Question

Problem 4. (3 points). Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements when solving. Assume that bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 4 are fixed Elements 1, 2 and 3 have Young's Modulus of Ei-300 Pa, E2-200 Pa, Es-200 Pa. All elements have o ae of 20 N 20 N Element 1Ele Element 3 Node 2 Node 3 Node 1 Node 4

Answer 1

Given, 20N Noel Nodo 3 Numer off modes4 Young's rodulMs aP-elamnds 112.anndる

Load appland at male, 2, 20 N Me83 a I-D For 1 2 니 [B] = 1x300厂1-1 -L 300 -30o 300 300 |2-0 fon Elomeut@ 1,多

X 200 1 -l -2ㆀ 200-13 3 Lk3]こー200-2007 200 200H x4 3 200 20o 2 200-2003 -200 20020 200 x4 200

2 3 Bo -30o o 300(300+200) -200 2 O 200 200 300 300 o (k] = hiy txt 1100-2001 →(5) 200 o o 200 2oo ha Ve 0 20 0 O

Cu2 300 -300 o 300 500 00 2000 20 l o 0-200 200 at and s fourth shocos ond columls 500-200-11-ch 一200 ltoo | 20 ら 500J2-200d3-20 →

800 240 8o0 500 C0.05)-200 d 20 d3こ0.025m d2 0.05m ch 0.025 m fan Node ︵ 30o x 0 05

Nocdle L(-200×0.025)+(200%) = Node R15 N NOTE