Question may use a textbook "Concepts and Applications of Finite Element Analysis 4th edition" Question about finite element of analysis.
Sections 3.4 and 3.5 of the textbook show that the three-noded CST shape functions permit u and v to be defined by complete linear functions in terms of a constant and x and y terms. Similarly, the six-noded LST has displacements defined by complete polynomials in terms of a constant, x, y, x2, xy, and y2. Consider now the rectangular elements Q4 and Q8 described in sections 3.6 and 3.7.
(a) The Q4 element has four nodes. What four polynomial terms are defined for this element?
(b) The Q8 element has eight nodes. What eight polynomial terms are defined for this element?
(c) The Q9 element has nine nodes. What additional polynomial term (beyond those defined by Q8) does the ninth node provide?