Introduction to Elasticity/Stress example 2

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Example 2[edit | edit source]

Given: A homogeneous stress field with components in the basis given by

Find:

  1. The traction () acting on a surface with unit normal .
  2. The normal traction () acting on a surface with unit normal .
  3. The projected shear traction () acting on a surface with unit normal .
  4. The principal stresses.
  5. The principal directions of stress.

Solution[edit | edit source]

Here's how you can solve this problem using Maple.
with(linalg):

sigma := linalg[matrix](3,3,[3,1,1,1,0,2,1,2,0]);


e2 := linalg[matrix](3,1,[0,1,0]);


e3 := linalg[matrix](3,1,[0,0,1]);


n := evalm((e2+e3)/sqrt(2));


sigmaT := transpose(sigma);


t := evalm(sigmaT&*n);


tT := transpose(t);


N := evalm(tT&*n);


tdott := evalm(tT&*t);


S := sqrt(tdott[1,1] - N[1,1]^2);


sigPrin := eigenvals(sigma);


dirPrin := eigenvects(sigma);


dirPrin[1];


dirPrin[2];


dirPrin[3];