Answer the questions concisely and with justification:

 (a) Are stresses constant within a four-node quadrilateral element?

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 (b) Are shape functions linear on the edge of a four-node quadrilateral element?

(c) Why do you need numerical integration?

 (d) How many integration points are commonly used in computing matrices for the fournode quadrilateral element?

 (e) A node k on a structure is connected by a rigid link to a fixed node j , as shown in Fig. P8.15 . Assuming small deformations, write the corresponding boundary conditions (constraint equation) in the form of b1Qkx + b2Qky = b0 . ( Hint : Refer to discussion in Chapter 3 .)


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