Determine shape functions of a bar element shown in the figure by assuming the following form of displacement: \(u(x)=a_{1} x+a_{2} x^{2}\); that is, obtain \(N_{1}(x)\) and \(N_{2}(x)\) such that \(u(x)=N_{1}(x) u_{1}+N_{2}(x) u_{2}\). Calculate axial strain \(\varepsilon_{x x}=\mathrm{d} u / \mathrm{d} x\) when \(u_{1}=u_{2}=1\) (rigid body motion). Explain why strain is not zero under the rigidbody motion.

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x = -1 y x = 1 X