Finite Element Method formulation, Civil Engineering

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1. [6 marks] Treating the bar illustrated above as being a one dimensional axial bar where plane sections remain plane and parallel, analyse the bar using the Galerkin finite element method. The coding solution for linear h-refinement and its manual solution for a limited number of linear elements are on Blackboard for your reference.

Consider h-refinement using three-noded quadratic elements, produce the manual solution for when the domain includes of 2 equal spacing quadratic elements. Generate the outcomes to produce:
a. Nodal displacements
b. Displacement at the left quarter of each element.
c. Normal stress at the left quarter of each element.

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