[SOLVED] UFMFVL-15-M Mechanics of Composites 24/25 Python

MODULAR PROGRAMME- COURSEWORK ASSESSMENT SPECIFICATION

Module Details

Module Code UFMFVL-15-M

Run 24/25

Module Title Mechanics of Composites

1 Introduction

This coursework is a team-based activity. Pair in groups of 2 and address Tasks 1 and 2.

2    Task 1- Laminate Analysis 35%

A laminate is made of n laminae each from different materials is subjected to three membrane forces and three bending moments as shown in Figure 1.

Figure 1: A laminate subjected to membrane forces and bending moments

where

•    Nx  = normal force resultant in the x direction (N/m)

•    Ny  = normal force resultant in they direction (N/m)

•    Nxy  = shear force resultant (N/m)

•    Mx  = Bending moment resultant in the x direction (N. m/m)

•    My  = Bending moment resultant in they direction (N. m/m)

•    Mxy  = Torsional moment resultant (N. m/m)

This laminate is made of nplies ( n   ≤   11) each having a thickness of tk  and an angle of θk  with the x axis (global coordinate). The material properties of one ply in its principal directions are given in Table 1.

Table 1: Mechanical properties of composite ply

E11	Longitudinal modulus of elasticity (Mpa)
E22	Transverse modulus of elasticity (Mpa)
G12	In–plane shear modulus (Mpa)
Xt	Tensile strength of ply in longitudinal direction (Mpa)
Xc	Compressive strength of ply in longitudinal direction (Mpa)
Yt	Tensile strength of ply in transverse direction (Mpa)
Yc	Compressive strength of ply in transverse direction (Mpa)
S	In–plane shear strength (Mpa)
θ12	Poisson’s ratio in plane 1-2
α1	Longitudinal coefficient of thermal expansion (μE/℃)
α2	Transverse coefficient of thermal expansion (μE/℃)
β1 *	Longitudinal moisture swelling coefficient (μE/%)
β2	Transverse moisture swelling coefficient (μE/%)

* Strain  is  measured  in μE  and ∆c  (change  in  concentration  of the  swelling  agent,  i.e. moisture) is percentage (%)

2.1 Part A- 20%

The laminate is subjected to membrane forces, bending moment, change of temperature ΔT and a moisture concentration of Δc. Design an interactive spreadsheet to calculate the:

1.   Factor of Safety (FoS) of each ply and the whole laminate based on maximum stress criterion.

2.   FoS of each ply and the whole laminate based on maximum strain criterion

3.   FoS of each ply and the whole laminate based on Tsai-Hill Criterion.

4.   FoS of each ply and the whole laminate based on Tsai-Wu Criterion.

5.   FoS of each ply and the whole laminate based on Hoffman criterion.

2.2 Part B – 10%

When one or more ply fails, using Ply by Ply Failure method calculate the following:

1.   FoS of each remaining ply and the whole laminate based on Interactive Tensor Polynomial

Theory – Tsai-Wu Criterion

2.   Continue this procedure until the catastrophic failure (automated process in excel)

2.3 Part C- 5%

Calculate buckling loads under various loads and boundary conditions.

2.4 Deliverables

A spreadsheet for the given task labelled with your name  and  student  numbers  and  a  clear description (within the spreadsheet) on how it works.

Important Note: This spreadsheet is essential for Task 2.

3    Task 2- Design and analysis of a composite pressure vessel      65%

3.1 Introduction- filament winding

Filament winding is used for the manufacture of parts with high fibre volume fractions  and controlled fibre orientation. Fibre tows are immersed in a resin bath where they are coated with low or medium molecular weight reactants. The impregnated tows are then literally wound around a mandrel (mould core) in a controlled pattern to form the shape of the part. After winding, the resin is then cured, typically using heat. The mould core may be removed or may be left as an integral component of the part.

The filament winding process was originally invented to produce missile casings, nose cones and fuselage structures, but with the passage of time industries other than defence and aerospace have discovered the strength and versatility of filament winding. Examples of products created using the process of filament winding include:

•    Tubes

•    Transmission poles

•    Aircraft fuselages

•    Gas, water, or tanks

•    Cement Mixers

•    Pipes

3.2 Brief

Your task is to use your laminate design spreadsheets and the Abaqus ®  finite element analysis software package to design a laminate layout for a pressure vessel as shown in Figure 2. The pressure vessel is made of ONLY laminate composites. It is subjected to an internal pressure of 55 bar. Your final design must have a FoS = 2.5.

Figure 2: General layout of a composite pressure vessel subjected to internal pressure

The pressure vessel is supported by two concrete supports as shown in Figure 2. The concrete supports are assumed to be rigid compared to the pressure vessel. The environmental effects of moisture maybe assumed to be negligible.

There are two inlets on each spherical end cap of the pressure vessel and there are two outlets on the top and bottom of cylindrical part as presented inFigure 2throughFigure 3. Diameters of inlets and outlets are 60 mm.

Dimensions of the pressure vessel are given in Figure 3andTable 2.

Figure 3: Geometrical dimensions of the pressure vessel

Table 2: Dimensions for the inner radius and position of supports

Group Number	R (mm)	D (mm)
1	375	1600
2	395	1700
3	370	1600
4	380	1700
5	360	1600
6	385	1700
7	365	1600
8	420	1700
9	405	1600
10	415	1700

Material properties for the lamina in the principal directions are given inTable 3.

Table 3: Lamina’s properties

E11	Longitudinal modulus of elasticity (Mpa)	110,000
E22	Transverse modulus of elasticity (Mpa)	7,500
G12	In–plane shear modulus (Mpa)	5,000
Xt	Tensile strength of ply in longitudinal direction (Mpa)	1,950
Xc	Compressive strength of ply in longitudinal direction (Mpa)	1,450
Yt	Tensile strength of ply in transverse direction (Mpa)	100
Yc	Compressive strength of ply in transverse direction (Mpa)	200
S	In–plane shear strength (Mpa)	160
P	Density (kg/m3 )	1,350
θ12	Poisson’s ratio in plane 1-2	0.3
α1	Longitudinal coefficient of thermal expansion (μE/℃)	13
α2	Transverse coefficient of thermal expansion (μE/℃)	35

3.3 Procedure

3.3.1  Engineering analysis of the pressure vessel

1.   Research on filament winding method (to determine the limitation of this method and

preferable angles of fibres etc.).

2.   Use the theory of pressure vessels (without consideration of the pressure vessel’s weight) to determine the applied longitudinal and hoop forces per unit length (Nx , Ny , Nxy , …).

3.   Use your spreadsheet to determine the best layout for the applied forces- using Solver® will help you significantly.

4.   Use your theoretical laminate layout from step 3 to analyse the pressure vessel using Abaqus® .

5.   Perform. a mesh study to determine the optimum size and shape of mesh.

6.   Reduce weights by adding patches around the holes instead of making the whole pressure vessel thicker.

7.   If your FoS is within limit goto step 8 otherwise change the thickness or angle of fibres or

size or orientation of patches to achieve the given FoS.

3.3.2 Advanced Analysis

8.   Investigate on the design and analysis of inlet and outlets and how this affects the FoS.

9.   Investigate if this vessel is suitable to carry liquid (density 1000 kg/m3 ) in addition to the given pressure and its weight. Ifnot, change the design to have a FoS of 2.5.

10. Investigation on environmental effect (when temperature changes ΔT  = 50℃) on FoS in addition to the given pressure, weight of liquid and vessel. If not, change the design to have a FoS of 2.5.

Note 1:

You need to document every step of your work. Remember that ONLY your report will be marked.

Note 2:

The output of this coursework will be a report in the style of a 10-page conference paper. Please use the provided template (Manuscript_template)