4 Structural Modelling

4.1 General

4.1.1 Evaluation of detailed stresses requires the use of refined finite element mesh in way of areas of high stress. This fine mesh analysis can be carried out by fine mesh zones incorporated into the cargo hold model.

Alternatively, separate local FE model with fine mesh zones in conjunction with the boundary conditions obtained from the cargo hold model may be used.

4.2 Extent of model

4.2.1 If a separate local fine mesh model is used, its extent is to be such that the calculated stresses at the areas of interest are not significantly affected by the imposed boundary conditions. The boundary of the fine mesh model is to coincide with primary supporting members in the cargo hold model, such as web frame, girders, stringers and floors.

4.3 Mesh size

4.3.1 The mesh size in the fine mesh zones is not to be greater than 50 x 50 mm.

4.3.2 The extent of the fine mesh zone is not to be less than 10 elements in all directions from the area under investigation. A smooth transition of mesh density from fine mesh zone to the boundary of the fine mesh model is to be maintained.

4.4 Elements

4.4.1 All plating within the fine mesh zone is to be represented by shell elements. The aspect ratio of elements within the fine mesh zone is to be kept as close to 1 as possible. Variation of mesh density within the fine mesh zone and the use of triangular elements are to be avoided. In all cases, the elements within the fine mesh model are to have an aspect ratio not exceeding 3. Distorted elements, with element corner angles of less than 45° or greater than 135°, are to be avoided. Stiffeners inside the fine mesh zone are to be modelled using shell elements. Stiffeners outside the fine mesh zones may be modelled using beam elements.

4.4.2 Where fine mesh analysis is required for main bracket end connections, including the end connection of hold frames of single skin bulk carriers, the fine mesh zone is to be extended at least 10 elements in all directions from the area subject to assessment, see Figure 9.

4.4.3 Where fine mesh analysis is required for an opening, the first two layers of elements around the opening are to be modelled with mesh size not greater than 50 x 50 mm. A smooth transition from the fine mesh to the coarser mesh is to be maintained. Edge stiffeners which are welded directly to the edge of an opening are to be modelled with shell elements. Web stiffeners close to an opening may be modelled using rod or beam elements located at a distance of at least 50 mm from the edge of the opening. Example of fine mesh zone around an opening is shown in Figure 10.

4.4.4 Face plates of openings, primary supporting members and associated brackets are to be modelled with at least two elements across their width on either side.

Figure 9 : Fine mesh zone around bracket toes

Figure 10 : Fine mesh zone around an opening

4.5 Transverse web frames

4.5.1 In addition to the requirements of [4.2] to [4.4], the modelling requirements in this sub-section are applicable to the analysis of a typical transverse web frame.

4.5.2 Where a FE sub model is used, the model is to have an extent of at least 1+1 web frame spaces, i.e. one web frame space extending either side of the transverse web frame under investigation. For bulk carriers, the web frame space is the longer space of web frames in the upper wing and the lower hopper tanks. The transverse web frames forward and aft of the web frame under investigation need not be included in the sub model.

4.5.3 The full depth and full breadth of the ship are to be modelled, see Figure 11.

Figure 12 shows a close up view of the finite element mesh at the lower part of the vertical web and backing brackets.

Figure 11 : Example of extent of local model for fine mesh analysis of web frame bracket connections and openings

Figure 12 : Close-up view of finite element mesh at the lower part of a transverse web frame

4.6 Transverse bulkhead stringers, buttress and adjacent web frame

4.6.1 In addition to the requirements of [4.2] to [4.4], the modelling requirements in this sub-section are applicable to the analysis of transverse bulkhead structures and adjacent web frame.

4.6.2 Due to the structural interaction among the transverse bulkhead, horizontal stringers, web frames, deck and double bottom, it is recommended that the FE local model represents a full section of the hull. Longitudinally, the ends of the model should be extended at least one web frame space beyond the areas that require investigation, see Figure 13.

4.6.3 Alternatively, it is acceptable to use a number of local models, as shown in Figure 14, to analyse different parts of the structure. For the analysis of the transverse bulkhead horizontal stringers the full breadth of the ship are to be modelled. For the analysis of buttress structure, the local model width should be at least 4+4 longitudinal spaces, i.e. four longitudinal spaces at each side of the buttress.

Figure 13 : Example of local model for fine mesh analysis of transverse bulkhead and adjacent structure

Figure 14 : Example of local analysis of transverse bulkhead structure using local models

4.6.4 Figure 15 shows the finite element mesh on a transverse bulkhead horizontal stringer. Figure 16 shows the local model for the analysis of buttress connections to transverse bulkhead and double bottom structure, and openings.

Figure 15 : Example of finite element mesh on transverse bulkhead horizontal stringer

Figure 16 : Example of local model for the analysis of buttress connections to bulkhead and double bottom structure, showing port half of model

4.7 Deck, double bottom longitudinal and adjoining transverse bulkhead vertical stiffeners

4.7.1 In addition to the requirements of [4.2] to [4.4], the modelling requirements in this sub-section are applicable specifically to the analysis of longitudinal and vertical stiffener end connections and attached web stiffeners.

4.7.2 Where a local FE model is used, each end of the model is to be extended longitudinally at least two web frame spaces from the areas under investigation. The model width is to be at least 2+2 longitudinal spaces. Figure 17 shows the longitudinal extent of the local model for the analysis of deck and double bottom longitudinal stiffeners and adjoining transverse bulkhead vertical stiffener.

4.7.3 The web of the longitudinal stiffeners outside of the fine mesh zone should be represented by at least 3 shell elements across its depth. Similar size elements should be used to represent the plating of the bottom shell and inner bottom. The flange of the longitudinal stiffeners and face plate of brackets should be modelled with at least two shell elements across its width at one side.

4.7.4 The mesh size and extent of the fine mesh zone is to be in accordance with [4.3.1], see also Figure 17.

4.8 Corrugated bulkheads

4.8.1 In addition to the requirements of [4.2] to [4.4], the modelling requirements in this sub-article are applicable to the analysis of connections of corrugated bulkheads to lower stool and the connection between lower stool and inner bottom.

4.8.2 The minimum extents of the local model are as follows, see also Figure 18:

a) Vertically, the model is to be extended from the bottom of the ship to a level at least 2 m above the corrugation and lower stool connection. The upper boundary of the local model is to coincide with the horizontal mesh line of the cargo hold FE model for the purpose of applying boundary displacements, see [4.2].
b) For transverse corrugated bulkheads, the local model is to be extended transversely to the nearest diaphragm web in the lower stool on each side of the fine mesh zone (i.e. the local model covers two lower stool transverse web/diaphragm spaces). The end diaphragms need not be modelled.
c) For the longitudinal corrugated bulkheads, the local model is to be extended to the nearest web frame on each side of the fine mesh zone (i.e. the local model covers two frame spaces). The end web frames need not be modelled.
d) For the corrugation and lower stool connection located close to the intersection of transverse and longitudinal corrugated bulkheads, such as for product tanker, the local model is to cover the structure between the diaphragms (in transverse direction) and web frames (in longitudinal direction) closest to the detail, whichever is relevant. In addition the local model is to be extended at least one diaphragm/web frame outside the intersection between the transverse stool and the longitudinal stool.
e) For lower stool to inner bottom connection, the connection between inner bottom, lower stool plate, diaphragm and double bottom girder, where applicable, is the centre of the fine mesh zone.

Figure 17 : Example of local model for fine mesh analysis of end connections and web stiffeners of deck and double bottom longitudinals

4.8.3 For corrugation connection, the fine mesh zone is to cover at least the corrugation flange under investigation, the adjacent corrugation webs and a further extension of 500 mm from each end of the corrugation web, i.e. the fine mesh zone covers at least four corrugation knuckles, see Figure 18 and Figure 19. The mesh size within the fine mesh zone is not to be greater than 50 x 50 mm.

Above figures show extent of local model and fine mesh zone on longitudinal corrugated bulkhead connection to lower stool. Similar extent applies to transverse corrugated bulkhead. The model extents shown above are the minimum extents.

Figure 19 : Example of partial local model for the analysis of connection of corrugated bulkhead to lower stool

4.8.4 Diaphragm webs, brackets inside the lower stool and all stiffeners on the stool plate and diaphragm are to be modelled at their actual positions within the extent of the local model. Shell elements are to be used for modelling of diaphragm, web and flange of vertically orientated stiffeners, and brackets in the fine mesh zone.

4.8.5 Horizontally orientated stiffeners within the fine mesh zone are to be represented by either shell or beam elements.

4.8.6 Figure 19 shows the details of finite element local model for the fine mesh analysis of longitudinal bulkhead to lower stool connection.

4.8.7 Figure 20 shows the details finite element local model for the fine mesh analysis of lower stool to inner bottom connection.

Figure 20 : Example of partial local model for the analysis of connection of lower stool to inner bottom

4.9 Hatch corner structures

4.9.1 In addition to the requirements of [4.2] to [4.4], the modelling requirements in this sub-article are applicable to the analysis of hatch corner structures.

4.9.2 The high stress areas, such as the hatch coaming end bracket, the hatch corner and the hatch end beam connection, need to be analysed by fine mesh model. The fine mesh zones should cover these areas, see Figure 21.

Figure 21 : Example of local model for the analysis of hatch opening structures