有限元分析基礎(chǔ)課后習(xí)題答案

1、 tdspnrte三角形單元i,j,m的j m邊作用有如圖所示線形分布面載荷，求結(jié)點載荷向量。解：面力移置公式： mjimjinnnnnnn000000426, 132, 62*63*2352, 426, 26*22*5165, 363,213*56*6mmmjjjiiicbacbacba),()(21mjiycxbaaniiii其中：)46(131)342(131)321(131yxnyxnyxnmji2134301402212165136122121a yxyxyxyxyxyxn460342033004603420321131所以 0)6(3)(121yqqqp dyyqqqyxyxyxy

2、xyxyxttdsyqqqyxyxyxyxyxyxre3100)6(3)(4600463420034233003211310)6(3)(46004634200342330032113112163121)6 , 5(213xxy載荷分布函數(shù)：積分函數(shù)： dyyqqqyyyytdyyqqqyyyyyyyytre0)6(3)(133130013313263130026313000013*3100)6(3)(47316004731632834200328342000013*3101216312163 dyyqqqqyyqqqqytdyyqqqqyyqqqqytre6312121212631212121

3、20)(36(*30)(36(*60027100)3)(2(*133130)3)(2(*263130013*310126323122126312631212632312212631263129292331)(321)36(3)(3)36(299331)(621)36(6)(6)36(qqyyqqyyqqdyyyqqdyyqqqqyyqqyyqqdyyyqqdyyqq 0210210031002182902990027100)3)(2(*133130)3)(2(*263130013*310121212126312121212qqqqtqqqqtdyyqqqqyyqqqqytre所以解：在如圖所示

4、坐標(biāo)下求解結(jié)點j的等效載荷：tqqqtqqxqqtxqqxqqdxyxtxqqqqjxjxjxjx121221303122121230121310)( 329(3103)9)(21(31031)3)(3在如圖所示坐標(biāo)下求解結(jié)點m的等效載荷：tqqqtqqqqtxqqxqqdxyxtxqqqqmxmxmxmx12122033122222103221310)( 329(3103)9)(21(31031)3)(3 021021003101212qqqqtre所以ijmjimijjimmijimjmiimjjmimjijmmjixxcyybyxyxaxxcyybyxyxaxxcyybyxyxa,解：a

5、acaabaaaaaacbaaacaabaammmjjjiii0,0,0*0*0, 000, 00*0000,0, 0*00*02 mjimjinnnnnnn000000),()(21mjiycxbaaniiii221001010121aaaa yxayxyxayxanayxaayaxaanayayxanaxyaxanmji0000001)(1)00(1)00(12222 10003101310310001310311103)411 (241210001411410411411)4121)(411 ()411 ()1 (22100011011)21)(1 ()1 (eeeed 321bbbb

6、11011010100001000111110011011000110000110000100212abababaaaabbccbabmjiiiiiiaacaabaaaaaacbaaacaabaammmjjjiii0,0,0*0*0, 000, 00*0000,0, 0*00*02 1101103130011310031011011010100001000110003101310aeaebds 10003101310ed 1101101010000100011ab 42311124111331300111011011011013100320211101101010000100011000310

7、131101101010000100011022etataetabdbktte 10003101310ed 1101101010000100011ab 42311124111331300111011011011013100320ettabdbktexypaa123412解： 0000000000000000003001310001101100011011001003130031114200111324201etk 4211310024131100111001001303100031013000111001000000000000000000202etk 42113100241311001140

8、023113042011310240111120041300311142001113242021etkkk0000000pr 載荷向量：10014140040400420000000042113100241311001140023113042011310240111120041300311142001113242013344332211pvuetpvuvuvuvuetpetpetvu0501001533100141400410050000044332211etpvuvuvuvu 10003101310ed 1101101010000100011ab 01101110001000010111ab

9、 12bb 031201010003101325000000110111000100001011000310131033221111atpatpetpaevuvuvubd 100210010003101320050000110111000100001011000310131022334422atpatpetpaevuvuvubd解： 10004202484100012102112)311 (231210001311310311311)3121)(311 ()311 ()1 (22100011011)21)(1 ()1 (eeeed 110110101000010001b 53411235211

10、442400211011011011024200416211101101010000100011020410241101101010000100018ettetabdbktte 1000420248ed 534112352114424002110110110110242004164321etkkkk 0000000000000000000000000000000000000000000000000000400042020000010011100000000000000000000000000000410053120000210035140000010011100000200024041k 53

11、4112352114424002110110110110242004164321etkkkk 000000000000000000000000000000000000000000000000000010110001000004240020000012530041000014350021000000000000000000000000000002420040000010110001162etk 000000000000000000000000000000000000000000000000000080008404000002002220000000000000000000000000000082001062400004200610280000020022200000400048081612etkk 8000840400000200222000000000000000000000000000008200106240000420061028000002002220000040004808000000000000000000000000000000000000000