Question: 23. A six-node finite element as shown in the figure is used for approximating the beam problem. (a) Write the expressions of displacements u(x,y) and

23. A six-node finite element as shown in the figure is used for approximating the beam problem.

(a) Write the expressions of displacements u(x,y) and v(x,y) in terms of polynomials with un¬

known coefficients. For example, u(x,y) = ao + oix + ¦ • ¦.

(b) Can this element represent the pure bending problem accurately? Explain your answer.

Bending moment M is applied at the edge 2-3.

(c) Can this element represent a uniformly distributed load problem accurately? The distribut¬
ed load q is applied along the edge 4-6-3.

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