# What is the correct statement regarding the shape function S of a linear triangular element?

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What is the correct statement regarding the shape function S of a linear triangular element?

(a) The first derivatives of S and hence, all the strains are element-wise constant

(b) The first derivatives of S are linear, but the strains are element-wise constant

(c) The first derivatives of S and hence the strains are linear functions

(d) The first derivatives of S are element-wise constant, but the strains are linear

This question was posed to me during an online interview.

This is a very interesting question from Plane Elasticity in chapter Plane Elasticity of Finite Element Method

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The correct choice is (a) The first derivatives of S and hence, all the strains are element-wise constant

To explain: A linear triangular element (number of nodes=3) has two degrees of freedom, ux and uy per node and a total of six nodal displacements per element. Since the shape functions are linear, their first derivatives are element-wise constant, and hence, all the strains computed for the linear triangular element are element-wise constant.

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