FINITE ELEMENT METHOD 335
For Gauss point –^1
3
,^1
3
,^2
⎛
⎝
⎜
⎞
⎠
⎟ ke is
ke^26 =^16
15
10
2.7375 0.5833 0.5750 –0.2875 –1.1667 –1.3687 –2.1458 1.0729
0.5833 7.0134 –0.1396 1.8198 –0.9646 –2.0417 0.5208 –6.7915
0.5750 – 0.1396 0.3126 –0.1563 0.2791 –0.2875 –1.1667 0.5833
–0.2875 1.8198 –0.1563 0.5471 –0.1396 –0.3252 0.5833 –2.0417
–1.1667 – 0.9646 0.2791 –0.1396 1.9292 0.5833 –1.0416 0.5208
–1.3687 –2.0417 –0.2875 –0.3252 0.5833 1.1533 1.0729 1.2136
–2.1458 0.5208 –1.1667 0.5833 –1.0416 1.0729 4.3541 –2.1770
1.0729 – 6.7915 0.5833 –2.0417 0.5208 1.2136 –21770 7.6196
×
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥
⎥
⎥⎥
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
For –^1
3
, –^1
3
,^3
⎛
⎝
⎜
⎞
⎠
⎟ ke is
ke^36 =^16
15
10
4.3541 2.1770 –1.0416 –1.0729 –1.1667 –0.5833 –2.1458 –0.5208
2.1770 7.6196 –0.5208 1.2136 –0.5833 –2.0417 –1.0729 –6.7915
–1.0416 –0.5208 1.9292 –0.5833 0.2791 0.1396 –1.1667 0.9646
–1.0729 1.2136 –0.5833 1.1533 0.2875 –0.3252 1.3687 –2.0417
–1.1667 –0.5833 0.2791 0.2875 0.3126 0.1563 0.5750 0.1396
–0.5833 –2.0417 0.1396 –0.3252 0.1563 0.5471 0.2875 1.8198
–2.1458 –1.0729 –1.1667 1.3687 0.5750 0.2875 2.7375 –0.5833
–0.5208 –6.7915 0.9646 –2.0417 0.1396 1.8198 –0.5833 7.0134
×
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥⎥
⎥
⎥
⎥
⎥
⎥
while for^1
3
, –^1
3
,^4
⎛
⎝⎜
⎞
⎠⎟
ke is
ke^46 =^16
15
10
1.9292 0.5833 –1.0416 0.5208 –1.1667 –0.9646 0.2791 –0.1396
0.5833 1.1533 1.0729 1.2136 –1.3687 –2.0417 –0.2875 –0.3252
–1.0416 1.0729 4.3541 –2.1770 –2.1458 0.5208 –1.1667 0.5833
0.5208 1.2136 –2.1770 7.6196 1.0729 –6.7915 0.5833 –2.0417
–1.1667 –1.3687 –2.1458 1.0729 2.7375 0.5833 0.5750 –0.2875
–0.9646 –2.0417 0.5208 –6.7915 0.5833 7.0134 –0.1396 1.8198
0.2791 –0.2875 –1.1667 0.5833 0.5750 –0.1396 0.3126 –0.1563
–0.1396 –0.3252 0.5833 –2.0417 –0.2875 1.8198 –0.1563 0.5471
×
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥⎥
⎥
⎥
⎥
⎥
⎥
Adding the four matrices above yields the element stiffness matrix, that is