Finite Element Methods · Weak formulations, Galerkin projection, and variational structure
A uniform axial bar of length 2.0 m and constant rigidity EA = 80 MN is fixed at x = 0…
Problem
A uniform axial bar of length 2.0 m and constant rigidity EA = 80 MN is fixed at x = 0 and represented by two equal two-node linear elements. It is subjected to an axial distributed load q(x) = 12 + 6x kN/m acting in the positive x-direction, where x is measured in meters, and to a concentrated force of 10 kN acting in the negative x-direction at x = 2.0 m. Using consistent element nodal loads for q(x), assemble the global load vector and stiffness equations, determine the nodal displacements, and compute the support reaction at x = 0.
Hint
For a linearly varying load, integrate the product of each linear shape function and (q(x)) over the element.
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