UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE, RAS AL KHAIMAH BENG(HONS) MECHANICAL ENGINEERING SEMESTER TWO EXAMINATION 2014/2015
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1 OCD5 UNIVERSITY OF BOLTON WESTERN INTERNATIONAL COLLEGE, RAS AL KHAIMAH BENG(HONS) MECHANICAL ENGINEERING SEMESTER TWO EXAMINATION 0/05 FINITE ELEMENT AND DIFFERENCE SOLUTIONS MODULE NO: AME6006 Date: Wenesa 0 June 05 Tme: 0:00 :00 INSTRUCTIONS TO CANDIDATES: Tere are FIVE questons on te paper. Answer an FOUR questons All questons carr equal marks. Marks for parts of questons are sown n brackets. Electronc calculators ma be use prove tat ata an program storage memor s erase or cleare pror to te examnaton. CANDIDATES REQUIRE: A Formula Seet (attace)
2 Page of 8 Western Internatonal College, Ras Al Kama BEng(Hons) Mecancal Engneerng Semester Examnaton 0/05 Fnte Element An Dfference Solutons Q. Te rectangular beam sown below n Fgure Q s rgl fxe at en A an smpl supporte at en B. A pont loa P s apple L along te lengt of te beam. Te beam span AB s L n total. Note B s a smple roller support, wlst en A s bult n. Te followng ata s gven E = 00 GNm -, I = 0 x 0-9 m, L =.6 m an P = 0 kn In answerng te questons below, ou soul splt te beam nto four equal sectons an use te Fnte Dfference meto of soluton, were: 6 a) State te Bounar Contons for te beam. ( marks) b) Establs te Benng Moment equatons for eac noe on te beam. (6 marks) Q contnue over te page P L L Fgure Q B A
3 Page of 8 Western Internatonal College, Ras Al Kama BEng(Hons) Mecancal Engneerng Semester Examnaton 0/05 Fnte Element An Dfference Solutons Q contnue c) Establs te Fnte Dfference equatons for eac noe. (7 marks) ) Determne te value of te reacton (R B )at te smple support B (6 marks) e) Determne te eflecton at te m-pont of te beam. ( marks) Total 5 marks Q. Analse te sprng assembl sstem usng FEM an etermne a) Te nvual stffness [k] matrx for eac element sown n te Fgure Q below. (5 Marks) b) Usng te superposton meto combne all matrx obtane n Q(a), an fn te global stffness matrx [K] (0 Marks) Fgure Q Total 5 marks Please turn te page
4 Page of 8 Western Internatonal College, Ras Al Kama BEng(Hons) Mecancal Engneerng Semester Examnaton 0/05 Fnte Element An Dfference Solutons Q. For te axall loae bar sown n Fgure Q below, Determne. a) Noal splacements. b) Element stresses. c) Support reacton. (0 Marks) (0 Marks) (5 Marks) E (Steel)=00 GPa, E (Copper)=00 GPa Fgure Q Total 5 marks Please turn te page
5 Page 5 of 8 Western Internatonal College, Ras Al Kama BEng(Hons) Mecancal Engneerng Semester Examnaton 0/05 Fnte Element An Dfference Solutons Q. Fgure Q below sows a beam wt a UDL over a span of metre, usng beam Elements for te structure sown, Take E=00 GPa, I = X 0 6 mm Determne. a) Vertcal eflectons at pont an pont. b) Slopes at pont an pont.. (0 marks) (0 marks) c) Deflecton at te centre of te porton of te beam carrng UDL (5 marks) Fgure Q Total 5 marks Please turn te page
6 Page 6 of 8 Western Internatonal College, Ras Al Kama BEng(Hons) Mecancal Engneerng Semester Examnaton 0/05 Fnte Element An Dfference Solutons Q5. a) Derve a Hermte sape functon [H] for te beam element sown n Fgure Q5a below. Make use of te Table for te bounar contons. (5 Marks) Fgure Q5a Table. b) For te sngle sprng element sown n Fgure Q5b below, erve te nvual stffness matrx [K] an obtan te matrx form [F] = [K] [U] (0 Marks) Fgure Q5b Total 5 marks END OF QUESTIONS
7 Page 7 of 8 Western Internatonal College, Ras Al Kama BEng(Hons) Mecancal Engneerng Semester Examnaton 0/05 Fnte Element An Dfference Solutons FORMULA SHEET FINITE ELEMENT AND DIFFERENCE SOLUTIONS Fnte Dfference Equatons for Beam Deflecton: 6 Beams:
8 Page 8 of 8 Western Internatonal College, Ras Al Kama BEng(Hons) Mecancal Engneerng Semester Examnaton 0/05 Fnte Element An Dfference Solutons Hermte sape functons.
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