5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 94
© C.G. Daley
Example 3 using MAPLE 14 to solve differential equations for beam
by: Claude Daley
> restart;
The following aliases simplify the definition of loads.
> dist_load := (w,a,b) -> w*Heaviside(x-a)- w*Heaviside(x-b): # distributed force
Length, Stiffness, Load at "a", Load at end, Location of "a"
> L := 10: EI := 10^6:
> wa:=5:we:=5:a:=2: b:=6:
> loads := -dist_load(wa,a,b)-(x-a)/(b-a)*dist_load(we-wa,a,b);
> plot(loads,x=0..L,title=`LOADS`, color=blue);
> supports := {y(0)=0, D(y)(0) = 0, D(y)(L) =0, D(D(D(y)))(L)=0}:
> de := EI*diff(y(x),x$4) = loads; # Form differential equation
> dsolve({de}union supports ,y(x)): # Solve boundary value problem
> yy := rhs(%): # Extract deflection
> th := diff(yy,x): # Extract slope
> m := EI*diff(yy,x$2): # Extract moment
> v := EI*diff(yy,x$3): # Extract shear
> plot(v,x=0..L,title=`Shear`, color=blue);
> plot(m,x=0..L,title=`Bending Moment`, color=blue);
> plot(th,x=0..L,title=`Beam Slope`, color=blue);