Prob,6.2
What is the maximum fiber volume fraction V
f
that could be obtained in a
unidirectionally reinforced with optimal fiber packing?
Consider a triangular area inscribed on a close-packed
section as shown,The enclosed fiber area includes half of
the three circles located on the midsides,and one-sixth of the
three circles at the vertices,The area of fibers in the triangle
is then
A[f]:=(3*(1/2)+3*(1/6))*Pi*r^2;
A,= 2 π r
2
f
The area of the equilaterial triangle,with sides of 4r,is
A[t]:=4*r^2*sqrt(3);
A,= 4 r
2
3
t
Packing density is then
Digits:=4;p:=evalf(A[f]/A[t]);
p,=,9072
What is the maximum fiber volume fraction V
f
that could be obtained in a
unidirectionally reinforced with optimal fiber packing?
Consider a triangular area inscribed on a close-packed
section as shown,The enclosed fiber area includes half of
the three circles located on the midsides,and one-sixth of the
three circles at the vertices,The area of fibers in the triangle
is then
A[f]:=(3*(1/2)+3*(1/6))*Pi*r^2;
A,= 2 π r
2
f
The area of the equilaterial triangle,with sides of 4r,is
A[t]:=4*r^2*sqrt(3);
A,= 4 r
2
3
t
Packing density is then
Digits:=4;p:=evalf(A[f]/A[t]);
p,=,9072
