Problem 3 Consider Again The Boundary Value Problem Introduced In Problem 2 We Wish Now To Obtain An Approximate Sol 1 (120.29 KiB) Viewed 57 times
Problem 3 Consider Again The Boundary Value Problem Introduced In Problem 2 We Wish Now To Obtain An Approximate Sol 2 (104.69 KiB) Viewed 57 times
Problem 3: Consider again the boundary value problem introduced in Problem 2. We wish now to obtain an (approximate) solution by means of the Finite Element Method. (a) Consider three (linear) elements as shown below. Elements one and two have length L/4 and element three has length L/2. Construct the complete, final system of equations KU = P. Use the global node numbering indicated below. Note: You may directly use the element stiffness matrix and element load vector (i.e. there is no need to derive the element stiffness matrix or element load vector). Make sure to clearly state the connectivity vectors, etc. (1) (2) (3) 2 3 1 4 (b) Solve for the free degrees of freedom. (c) Give an explicit equation/expression for the displacement field un(x).
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
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!