Bar And Rod Elements
The bar element stiffness is
K=lAE⎣⎢⎢⎢⎢⎢⎢⎢⎡100000−100100000000000⎦⎥⎥⎥⎥⎥⎥⎥⎤ The mass matrix is
M=ρAl⎣⎢⎢⎢⎢⎢⎢⎢⎡310310031610031061003100610031⎦⎥⎥⎥⎥⎥⎥⎥⎤ And the geometric stiffness is
Kg=lFx⎣⎢⎢⎢⎢⎢⎢⎢⎡00100100000−100100−1001⎦⎥⎥⎥⎥⎥⎥⎥⎤ The rod element stiffness is
K=⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡lAE00000000lGJ00000000000−lAE00000lAE00000000000000000000−lGJ00000lGJ00000000000000000000000⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤