Question

finite element method

OP QUESTION 1 (20 Marks) Calculation question (a)In a thin loaded plate shown in Figure 1, an area originally bounded by ABCD deformed to A', B', C' and D' upon loading. Estimate the strains,Exx, Eyy and Ey, and stresses, ox, Oyy and oxy of the element. Given that: E= 200 GPa and v 0.28. (10 Marks) All units are in mm Y 1 C (0,008,1.002) D 1,1) ko,1) B (1.005,0.002) A' (0.002,0.001) A X (0,0) (1,0) Figure 1. Diagram for Question 1 (b)Integrate the following integral using Quadrature numerical integration technique with one and three Gauss Points. (10 Marks)

Answer 1

Question'- Seltion Given thesd platle n loaded Tn Co.008,1.00l (1005,0.002) ( o'00%) X A CO1O) o Gpa 200 have to estiwd tstrains svesses **3. above daqo dala, Rou dux (1.00 5- 0.002)- (1-0) oo (LO)

|O0 3- OO 3 to deenie Egy hase Noo pe Juy Eyy dy Fre give d'igrou dsla, (1-002-001)--o) (1-0) have to deDesuine Novo oe duy dux 2. Exy C05- 0.002)-(1-6) (102-o 1)-() C1-0) (1-0) C003-1)Co1- 2x (1-91 3

O 2 to dederwive R have slresseg Nou we Exx (4C-29) |-V Exy 200 X1O 9iven E o. 2%. E4y.001Eyo 00 in aboue expeirou cnous Exx -0 003, SubrtiheDe Rere vfes PI-O-28 .28 o28 3 O 28 l-O 28 +0.28)(1-20-13) D 28 I-o 28 O 28 O.003 3 200X1O rO.003 72 O2e 28 O.001 O 28 O.28 1-28-0.5) 002 o28 28 S.00 3 1 28xoP O.002 5

T065 solio have tolegnae R/ng wevi ca) idequapion re Gau pois Noo we legro inguadalae tehingue huu One Gau's - point uoae One- ) dcb-o)f (b b a- Nao 2. er) sinxx P sin +)d 1+1) o)

Nowo Gau Guodráhixe poina C On 2 sin -o.099 2. 2993 Psimtd x C-0.0994)0+x O.0522+ »T29 O 666