned, i.e. no staggering in way of thickness change is required. The geometry of the weld and construction misalignment is not required to be modelled.

2.1.6

All structure in close proximity to the very fine mesh zones is to be modelled explicitly with shell elements. Triangular elements are to be avoided where possible. Use of extreme aspect ratio (e.g. aspect ratio greater than 3) and distorted elements (e.g. element’s corner angle less than 60 deg or greater than 120 deg) are to be avoided.

2.1.7

Where stresses are to be evaluated on a free edge, such as cut-outs for stiffener connections at web frames, edge of plating and hatch corners, beam elements having the same depth as the adjoining plate thickness and negligible width is to be used to obtain the required local edge stress values.

2.2 Hopper knuckle welded connection

2.2.1

In addition to the general requirements in [2.1], the modelling requirements in this sub-article are applicable to the modelling of bilge hopper lower-knuckle and upper-knuckle welded connections.

Any scarfing brackets on the web frame adjoining the inner bottom plating, the first longitudinal stiffeners away from the knuckle hot spot as well as any carlings and brackets offset from the main frames are to be modelled explicitly using shell elements. Longitudinal stiffeners further away from the knuckle may be modelled by beam elements. The inner bottom plate ‘overhang’ outboard of the girder is to be modelled using shell elements up to the extent of the scarfing bracket. Away from the scarfing bracket in longitudinal direction, the inner bottom plate ‘overhang’ may be modelled using line elements of equivalent the area. Any perforations, such as cut-outs for cabling, pipes and access that are within one stiffener space from the knuckle point are to be modelled explicitly.

2.2.4

Figure 3, Figure 4 and Figure 5 show typical local finite element models of the hopper knuckle connection and close-up views of the t_n50 × t_n50 mesh zone.

2.3 Horizontal stringer heel connection

2.3.1

In addition to the general requirements in [2.1], the modelling requirements in this sub-article are applicable to the modelling of horizontal stringer heel connections.

Shell elements are to be used for modelling the stringer heel connection and adjacent stiffeners. The first longitudinal and vertical stiffeners away from the heel hot spot are to be modelled explicitly using shell elements. Longitudinal and vertical stiffeners further away from the hot spot may be modelled by beam elements. Figure 7 shows a typical finite element model of the stringer heel connection with the very fine mesh zone having t_n50 × t_n50 mesh size.

2.4 Lower stool – inner bottom connection

2.4.1

In addition to [2.1], the modelling requirements in this sub-article are applicable to the assessment of the connection between lower stool plate and inner bottom plate.

2.4.2

Diaphragm webs, brackets inside the lower stool and stiffeners on the stool plates are to be modelled at their actual positions within the extent of the local model. Shell elements are to be used for modelling of diaphragms and brackets. The first vertical or horizontal stiffeners on the lower stool plate and the first longitudinal stiffeners on the inner bottom are to be represented by shell elements, other stiffeners may be represented by beam elements. Figure 8 shows a typical finite element model of the lower stool - inner bottom connection with very fine mesh zone having t_n50 × t_n50 mesh size.

2.5 Lower stool – corrugated bulkhead connection

2.5.1

In addition to [2.1], the modelling requirements in this sub-article are applicable to the assessment of the connection between lower stool plate and corrugated bulkhead.

2.5.2

Diaphragm webs, brackets inside the lower stool and stiffeners on the stool plates are to be modelled at their actual positions within the extent of the local model. Shell elements are to be used for modelling of diaphragms, and bracket. The first vertical or horizontal stiffeners on the lower stool plate are to be represented by shell elements, other stiffeners may be represented by beam elements. Figure 9 shows a typical finite element model of the lower stool - corrugated bulkhead connection with very fine mesh zone having t_n50 × t_n50 mesh size.

2.6 Side frame bracket to hopper sloping plate connections

2.6.1

In addition to the general requirements in [2.1], the modelling requirements in this sub-article are applicable to the modelling of a side frame to hopper sloping plate bracket connections.

2.6.2

Shell elements are to be used for modelling the side frame bracket, hopper tank sloping plate and adjacent stiffeners. Figure 10 shows a typical finite element model of the side frame bracket to hopper sloping plate connection with the very fine mesh zone having t_n50 × t_n50 mesh size.

2.6.3

2.7 Side frame bracket to the upper sloping / flat bottom wing tank connections

2.7.1

In addition to the general requirements in [2.1], the modelling requirements in this sub-article are applicable to the modelling of a side frame bracket to upper sloping/flat bottom wing tank connections.

2.7.2 Shell elements are to be used for modelling the side frame bracket, upper sloping or flat bottom plate and adjacent stiffeners. Figure 11 shows a typical finite element model of the side frame bracket to upper sloping wing tank with the very fine mesh zone having t_n50 × t_n50 mesh size.

2.7.3

2.8.1

In addition to the general requirements in [2.1], the modelling requirements in this sub-article are applicable to the modelling of hatch corners/hatch coaming end bracket. The selection of hatch corners / hatch coaming end bracket for fatigue analysis is to be determined based on the level of stresses obtained from the cargo hold FE analysis.

2.8.2

2.8.3

The primary supporting members and coaming stays are to be represented by shell finite elements having both membrane and bending properties. Figure 12 shows a typical FE model of the toe connection of a longitudinal hatch coaming end bracket to the deck plating with the very fine mesh zone having t_n50 × t_n50 mesh size.

2.8.4

The level of FE mesh refinement is to be such as to enable stress concentrations arising from the hatch corner geometry to be captured in the hot spot stress. The plate edge of hatch opening corners at the level of upper deck and cross deck structure is to be assessed. The free edge of hatch coaming end bracket and bracket toe welded connection to the deck plating are also to be assessed. Beam elements having the same depth as the adjoining plate thickness and negligible width are to be used at a plate edge of hatch opening corners or free edge of the hatch coaming end bracket to obtain the required local edge stress values as outlined in [2.1.7].

2.8.5

The local structural geometry, particularly in the areas of concern, is to be represented. The hatch corner area is to be meshed using elements with a sufficiently small size to capture the local stress on the edge. In general, a minimum of 15 elements in a 90 degree arc are to be used to describe the curvature of the hatchway radius plating for a rounded corner (see Figure 13). For an elliptical or parabolic corner, a minimum of 15 elements are to be used from the inboard radius end to a point on the edge located at half the longitudinal distance of the semi- major axis. A total of 20 elements are to be used at the elliptical edge of the hatch corner (see Figure 14). However, the element edge dimensions along the free edge of the radius need not be less than the thickness of the plating being represented and also should not be greater than 5 times the thickness of the plating being represented. Except where necessary from practical meshing considerations, this level of idealisation is to be maintained over the bracket plating and is to extend into the stringer plating, deck plating and coaming. Mesh transitions should not be arranged close to bracket toes.

2.9 Boundary conditions

2.9.1 Cargo hold model

The boundary conditions to be applied to the ends of the cargo hold model are to be in accordance with Ch 7, Sec 2, [2.5].

2.9.2 Separate local finite element model

Where a separate local finite element model is used for evaluating the hot spot stress range, the boundary conditions and application of loads are to be in accordance with Ch 7, Sec 3, [4.2].

Figure 2 : Very fine mesh areas incorporated directly into the cargo hold model

Figure 3 : Local very fine mesh model (t_n50 × t_n50) of hopper knuckle connection between inner bottom and hopper plate

Figure 4 : Local very fine mesh model (t_n50 × t_n50) of hopper knuckle connection between inner bottom, hopper plate, web frame, girder and bracket

Figure 5 : Local very fine mesh model (t_n50 × t_n50) of upper hopper knuckle connection between inner side shell and hopper plate

Figure 6 : Transition area between coarse and very fine mesh

Figure 7 : Finite element model of stringer heel connection

Figure 8 : Local FE model of lower stool connection between inner bottom and lower stool plate, t_n50 × t_n50 mesh

Figure 9 : Local finite element model of lower stool - corrugated bulkhead connection between corrugated bulkhead and lower stool plate, t_n50 × t_n50 mesh

Figure 10 : Local finite element model of side frame bracket, t_n50 × t_n50 mesh

Figure 11 : Local FE model of upper side frame bracket, t_n50 × t_n50 mesh

Figure 12 : Local FE model of longitudinal hatch coaming end bracket to the deck plating with very fine mesh zone, t_n50 × t_n50 mesh

Figure 13 : Mesh density for rounded hatch corner

Figure 14 : Mesh density for elliptical hatch corner