Finite Element Modelling of Rectangular PlateLet’s Get Started…

Introduction to composite A laminate is a material which can be constructed by uniting two or more layers of material together that is by stacking together several laminas.

Composite structures typically consist of laminates stacked from layers with different fiber orientation angles.

The layer thickness is normally fixed, and fiber orientation angles are often limited to a discrete set such as 0°, ±30°, ±45°, ±75°, and 90

A unidirectional laminate is a laminate in which all fibers are oriented in the same direction.

Cross-ply laminate is a laminate in which the layers of unidirectional lamina are oriented at right angles to each other and quasi-isotropic laminate behaves similarly to an isotropic material; that is, the elastic properties are same in all direction.

Aim

The aim of this project is to perform a modal analysis to determine the natural frequencies and mode shapes of Aluminum Plate and composite plate using Finite Element Analysis (FEA) and then compare the results.

Methodology

This project performs modal analysis on Clamped plates for Aluminum 1060 alloy and E glass fiber.

Solid Works is used in finite element modelling for isentropic Aluminum Plate.

Ansys is used in case of finite element modelling of Composite plate.

To simulate the Clamped or fixed boundary conditions, specified displacements were placed on the all four side faces.

Properties of Al 1060 alloy plate

Mass 4.725 kgDensity 2700 kg/m^3Length 0.50 mWidth 0.35 mThickness 0.01mYield Strength 2.75e+007 N/m^2Tensile Strength 6.89e+007 N/m^2Elastic Modulus 6.9e+010 N/m^2Poisson’s ratio 0.33Shear Modulus 2.7e+010 N/m^2

Model of Al plate

Boundary Conditions

All 4 side Faces are Clamped or fixed.

Model type

Linear Elastic Isotropic

Load Conditions

Applied Load in z direction 500 N

Mesh Information

Mesh Type Solid Mesh

Mesher Used Curvature based

Total Nodes 23839

Total Element 13926

Jacobian points 4 points (Rectangular mesh)

Total Deformation

Von Mises Stress

Modal Analysis

The modal analysis is performed by using Solid Works for Al plate and ANSYS for Composite plate.

For each case, five frequencies and five mode shapes are computed. The mode shapes are plotted for each frequency over the geometry.

1st Mode Shape (553.83 Hz)

2nd Mode Shape (882.18 Hz)

3rd Mode Shape (1325.9 Hz)

4th Mode Shape (1427.5 Hz)

5th Mode Shape (1625.8 Hz)

Results for Al Plate

Mode Frequency (Hz)

1st 553.83

2nd 882.18

3rd 1325.9

4th 1427.5

5th 1625.8

Modal Analysis

Max. Deformation 1.405e-002 mm

Max. Von Mises Stress 1.179e+006 Pa

Static Analysis

Properties of Composite plate (Epoxy E glass)

Length 0.50 m

Width 0.35 m

Thickness 0.01 m

Density 1850 kg/m^3

Orthotropic Elastic Properties of Epoxy E glass

Young's Modulus X direction 35 GPa Shear Modulus XY 4.7 GPa

Young's Modulus Y direction 9 GPa Shear Modulus YZ 3.5 GPa

Young's Modulus Z direction 9 GPa Shear Modulus ZX 4.7 GPa

Poisson's Ratio XY 0.28

Poisson's Ratio YZ 0.4

Poisson's Ratio ZX 0.28

ModelBoundary Conditions

All 4 side Faces are Clamped or fixed.

Model type

Orthotropic Elastic

Load Conditions

Applied Load in z direction 500 N

Model

Model was developed using ACP module of ANSYS.

First of all, Epoxy E glass properties was entered as engineering data.

Fabric of E glass is defined.

Sub- laminate of 10 layers of fabric is defined.

Thickness of each layer 0.001 m

Stacking Sequence is defined as 0, 45, 90,-45, -90, 0, 45, 90,-45, -90

Finally Solid Model generated for analysis.

Mesh Information

Nodes 85200Elements 76230

Total Deformation

Von Mises Stress

1st Mode Shape (445.01 Hz)

2nd Mode Shape (736.28 Hz)

3rd Mode Shape (1089.2 Hz)

4th Mode Shape (1222.6 Hz)

5th Mode Shape (1361.1 Hz)

Results for Composite Plate

Mode Frequency (Hz)

1.445.01

2. 736.28

3. 1089.2

4. 1222.6

5. 1361.1

Modal Analysis

Max. Deformation 1.5744e-003 mm

Max. Von Mises Stress 7.8096e+005 Pa

Static Analysis

Comparison of FrequenciesAl 1060 Plate Composite Plate

Comparison

Al 1060 Plate Composite Plate

ConclusionsIn Case of Composite Plate the Max Deformation is almost 10 times less than that of Al 1060 plate for same geometry and loading conditions.

In Case of Composite Plate the Max Von mises stress is almost 1.5 times less than that of Al 1060 plate for same geometry and loading conditions.

Modal Frequencies are also coming less in case of composite plate.

Thanks