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prob_07_03_06

# prob_07_03_06 - Problem 7.3-6 Given Let uniform pressure p...

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1 2 3 4 5 6 7 8 9 10 r, x s, y t, z Pressure p acts on the bottom (-z) face Problem 7.3-6 Given: Let uniform pressure p act normal to one face of a quadratic tetrahedron that has straight edges and midedge nodes. What are the consistent loads at the nodes on this face. Solution: Let us make the element aligned with the x-y-z axes so this can be as easy as possible. We will use area coordinates to obtain an exact solution. From Eq. 7.3-4, for a planar 2-D element N 1 ξ 1 2 ξ 1 1 ( ) = N 2 ξ 2 2 ξ 2 1 ( ) = N 3 ξ 3 2 ξ 3 1 ( ) = N 4 4 ξ 1 ξ 2 = N 5 4 ξ 2 ξ 3 = N 6 4 ξ 3 ξ 1 = Adapt these for the bottom face of the 3-D element using N 5 4 ξ 1 ξ 2 = N 8 4 ξ 2 ξ 3 = N 6 4 ξ 3 ξ 1 = N d N 1 0 0 0 N 1 0 0 0 N 1 N 2 0 0 0 N 2 0 0 0 N 2 .... .... .... N 10 0 0 0 N 10 0 0 0 N 10 u 1 v 1 w 1 u 2 v 2 w 2 .... u 10 v 10 w 10 =

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prob_07_03_06 - Problem 7.3-6 Given Let uniform pressure p...

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