restart: Example of use of MAPLE 14 to solve differential equations for beam by: Claude Daley 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The following aliases simplify the definition of loads. step_load := (x) -> Heaviside(x); # distributed force dist_load := (w,a,b) -> w*step_load(x-a)- w*step_load(x-b); # distributed force

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Zio2JUkid0c2IkkiYUdGJUkiYkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJjkkIiIiLUkqc3RlcF9sb2FkR0YlNiMsJkkieEdGJUYuOSUhIiJGLkYuKiZGLUYuLUYwNiMsJkYzRi45JkY1Ri5GNUYlRiVGJQ==

The following aliases simplify the definition of derivatives (used for boundary conditions). D3 := (x) -> D(D(D(x))); # short form for 3rd derivative D2 := (x) -> D(D(x)); # short form for 2nd derivative D1 := (x) -> D(x); # short form for 1st derivative

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Length, Stiffness, Load at "a", Load at end, Location of "a" L := 2; EI := 1;

IiIj

IiIi

wa:=1;we:=3;a:=.5;

IiIi

IiIk

JCIiJiEiIg==

loads := -we*x/L; #loads := -dist_load(wa,a,L)-(x-a)/(L-a)*dist_load(we-wa,a,L);

LCRJInhHNiIjISIkIiIj

plot(loads,x=0..L,title=`LOADS`, color=blue);

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supports := {D1(y)(0) = 0, D2(y)(L)=0,y(L)=0,y(0)=0}: de := EI*diff(y(x),x$4) = loads; # Form differential equation

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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

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LCYqJEkieEc2IiIiIyMhIiQiIiUjIiNGIiM/IiIi

plot(yy,x=0..L,title=`Beam Deflection`, color=blue);

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plot(th,x=0..L,title=`Beam Slope`, color=blue);

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plot(m,x=0..L,title=`Bending Moment`, color=blue);

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plot(v,x=0..L,title=`Shear`, color=blue);

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subs(x=0,m);

IyEiKCIjNQ==

plot(cos((1/2)*x)+sin(2*x), x = 0 .. 4*Pi);

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