Relevant Structural Analysis Methods for Specific Design Stages

Shipbuilding design offices face very challenging situations (especially for passenger and other complex ships). The products are one-of-a-kind or at least on short series and the resulting ships are designed and built within two years

Figure 18.65 A Typical FEM/BEM Model for Analysis of the Pressure Vessel (109). (a) Typical BEM model, and (b) Typical FEM model.

(b)

Author:

Please advise what symbold is needed.

(a)

for 20 to 30 years of operation. Another impact on design activities that is also challenging is that the design overlaps the production. To clarify the actual situation, a common view of the design workflow for a commercial ship in the shipyard is shown in Table 18.VII.

18.7.5.1 Basic design

The Basic Design is the design activities performed before order. This phase does not overlap with the production but is very short and will become the technical basis for the contract. The shipyard must be sure that no technical prob-lem will appear later on, to avoid extra costs not included in the contract. The structural analysis carried out in this phase must be as fast as possible because the allocated time is short. The most time consuming task for analysis is the data input. The more detailed are the data more accurate the results. There are three kinds of early analysis:

1. First principles methods: Very simplified geometric rep-resentation of the structure. These methods are dedicated to an assessment of the global behavior of the ship. They mainly use empirical or semi-empirical formulas.

2. Two-dimensional (or almost 2D) geometry-based meth-ods: These methods are based on one or more 2D views of the ship sections. The expected results may be:

• Verification of main section scantlings,

• Global strength assessment,

• Global vibration levels prediction,

• Ultimate strength determination, and

• Early assessment of fatigue Two main approaches exist:

— The main section of the ship is modeled a 2D way (including geometry and scantlings) then global, and possibly local, loadings are applied (bending mo-ments, pressures, etc.). All major Classification So-cieties provide today the designer with such tools (Table 18.VIII).

— Various significant sections are described as beam cross section properties (areas, inertias, etc.) and then the ship is represented by a beam with variable prop-erties on which global loading is applied.

3. Simple three-dimensional models: These models are use-ful when a more detailed response is needed. The idea is to include main surfaces and actual scantlings (or from the main section when not available) in a 3D model that can be achieved in one or two weeks. This approach is mainly dedicated to novel ship designs for which the feedback is rather small.

18.7.5.2 Production design

The most popular method for structural analysis at the pro-duction design stage remains the Finite Elements Analysis (FEA). This method is commonly used by Shipyards, Classi-fication Societies, Research Institutes and Universities. It is very versatile and may be applied to various types of analysis:

• global and local strength,

• global and local vibration analysis (natural frequencies with or without external water, forced response to the propeller excitation, etc.),

• ultimate strength, and

• detailed stress for local fatigue assessment,

• fatigue life cycle assessment,

• analysis of various non-linearities (material, geometry, contact, etc.), and

• collision and grounding studies.

The two main approaches for solving the physical prob-lem are:

1. implicit method is used to solve large problems (both lin-ear and non linlin-ear) with a matrix-based method. This is TABLE 18.VII Timing of a Design Project

Basic Design

Concept Design 1 or 2 days

Preliminary Design About 1 week

Contract Design Months

Receive Order Production Design

Complete Functional Design 1 or 2 months

Production Design 6–10 months

TABLE 18.VIII Classification Society Tools Overview (110) Classification Society Product

American Bureau of Shipping (ABS) ABS Safe Hull

Bureau Veritas (BV) VeriSTAR

Det Norske Veritas (DNV) Electronic Rulebook &

Nauticus HULL Germanisher Lloyd (GL) GL-Rules & POSEIDON Korean Register of shipping (KRS) KR-RULES, KR-TRAS Lloyd’s Register of Shipping (LR) Rulefinder, ShipRight Nippon Kaiji Kyokai (NK) PrimeShip BOSUN

the favored method for solving global and local linear strength and vibration problems. But it can also be ap-plied to non linear calculations when the time step re-mains rather large (about 1/10 to 1 second), and 2. explicit method is mainly used for fast dynamics (as

col-lision and grounding or explosion) where time step is quite smaller. This method allows using different for-mulations for structural elements (Lagrangian) and fluid elements (Eulerian).

One interesting result from research that is being intro-duced today is the reliability approach (see Chapter 19).

This approach introduces uncertainties within the model (non planar plates, residual stresses from welding, dis-crepancies in the thickness…) to provide the designer with a level of reliability for a given result instead of a deter-ministic value.

For FEA models, the modeling time is usually assumed to be 70% of the overall calculation time and results ex-ploitation 30%. The computation itself is regarded as neg-ligible (excepted for explicit analysis). So the main efforts today are focused on reducing the modeling time.

18.7.6 Optimization

Optimization is a field in which much research has been car-ried out over a long time. It is included today in many soft-ware tools and many designers are using it. The aim of optimization is to give the designers the opportunity to change design variables (such as thickness, number and cross section of stiffeners, shape or topology) to design a better structure for a given objective (lower weight or cost).

Optimization can be performed both at basic and pro-duction design stages:

• Basic Design: Even with simplified models, the designer can optimize the scantlings. It can be used for instance to find out the minimal scantlings for a novel ship for which the yard have a lack of feedback,

• Production Design: Optimization can be used for three main purposes:

— Scantlings optimization, which gives the user the minimum scantlings for a given structure. The num-ber of longitudinals and the frame spacing for a given cargo hold/tank can also be optimized (105).

— Shape optimization (111), which uses a given topol-ogy and scantlings to provide the user the minimum, required area of material (reducing holes in a plate for instance), and to improve the hull shape consid-ering the fluid-structure interaction.

— Topology optimization (112) which uses a given scantlings and allows the user to find out where to

put material. An academic example of topology op-timization is given on Figure 18.66.

Weight is the most usual objective function for structure optimization. Minimizing weight is of particular impor-tance in deadweight carriers, in ships required to have a limited draft, and in fast fine lined ships, for example, pas-senger vessels. However, it is well know that the lowest weight solution is not usually the lowest acquisition cost.

Today, cost is becoming the usual objective function for op-timization (124).

For the other ship types it is still desirable to minimize steel weight to reduce material cost but only when this can be done without increasing labor costs to an extent that ex-ceeds the saving in material costs. On the other hand, a re-duction in structural labor cost achieved by simplifying construction methods may still be worthwhile even if this is obtained at the expense of increasing the steel weight.

Rigo (105) presents extensive review of ship structure optimization focusing on scantling optimization. Vander-plaats (113), and Sen and Yang (114) are standard reference books about optimization techniques. Catley et al (115), Hughes (3) and Chapter 11 of this book also contain valu-able information on structure optimization.

18.7.6.1 Scantling optimization procedure

A standard optimization problem is defined as follows:

• X_i(i = 1, N), the N design variables,

• F(X_i), the objective function to minimize,

• Cj(X_i) ≤CM_j( j = 1, M), the M structural and geomet-rical constraints,

• X_{i min}≤X_i≤X_{i max}upper and lower bounds of the X_i de-sign variables: technological bounds (also called side constraints).

Figure 18.66 Topology Optimization

Constraints are linear or nonlinear functions, either ex-plicit or imex-plicit of the design variables (XI). These con-straints are analytical translations of the limitations that the user wants to impose on the design variables themselves or to parameters like displacement, stress, ultimate strength, etc. Note that these parameters must be functions of the de-sign variables.

So it is possible to distinguish:

Technological constraints (or side constraints) that provide the upper and lower bounds of the design variables. For ex-ample:

X_{i min} = 4mm ≤X_i≤X_{i max} = 40 mm, with:

X_{i min}= a thickness limit dues to corrosion,

X_{i max}= a technological limit of manufacturing or assembly.

Geometrical constraints that impose relationships between design variables in order to guarantee a functional, feasi-ble, reliable structure. They are generally based on good practice rules to avoid local strength failures (web or flange buckling, stiffener tripping, etc.), or to guarantee welding quality and easy access to the welds. For instance, welding a plate of 30 mm thick with one that is 5 mm thick is not recommended. Hence, the constraints can be 0.5 ≤X2 / X1

≤2 with X1, the web thickness of a stiffener and X2, the flange thickness.

Structural constraints represent limit states in order to avoid yielding, buckling, cracks, etc. and to limit deflection, stress, etc. These constraints are based on solid-mechanics phe-nomena and modeled with rational equations. Rational equa-tions mean a coherent and homogeneous group of analysis methods based on physics, solid mechanics, strength and stability treatises, etc. and that differ from empirical and parametric formulations. Such standard rational structural constraints can limit:

• the deflection level (absolute or relative) in a point of the structure,

• the stress level in an element:σx ,σy,and σc= σvon Mises,

• the safety level related to buckling, ultimate resistance, tripping, etc. For example:σ/σult≤0.5.

For each constraint, or solid-mechanics phenomenon, the selected behavior model is especially important since this model fixes the quality of the constraint modeling. These behavior models can be so complex that it is no longer pos-sible to explicitly express the relation between the param-eters being studied (stress, displacement, etc.) and the design variables (XI). This happens when one uses mathematical models (FEM, ISUM, BEM, etc.). In this case, one

gener-ally uses a numeric procedure that consists of replacing the implicit function by an explicit approximated function ad-justed in the vicinity of the initial values of the design vari-ables (for instance using the first or second order Taylor series expansions). This way, the optimization process be-comes an iterative analysis based on a succession of local approximations of the behavior models.

At least one constraint should be defined for each fail-ure mode and limit state considered in the Subsection 18.6.1.

When going from the local to the general (Figure 18.38), there are three types of constraints: 1) constraints on stiff-ened panels and its components, 2) constraints on trans-verse frames and transversal stiffening, and 3) constraints on the global structure.

Constraints on stiffened panels (Figure 18.22): Panels are limited by their lateral edges (junctions with other pan-els, AA’ and BB’) either by transverse bulkheads or trans-verse frames. These panels are orthotropic plates and shells supported on their four sides, laterally loaded (bending) and submitted, at their extremities, to in-plane loads (compres-sion/tensile and shearing).

Global buckling of panels (including the local transverse frames) must also be considered. Panel supports, in partic-ular those corresponding to the reinforced frames, are as-sumed infinitely rigid. This means that they can distort themselves significantly only after the stiffened panel col-lapse.

Constraints on the transverse frames (Figure 18.23): The frames take the lateral loads (pressure, dead weight, etc.) and are therefore submitted to combined loads (large bend-ing and compression). The rigidity of these frames must be assured in order to respect the hypotheses on panel bound-ary conditions (undeformable supports).

Constraints on the global structure (box girder/hull girder) (Figure 18.46): The ultimate strength of the global structure or a section (block) located between two rigid frames (or bulkheads) must be considered as well as the elastic bending moment of the hull girder (against yielding).