FEM for engineering applications (SE1025), 6 hp, Fall 2011

Transcription

1 KTH Slid Mechanics SE1025 FEM. FEM fr engineering applicatins (SE1025), 6 hp, Fall 2011 FEM fr engineering applicatins (SE1025), 6 hp, Fall General infrmatin The curse gives an intrductin t energy principles in slid mechanics and t apprximate methds fr numerical analysis f engineering prblems with the Finite Element Methd (FEM). Specifically, linear elast-static slid mechanic prblems and heat cnductin prblems will be treated in detail. The gal is that the student after cmpletin f the curse shuld be able t frmulate finite element equatins fr slid mechanics and heat cnductin prblems explain the meaning f an apprximate slutin carry ut technical cmputatins using a finite element prgram interpret the derived numerical results. As prerequisites, the student shuld have a gd knwledge in strength f materials, mechanics and mathematics. The student shuld be well acquainted with matrix algebra and methds fr slving linear systems f equatins. A central part f the curse is based n matrix frmulated methds. The hmewrk assignments will be easier t slve if the student als have sme experience in using mathematic prgrams such as Matlab, Maple r Mathematica. The cntents f the curse can be divided int tw main tpics: energy methds and the Finite Element Methd (FEM), where the latter stands fr the majr part f the curse. 2. Teachers and hme page T.Christian Gasser (Lectures, Examiner) tg@hallf.kth.se Phne: Hui Huang (Tutrials, Cmp.-labs) huih@kth.se Phne: Andrii Grytsan (Tutrials, Cmp.-labs) grytsan@kth.se Hme page: (click n SE1025) Page 1 f 6

2 KTH Slid Mechanics SE1025 FEM. FEM fr engineering applicatins (SE1025), 6 hp, Fall Literature G. R. Liu & S.S. Quek (2003) The finite element methd A practical curse. Butterwrth- Heinmann, Oxfrd, UK. (referred t as LQ in the syllabus). Nte: Available as an electrnic text bk at the KTH library. Can be dwn laded frm: click n E-bks in the right clumn; click n Materials & Mechanical Cllectin ; search fr Liu as authr; click n Bk Details ; click n the yellw buttn Read Bk a pdf-versin appears, which can be dwn laded. Lecture slides and Jnas Faleskg (2008) FEM fr Engineering Applicatins Exercises with Slutins. Dept. f Slid Mechanics, KTH. Included in a curse package, sld at the student ffice at Dept. f Slid Mechanics, prize 100 SEK. (referred t as EX in the syllabus). Sme material n energy principles and strng/weak frm f differential equatins will be handed ut during lectures. Reference bks f particular interest: J.N. Reddy (2005) An Intrductin t the Finite Element Methd. McGraw-Hill (ISBN ); J. Fish, T. Belytschk (2007) A first curse in Finite Elements, Jhn Wiley & Sns, Ltd (ISBN ). Zienkiewicz and Taylr (2000) The Finite Element Methd. The Basis, Butterwrth- Heinmann, Oxfrd, UK. Nte: The pen hurs fr the student expeditin at the Dept. f Slid Mechanics, Osquars Backe 1, are 9-11 am, Mnday-Tuesday, Thursday-Friday. Phne: Schedule Time and place fr the lectures and tutrials (prblem slving sessins) are listed belw. In ttal 17 lectures (L), 8 tutrials (T) and 2 cmputer wrkshps (W) are given during the curse. Each lecture and tutrial crrespnds t 2x45 minutes. The tw wrkshps, each 4 hurs (2 time slts/lab), will be held in the cmputer rm GLADER, Brinellvägen 64. Mnday Tuesday Wednesday Thursday Friday Week 35, Aug Sep. 2 L1: 15-17, D3 L2: 15-17, V3 L3: 10-12, V3 L4:15-17, V3 Week 36, Sep. 5- Sep. 9 T1: 15-17, E35/E33 L5: 8-10, D3 L6: 15-17, E2 L7:10-12, M3 T2: 8-10, L21/L22 Week 37, L10: 10-12, E3 W1 grp1: 13-17, L8: 15-17, V3 L9: 15-17, V3 Sep. 12- Sep. 16 Deadline HW1 Glader Week 38, W1 grp2: 8-12, Sep. 19- Sep. 23 Glader T3: 8-10, E33/E32 L11: 8-10, E2 L12: 13-15, E3 L13: 8-10, E2 Week 39, T4: 15-17, E35/E32 L14: 15-17, E2 T5: 13-15, D34/E31 L15: 13-15, V3 Page 2 f 6

3 KTH Slid Mechanics SE1025 FEM. FEM fr engineering applicatins (SE1025), 6 hp, Fall 2011 Sep. 26- Sep.30 Week 40, Oct. 3- Oct. 7 Week 41, Oct. 10- Oct. 14 Week 42, Oct. 17- Oct. 21 W2 grp1: 8-12, Glader L16: 15-17, E2 Deadline HW2 W2 grp2: 8-12, Glader L18: 13-15, E3 T7: 15-17, D41/E33 T6: 15-17, E32/E33 L17: 8-10, E2 Exam: 14-19, V12/V23/V33 T8: 8-10, D34/D35 Deadline HW3 5. Assessment Hmewrk assignments, HEM1 (1.5 hp) HEM1 is cmpulsry and cnsists f three hmewrk assignments (HW1) and crrespnds t 1,5 credits (hp). The fllwing applies: Shuld be slved in grups f tw r three students and shuld be presented in written reprt, where the prblem statement, the slutin steps and the results shuld clearly stated. Nte that printuts frm varius mathematic prgrams can be added t the reprt, but nly as an appendix. Reprts cnsisting slely n such printuts will nt be graded! The hmewrk slutins shuld be handed t ne f the teachers r put in the bx utside the ffice at the latest 6pm the day f the deadline (the department dr clses at 6pm). T pass HEM1, a ttal f 12 pints ut f 25 pints available n HW1, HW2, HW3, is required. Als nte that, if the written exam is passed, HEM1 is autmatically passed. Pints earned in the hmewrk assignments, renders extra bnus pints at the written exam. The bnus pints, p bnus, are determined based n the sum f the pints earned in the hmewrk assignments accrding t pbnus = 1 if (6 phmewrk < 10) = 2 if (10 phmewrk < 14) = 3 if (14 phmewrk < 18) = 4 if (18 phmewrk < 22) = 5 if (phmewrk 22) The bnus pints can be used n future exams until August 2012 and the hmewrk assignments will be available at the beginning f the curse. Nte that the slutins fr sme f the prblems can be verified by slving the crrespnding prblem using simple FEM-based Matlab prgram, which can be dwn laded frm the hme page. The deadlines fr the hmewrk assignments are HW1: Thursday, September 15 HW2: Tuesday, Octber 4 HW3: Friday, Octber 14. Page 3 f 6

4 KTH Slid Mechanics SE1025 FEM. FEM fr engineering applicatins (SE1025), 6 hp, Fall 2011 Cmputer wrkshps, LAB1 (0 hp) The purpse f the tw cmpulsry cmputer wrkshps is t btain sme experience n hw t slve elast-static and heat cnductin prblems with a cmmercial finite element sftware. In this curse the multi-physics FEM prgram ANSYS is used. Of special interest is hw an engineering prblem is set up fr analysis by FEM, i.e. pre-prcessing, and the interpretatin f results, i.e. pstprcessing. A student versin (limited nly in prblem size) f ANSYS can be btained frm the library, KTHB. Written examinatin (TEN1; 4.5 hp) A written 5-hurs exam, cvering the whle curse, will take place n Tuesday, Octber 20, 2pm- 7pm, in Lecture halls V12, V23 and V33. In rder t participate in the exam, the student must register his/her participatin at the latest tw weeks prir t the date f the exam. This is dne using the KTH web page My pages. A secnd exam will be rganized in March 2012 fr thse wh may fail the first exam. The written exam is cmpsed f abut 5 prblems, which if crrectly slved gives 25 pints. Cunting the 5 pints which can be earned by crrectly slving the hmewrk assignments, a ttal f 30 pints can be btained at the exam. The grading will be made accrding t ECTS as: pints pints < pints < pints < pints < pints < 12 pints <10 grade A grade B grade C grade D grade E (pass) grade FX grade F (fail) Students, wh btain grade FX, will be ffered t d a cmplementary exam 4-6 weeks after the rdinary exam. 6. Syllabus Class Tpics Literature Sectins L1 Intrductin Elastic energy Handut L2 Discrete systems, Castiglian s therems Handut L3 Matrix frmulated structural mechanics Slides Page 4 f 6

5 KTH Slid Mechanics SE1025 FEM. FEM fr engineering applicatins (SE1025), 6 hp, Fall 2011 L4 Direct matrix methds, spring/truss structures Slides L5 Principle f virtual wrk, Strng/weak frms, Apprximate methds, Displacement interplatin and FEM-prcedure, FEM- Eqs. Handut; LQ: chap. 3 T1 Prblems n energy principles and matrix frmulated EX 1.6, 2.1, 2.2 structural mechanics - direct methd L6 FEM fr trusses, 1D-example LQ: chap. 1, 3, 4 L7 Accuracy, Higher rder elements, FEM fr truss structures, 2Dexample T2 FEM-analysis f trusses (1D) and truss structures (2D), shape functins LQ: chap. 3, 4 EX 4.1, 3.3, 5.2 L8 FEM fr beams, strng/weak frms, FEM-Eqs., LQ: chap. 2, 5 L9 cnt. FEM fr beams, 1D-example, features f FEM slutins LQ: chap. 2, 5 L10 FEM fr planar frames with beam elements LQ: chap. 5, 6 L11 T3 FEM fr 2D & 3D slids in general, 2D analysis with CSTelement FEM-analysis f beams (1D) and planar frames (2D), shape functins LQ: chap. 2, 7, 9 EX 4.6, 5.4, 5.6 L12 cnt. 2D FEM analysis with CST-element LQ: chap. 7, EX 6.12 T4 FEM-analysis f 2D elast-static prblem with CST-element EX 6.14a,c L13 L14 Rectangular and isparametric 4-nde elements, crdinate transfrmatin cnt. 2D 4-nde elements, Cnsistent ndal frces, Num. integratin LQ: chap. 7 LQ: chap. 7, EX 6.7 T5 Cnsistent ndal frces, Gauss integratin EX 6.8b, 6.9, 6.10 L15 3D FEM analysis, Mdeling aspects, Cnvergence, Substructuring LQ: chap. 9, 11 T6 Element technlgy, isparametric elements EX 6.2, 6.3, 6.4, 6.19 L16 FEM fr heat cnductin LQ: chap. 12 L17/L18 FEM fr therm-mechanical prblems LQ: chap. 12 T7 FEM-analysis f therm-mechanical prblems EX 7.2, 7.3 T8 Repetitin, slving exam type f prblems Handut 7. Prblems recmmended fr exercise. Energy principles Castiglian s therems: , (1.6) Matrix frmulated structure & slid mechanics Spring structures: 2.4, 2.3, , 2.11 (2.1, 2.2) Page 5 f 6

6 KTH Slid Mechanics SE1025 FEM. FEM fr engineering applicatins (SE1025), 6 hp, Fall 2011 Strng/weak frm in general 3.1, 3.2 (3.3) FEM fr trusses & truss structures 3.4, 3.5, 4.2, 4.3, 4.5 (5.1, 4.1, 4.4, 3.3, 5.2) FEM fr beams & planar frames: , 4.9, 5.5 ( , 5.3, 5.4, 5.6) FEM fr 2D/3D slids: 6.5, 6.6, 6.11, , 6.21 ( , , 6.12, 6.19) FEM fr heat cnductin & therm-elastic prblems 3.9, 3.10, ( ) Nte that prblems in parenthesis are slved during lectures r tutrial sessins. Page 6 f 6