AE7723 - Finite Element Analysis of Laminated Composite Structures

Assignment Task

1. Description

Laminated composite panels have been widely used in engineering applications due to their excellent high strength-to-weight ratio, modulus-to-weight ratio, and the controllability of the structural properties with the variation of fibre orientation and the lamina number. However, in such applications, the structures are susceptible to buckling as usually the thickness of composite laminates being significantly smaller than the width and length of the panels. Buckling is a very dangerous phenomenon related to thin-walled structures because it can appear well before the developed stresses in a structural member reach the compressive yield strength of the respective member.

A rectangular plate of dimensions (i.e. length × width) under a uniaxial compressive load is shown in Figure 1. 

For such a plate, with anti-symmetric laminated composite structure and with simply supported edges, the buckling load (N/m) is given by

In these equations, the coefficients from the , and matrices are those appearing in the formulation of the Classical Lamination Theory (CLT). The critical buckling load is obtained when . For the needs of the present assignment, consider a simply supported rectangular plate with , moduli of elasticity and , shear modulus , Poisson’s ratio , thickness of each lamina equal to 0.3 mm and density .The lay-up of the laminate are defined later.

2. Deliverables

Part 1 - Theoretical questions

i. What is delamination in fibre reinforced composite materials

ii. Write an example for following laminates lay-up 

• Asymmetric laminate
• Cross-ply
• Cross-ply symmetric
• Angle ply symmetric
• Balanced angle ply
• Quasi-isotropic

iii. How the results from the FE analysis of a laminated composite plate are validated? 

iv. What is a "mesh independent result"?

v. What is buckling and why is it important in engineering?

Part 2 - Analytical computation of the critical buckling load

Using the data given and the theory described in Section 1, the critical buckling load for the following laminate is required to be computed analytically:

For this part of the assignment, it is recommended that a spreadsheet in Excel or a MATLAB code or equivalent to be used for the calculations.

Part 3 - Critical buckling load using FEA / Eigenvalue analysis

For the data given in the description and for the [0/90/±45] ₂ laminate, find the critical buckling load using eigen solution in FEA. It is required initially a mesh sensitivity analysis be carried out to obtain the mesh independent results.

Part 4 - Critical buckling load using FEA / Nonlinear analysis

For the data given in description and for the laminate given in Part 2, find the critical buckling load by n onlinear analysis . Here also It is required initially a mesh sensitivity analysis be carried out to obtain the mesh independent results. Show the post-buckling results on a graph and extract the critical buckling load.

Part 5 - Comparison between analytical and numerical results

Compare the critical buckling load obtained in Parts 2 to 4 for the [0/90/±45] ₂ laminate and comment on the accuracy of the results. Which method you recommend?

Part 6 - Analysis of complex structures

In the aerospace industry, FRP composites are used extensively in various structural components such as wings and fuselage. In this part, eigen buckling analysis of a stiffened FRP composite panel is used for determination of critical buckling load. A schematic of the panel with four L-shape stringers attached to the skin is shown in Figure 2. The stringers are apart equally with a distance between the centrelines of 152mm. The task is to find the optimum laminate design of this stringer stiffened composite panel for carrying maximum buckling load.

The panel is made of CFRP laminate (with perfect bonding) and have the same material properties as given in the description section. The objective is to find the stiffened CFRP panel which can carry a load of 325 kN/m with a factor of safety 2 without buckling.

Assume the skin and the end of stringers are fixed at one end as shown with arrows at the right hand-side in Figure 2(a), and all other sides of the skin are fixed in out-of-plane direction.

The candidate design parameters to be examined are the following:

• CFRP ply thickness: 0.15mm, 0.3mm, and 0.5mm
• Laminate lay-up for skin and stringers: [0/90/±45] ₂ , [0/45/90/30] _s , [45/0/90/60] _s and [±45] _2s ,

Therefore, you need to solve 12 cases, using eigen buckling analysis to find the critical buckling load. Use 22 mm mesh for all cases in the FEA. Complete the following Table and present the critical buckling load results versus laminates in a bar chart for different ply thicknesses.

Part 7 - Conclusions + Presentation

State in a clear and straightforward manner the main conclusions/results of your investigation.

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