Homework Project 6
Composite Materials
Advanced Topics in Finite Elements
Summer 2015
John Connor
System Description
Composite materials are used to strengthen a base metal; usually the composite material will help
prevent a specific failure. For instance to strengthen concrete a web of steel reinforcement is
added to give tensile strength to the concrete. Composites have become increasingly used as
nanotechnology becomes more prevalent in material science.
In this homework I will evaluate 2 plates at the same time and compare an aluminum/composite
plate with an aluminum plate. The stresses and defections of these plates will be determined by
clamping one edge and applying a pressure load.
Governing Equations, Boundary Conditions and Input Data
Beam and plate equations are defined in Roark’s Formulas for Stress and Strain, the equations
presented in Roark’s provide stress and displacement equations for several types of boundary
conditions and loading scenarios.
Input data from MatWeb, Roark’s, and Accuratus are shown below in Table 1.
Table 1- Input Data
Name
Value [Unit]
Plate Length/Width
0.3 [m]
Plate Thickness
0.009 [m]
Uniform Pressure
1000 [Pa]
Aluminum - Elastic
68.9[GPa]
Modulus
Aluminum - Poisson’s 0.33
Ratio
Aluminum - Density
2700 [kg/m3]
Aluminum Oxide 300 [GPa]
Elastic Modulus
Aluminum Oxide 0.21
Poisson’s Ratio
Aluminum Oxide –
3690[kg/m3]
Density
1
Source
Assignment Sheet
Assignment Sheet
Assumed
MatWeb
MatWeb
MatWeb
Accuratus
Accuratus
MatWeb
The Galerkin finite element variation formulation used for the finite element analysis is:
∫ 𝑢̇ 𝑣𝑑𝑥 + ∫ 𝑢′ 𝑣 ′ 𝑑𝑥 = 0
Description of the Finite Element Model
For this Abaqus CAE model one part was made to the length and width specified in Table 1 and
with a total thickness of 0.018m, which is then split into two pieces to give a composite plate.
This model was then copied such that different material properties could be applied to give the
homogeneous and composite plates shown in Figure 1. The green sections in Figure 1 denote the
Aluminum sections while the tan represents the Aluminum Oxide section. The mesh applied to
each of the plates is shown in Figure 2.
Figure 1 – Analysis Overview
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Figure 2 – Plate Mesh
Fixed boundary conditions were added to one side of each of the plates to simulate a clamped
plate. A pressure was applied to the tops of the plates to load the plates. These conditions are
shown in Figure 3.
Figure 3- Loads and Boundary Conditions
Results, Discussion and Conclusion
The stress and displacement results of the analysis are shown in Figures 4 and 5, the pictures
show the plates cut in half to better see how the plate behaves. The results of the homogeneous
plate were using to validate the entire model by comparing the results to the results using the
Roark’s equations, shown in Table 2.
Figure 4 – Stress in the Plates
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Figure 5 – Displacement of the Plates
The results of the comparison between the homogenous plate and the Roark’s equations are
shown below these results show that the model is within the expected accuracy range and as such
validate the model for both plates under this loading condition.
Table 2 – Validation of the Homogenous Plate
FEA Results
Roark’s Equation Results
Stress [MPa]
Displacement
Stress [kPa]
Displacement
[µm]
[µm]
Homogenous
54.19
0.284
85.5
0.278
Plate
The analysis shows that the addition of the composite to the plate section had a dramatic result
on the overall stiffness of the plate which increases stress and decreases the displacement. The
combination of the composite allows for a change in material properties which can be beneficial
under certain loading conditions. In conclusion, by applying the composite to the base metal one
can increase the stiffness of the plate while not sacrificing all of the elasticity of the base metal.
References
1. Aluminum; MatWeb;
<http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6>
2. Young, Warren; Bundynas, Richard; Roark’s Formulas for Stress and Strain Ed. 7;
McGraw-Hill; Dated 2002
3. Aluminum Oxide; Accuratus; < http://accuratus.com/alumox.html>
4. Zienkiewicz, O. (2013). Finite Element Method: Its Basis and Fundamentals. ButterworthHeinemann Ltd.
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