MEC 455 cfw_ APPLIED STRESS ANALYSIS
HANDOUT # 1
TENSORS WITH INDICIAL NOTATION
(a) SCALAR
Rank 0 ! 1 component
no index
e.g., temperature T , density , hydrostatic stress h , eective stress e .
(b) VECTOR
Rank 1 ! 3 components 1 index
e.g., position xi ,
MEC455/530 Applied Stress Analysis
Anisotropic Materials
General Anisotropic Materials (Independent Constants: 21)
x C11
y C12
Some minerals (triclinic)
C
z = 13
xy C14
C
yz 15
microcline
C
zx 16
Monoclinic Materials (Independent Constants: 13)
MEC455/530 Applied Stress Analysis
y
y
2D Mohrs Circle
Construction procedure for given x, y, xy
x
1. Compute the center of circle C = (x + y)/2
x y
2. Compute the radius of circle R =
2
xy
2
+ xy 2
xy
x
y
3. Draw the circle on coordinates.
(y, xy )
4.