Elasticity/Kinematics example 3
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Example 3[edit | edit source]
Given:
Unit square with displacement fields :
- .
- .
- .
Sketch: Deformed configuration in plane.
Solution[edit | edit source]
The displacement . Hence, . In the reference configuration, and . Hence, in the plane, the initial square is the same shape as the unit square in the plane. We can use Maple to find out the values of and after the deformation .
with(linalg):</code> X := array(1..3): x := array(1..3): u = array(1..3): e1 := array(1..3,[1,0,0]): e2 := array(1..3,[0,1,0]): e3 = array(1..3,[0,0,1]): ua := evalm(k*X[2]*e1 + k*X[1]*e2): ub := evalm(-k*X[2]*e1 + k*X[1]*e2); uc := evalm(k*X[1]^2*e2);
xa := evalm(ua + X); xb := evalm(ub + X); xc := evalm(uc + X);</code>
Plots of the deformed body are shown below