Determine Jacobian of the eight-node rectangular element of Fig. P9.13 in terms of the parameter a.
Save your time - order a paper!
Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlinesOrder Paper Now
Using the coordinate system (x, y), which coincides with the natural coordinate system (ξ, η), we obtain
which is zero at (i) (ξ, η)=(−1, −1) when a = 0.5 (left quarter point) and (ii) (ξ, η) = (1, −1) when a = −0.5 (right quarter point). The Jacobian is negative when the node is placed inside a quarter point and the nearest corner node.