prob_03_03_03 - Problem 3.3-3 Given A uniform bar elemen of...

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Problem 3.3-3. Given: A uniform bar elemen of length L has a node at each end and a node at the middle as shown. Find: the element stiffness matrix that operates on the nodal d.o.f. u 1 , u 2 , u 3 . Solution: x 1 0 = x 2 L 2 = x 3 L = NN 1 N 2 N 3 () = N 1 x 2 x x 3 x x 2 x 1 x 3 x 1 = L 2 x Lx L 2 L = 1 L 2 L 2 3L x 2x 2 + = N 2 x 1 x x 3 x x 1 x 2 x 3 x 2 = x ()Lx L 2 L 2 = 4 L 2 xL x 2 = N 3 x 1 x x 2 x x 1 x 3 x 2 x 3 = x L 2 x L L 2 = 1 L 2 2 = B x N 1 d dx N 2 d N 3 d d = x 1 L 2 L 2 x 2 + d d 4x L 2 x 4 L 2 x 2 d d 4L 8x L 2 x 1 L 2 2 d d L4 x L 2 B 1 L 2 3 L + 4 L 2
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prob_03_03_03 - Problem 3.3-3 Given A uniform bar elemen of...

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