Problem 2: An axial bar is constrained between rigid supports as indicated in the figure below. The bar has length L and

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Problem 2 An Axial Bar Is Constrained Between Rigid Supports As Indicated In The Figure Below The Bar Has Length L And 1 (104.69 KiB) Viewed 78 times

Problem 2: An axial bar is constrained between rigid supports as indicated in the figure below. The bar has length L and axial rigidity EA. A uniformly distributed load q acts on the first half of the bar and a concentrated force Q=qL/4 acts at the center of the bar as indicated. Note that the distributed load acts to the left and the concentrated load acts to the right. X 9 L/2 9. PL PR A symmetric weak-form statement of the problem is as follows. In terms of the usual notation, let L/2 W* = PLu* (0) + PRu* (L) + Qu* (L/2) - qu* (x) dx [² L du du* EA dx dx d.x Among all displacement fields that satisfy the essential boundary conditions, the actual displace- ment field is the one for which W* = 0 for every test function u* (x). Use Galerkin's method to obtain an approximate solution to the boundary value problem. To do so, take the trial field as X X UN(x) = a₁ + a₂ (7) + α3( (4) L NOTE: You need not find the reactions as part of the solution process. L/2