Question

Solve example Problem #1.1 of your book using (8-element) (i) Direct formulation (ii) Minimum Total Potential Energy Formulation (iii) Weighted Residual Formulation a. Collocation Method b. Subdomain Method e. Galerkin Method d. Least-Square Method Then compare your results with exact solution. Summarize your results in the attached table (2* Page). Consider at least 6 digits after decimal point. Example 1.1 Approximating how much the bar will deflect at various points along its length when it is subjected to the load P. In order to obtain numerical values of the nodal displacements, let us assume that E=10.4 10Ilin" (aluminum) W-2 in W2-1 in t = 0.125 in L-10 in P = 1000 lb.

Answer 1

Answer from the given data. (sin Join P-1000 lb P= 10coll Area @ Mode I *t → A 21ex 0.125 in P. A = 0;25in Area Mode 2 Witho, * 2+1 2 * 0.125 A-0-1875 in Area of mode 3 → → A₃ - Wext 120.125 A = 0.125 in

Average area a elements 1 :- Ä 0.25 +0.1875 021815 in Element 3: Auerg area 9 6.1845 +0.125 Az = 0.15625 int vector Global force Дь Finite Element equation A 3 2:43 1 element ☺ o 21875 x 16.4 x 10 5 455 Lu55 455 455 JM) 03

for element 015625 10 4 10 15625 103 125 -325 £325 325 Boundary conditions. to node 6 fixed uco us +455 10 6.-825 -325 ol We cancelling rows, colums gero displacement.wigu 16% (+84, -32543) 10% (-325 4.782300) - 0.00219 in 1006 0.00527 in

Elut stres in Elements - EH do for element olm Ex 4.0 = 10.4x10C (0.002-) a = 4555-2 Iblis for element ① -Exug-u 0.0052 -0.00219 10.4x100 J 6406.4 e blin