An interactive introduction to MATLAB

C.2plotting 81

yandzin the horizontal plane, and the normal stress in the vertical

direction.

16. 3D plotting
    A defect in a crystal lattice where a row of atoms is missing is called an
    edge dislocation, as shown in Figure 23. The stress field around an edge

x

y

Edge

dislocation

Plot

domain

Figure 23: Edge dislocation

dislocation is given by:

σxx=

−Gby(3x^2 +y^2 )

2π( 1 −ν)(x^2 +y^2 )^2

,

σyy= Gby(x

(^2) −y (^2) )
2π( 1 −ν)(x^2 +y^2 )^2

,

τxy= Gbx(x

(^2) −y (^2) )
2π( 1 −ν)(x^2 +y^2 )^2

,

whereGis the shear modulus,bis the Burgers vector, andνis Poisson’s

ratio. Make 3dsurface plots of the stress components (each in a separate

figure window) due to an edge dislocation in aluminium for whichG=

27.7× 109 Pa,b=0.286× 10 −^9 m, andν=0.334. Plot the stresses in the

domain− 5 × 10 −^96 x 65 × 10 −^9 mand− 5 × 10 −^96 y 6 − 1 × 10 −^9 m.

Plot the coordinatesxandyin the horizontal plane, and the stresses in

the vertical direction.

17. 3D plotting
    Molecules of a gas in a container are moving around at different speeds.
    Maxwell’s speed distribution law gives the probability distributionP(v)
    as a function of temperature and speed:

P(ν) =4π

(

M

2πRT

) (^32)
v^2 e
−2RTMv^2
,