Material and Computational Mechanics Group 1

Ship Structures - Basic Course (MMA130)Ragnar Larsson

Department of Applied MechanicsChalmers University of Technology

Material and Computational Mechanics Group 2

à Ship Structures - Problem characteristics

üSize

Largest man made mobile structure!

Complex 3D geometry

üFunctional multiplicity of components

Stability (against capsizing - structural stability)

Low resistance

High propulsive efficiency ...

üHighly variable loading

Static loading (dead load, cargo, bouyant pressure in calm water)

Dynamic loading (wind, wave induced, bouyant pressure, engine, propeller ...)

Note, there is no fixed foundation! Load equilibrated by buoyant pressure fl Fluid structure interaction

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Material and Computational Mechanics Group 3

üShip failure modes

Structural failure is not allowed to occur!!! Crucial in ship design.

Ship = redundant welded stiffened plate-shell structure

Issues to be considered:

- Excessive material yielding (stress analysis, material modeling)

- Buckling phenomena induced by compressive stresses (stability analysis)

- Fatigue phenomena (induced cracking) (fatigue modeling, fracture mechanics)

- Brittle fracture (fracture mechanics)

Material and Computational Mechanics Group 4

L1. Ship structural loads, PNA 203-213

àStatic loads

üCalm water loads

Difference between weight (ship+cargo) and the buoyancy of the ship incalm water

Vary from voyage to voyage, various load cases due to ship loading

Number of load cycles are 100-1000.

Determined by

- "typical" load cases

- "worst" load case

- Statistical methods

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Material and Computational Mechanics Group 5

üMax static loads

Mobile loads on ship: Heavy trains or trucks

Wave induced loads (usually induces worst case):

Hogging

Sagging

üDynamic loads

Wave induced dynamic loads

Low frequency loads: same periodicity as waves (T = 5 − 20 s )

Inertia can usually be omitted fl Quasi-static solution

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Material and Computational Mechanics Group 6

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üModeling philosofy - Preliminary design stage

Note! All forces are taken from simple approximate methods (determinedby classification societies)

Note! loading have both global (overall) and local structural effects

Note! Design concerns both:Stress (deformation) - Stability - Vibration analyses

Primary (overall) structure

a) Beam theory: bending - torsional response

b) Classification rules (international codes)

c) FE modeling (simplified structure)

Second and tertiary (local) structures

d) Plate theory (effective breadth of stiffened plating)

e) Buckling phenomea (beams and plates)

f) FE modeling (detailed structure)

Note! a) main focus of this course

d,e) main focus of Ship Structures Advanced course, Q4

c) main focus FEM course in Q3

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Material and Computational Mechanics Group 7

Course outline

üAim of the course

The course intends to give the student basic knowledge of ship structures, focused on theanalysis of their strength. The theory is general while the applications are mainly on shipstructures. The randomness or uncertainty to predict both the loads imposed on shipstructure and the ability of the structure to withstand those loads are studied.

üContents of the course

In this course the engineering theory of bending and torsion of thin-walled elastic beams istreated in depth. Topics studied include:

Elongation of an axially loaded bar. Bending - Bernoulli's hypothesis. Navier's stress formula. Shearing stresses. Saint-Venant's theory of torsion. Thin-walled sections. Vlasov's theory of torsion. The effect of preventing warping.

The reliability of structures is treated by studying deterministic (or safety factor) methods,semiprobablilistic (or reliability index) methods and fully probabilistic methods.

Material and Computational Mechanics Group 8

Material and Computational Mechanics Group 9

ü Course Overview

Material and Computational Mechanics Group 10

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Material and Computational Mechanics Group 12

üBeam theory: integration of stress resultants

Static loads

Quasi static loads

Note! Loads /m = Buoyancy /m - Weight /m ; Weight = ship load +cargo

May be integrated in practical situation as

(1)Vj = ‚i=1

j

pi ∆xi , j = 1, 2, 3. .. N

(2)Mj = ‚i=1

j

Vi ∆xi , j = 1, 2, 3. .. N

Dynamics loads (inertia included, m x..

≠ 0);

Initial design: Static + quasi static loads and ship considered asthin-walled beam

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Material and Computational Mechanics Group 13

Material and Computational Mechanics Group 14

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Material and Computational Mechanics Group 18

Material and Computational Mechanics Group 19