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TitleDetermination of Mechanical Properties of Individual Living Cells
LanguageEnglish
File Size1.9 MB
Total Pages136
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Page 1

Determination of Mechanical Properties of

Individual Living Cells

Marjan Molavi Zarandi

A Thesis

in

The Department

of

Mechanical and Industrial Engineering

Presented in Partial Fulfillment of the Requirements for
the Degree of Master of Applied Science (Mechanical Engineering) at

Concordia University
Montreal, Quebec, Canada

December 2007

© Marjan Molavi Zarandi, 2007

Page 2

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Page 68

4.1.2. FEA using COMSOL (FEMLAB)

A three-dimensional model of spherical cell is created in COMSOL to validate the

previous analysis in ANSYS. The proposed model, as previous model in ANSYS, has the

properties according to Table 4.2

Table 4.2 — Dimensional and mechanical properties of the model

Cell property

Young's modulus (E)

Density (p)

Poisson's ratio (nu)

Radius

Thickness

Unit

MPa

kg/m

1

m

m

0.75

1000

0.4999

3e-6

0.1e-6

All degrees of freedom are constrained at the bottom same as in the ANSYS model. The

element type used for the numerical analysis for this model is Argyris shell (simple but

sophisticated 3-node triangular element for computational simulations of isotropic and

elastic shells). Figure 4.9 shows the spherical cell model.

Figure 4.9 — Spherical cell model

50

Page 69

The boundary conditions and mesh shapes for this model are shown in the Figure 4.10.

As mentioned earlier, all degrees of freedom are constrained at the bottom.

y-vi^-*

Figure 4.10 — Boundary conditions and mesh shape

The modal analysis is done with COMSOL and natural frequencies are obtained. Figure

4.11 shows the first corresponding natural frequency ant its mode shape. The lateral

movement of sphere is clear from Figure 4.11.

51

Page 135

Effects of the inner sphere on the natural frequency of physical system are found by

locating a fluid filled sphere inside a sphere filled with water. To determine the effect of

boundary condition on this model, Figure III.7 and III.8 give values of the frequency

shifts associated with inner sphere.

3.50E-07

3.00E-07

2.50E-07

_ 2.00E-07

'c
£ 1.50E-07
to

g. 1.00E-07

5.00E-08

0.00E+00

-5.00E-08

31.5

20 40 60 80

Frequency (Hz)

100 120

Figure III.7 — Natural frequencies detected from top of the radius of 37 mm specimen filled with

water containing inner sphere

117

Page 136

3.00E-08

Frequency (Hz)

Figure III.8 — Natural frequencies detected from top of the radius of 37 mm specimen filled with

water containing inner sphere

118

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