Question: 3. The thickness variation of a linear rectangular element is given by 4 h(, ) = N;(, n)h; i=1 where N; is the bilinear

3. The thickness variation of a linear rectangular element is given by

3. The thickness variation of a linear rectangular element is given by 4 h(, ) = N;(, n)h; i=1 where N; is the bilinear shape function, and h; is the thickness value at node i. How many Gauss points are required to evaluate exactly the mass and stiffness matrices? 4. If the thickness variation of a linear quadrilateral is the same as the rectangular element in Problem (3), how many Gauss points are required to evaluate the mass matrix exactly? How many Gauss points are required to integrate the volume of the element exactly? How many Gauss points are required to integrate the stiffness matrix exactly? 5. Construct the shape functions for the 12-node rectangular element for one corner node and one side node.

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