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Finite Element Methods · Weak formulations, Galerkin projection, and variational structure

A bar on 0≤ x≤3 has piecewise-constant axial rigidity EA=2 for 0<x<1 and EA=5 for 1<x<3

Problem

A bar on \(0\le x\le3\) has piecewise-constant axial rigidity \(EA=2\) for \(0<x<1\) and \(EA=5\) for \(1<x<3\). There is no distributed load. The displacement is prescribed as \(u(0)=0\) and \(u(3)=1\). Write a weak formulation using an affine trial space and a homogeneous test space. Explain, in terms of the weak form, what continuity condition on the axial force must hold at the material interface \(x=1\). Do not solve for \(u\).

Hint

Put both prescribed endpoint values into the trial space and use zero endpoint values for the test space.

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