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1、10-6、試求圖示連續(xù)梁的剛度矩陣K(忽略軸向變形的影響)。Ox12EI2EI3EI4y①②③e解：(1)求單元?jiǎng)偠染仃噆單元①：∵uv111222======0，，，，，1θθ0uv001代入(10-6)式得：??12EI6EI??ll32①k=????64EIEI????ll22EI單元②：∵uv1122====uv0，θθ12==1且i2=l??84EIEI??42ii22??ll∴k②==??????24i22i??84EIEI????ll單元③：∵uv11==0，，，，θθ1=0u2=0v2=12=0單元代入(

2、10-6)式得：??46EIEI???2k③ll=????61EI2EI?????ll23e(2)各單元的定位向量λ①②③??12????3λλλ===????????234????(3)單元集成過(guò)程：e單元單元?jiǎng)偠染仃噆單元定位向量轉(zhuǎn)換碼集成過(guò)程中的階段結(jié)果(1)(2)↓↓1234(1)(2)?12EI6EI?(1)→10012EI6EI?32?(1)??(1)→1?ll?①??ll3264EIEI??(2)→2?00???64EIEI(2)→2?ll2?(2)????22??ll00003??4??0000??(1)

3、(2)↓↓1234(1)(2)?12EI6EI?00(1)??84EIEI?ll32???(1)→21??②??ll?6484EIEIEIEI?48EIEI(2)→3(1)→2+0???llll2?(2)????ll??48EIEI(2)→3?00??ll???4?0000?(1)(2)↓↓1234?12EI6EI?100(1)(2)?32?ll??(1)??46EIEI(1)→32?61EI2EI4EI0?③???2?lll2???ll(2)→4????61EI2EI(1)→3?04846EIEIE+?IEI?(2)?

4、2????ll23?llll???61EIE2I(2)→4?00??23?ll???12EI6EI?126??63?000000??32?2??2?llllll????????61EI24EIEI0?631240??640???ll2llEI???2EIl?∴k==?????=???0041EI26EI??EIll?4126??026?3???2????lllll??????61EI2EI61236??00??00????00?2322??ll?llll???10-7、試求圖示剛架的整體剛度矩陣(考慮軸向變形影響)。設(shè)各

5、桿幾何尺寸相同，244lm==5,0.5,124,amI=mE=310×MPa.Ox32320y①②0BC①1②A③③D40(3)(6)(3)(2)(1)(5)(2)(4)(1)①(6)(6)③(3)(5)(5)(2)(4)(4)(1)②解：(1)結(jié)點(diǎn)位移分量的統(tǒng)一編碼(總碼)即剛結(jié)點(diǎn)B處(123)(2)單元定位向量單元①單元②單元③①T(1)→→→0(1)1(1)1λ=(000123)(2)→→→0(2)2(2)2②T(3)→→→0(3)3(3)3λ=(123000)(4)→→→1(4)0(4)0(5)→→→2(5)0

6、(5)0③Tλ=(123000)(6)→→→3(6)0(6)0(3)單元集成過(guò)程EA44EI∵=×30010KN/m=×2510KN/mll?30000?30000???012300?1230??①②③4∴kkk===×10?0301000?3050?????3000030000??0??1230012?30?????030500?30100??a①②①②又∵單元①②：α==0,TI∴kkkk===??010000???100000????001000a單元③：α=90T=????000010??000100??????

7、?000001?120??30120?30???030000?3000??③==T③4×???∴kTTk1030010030050????1203012030??0?300003000??????30050300100??按單元①②③的順序進(jìn)行單元集成單元①：(4)(5)(6)↓↓↓123(1)→1??30000??4(2)→20123?×010??(3)→3????0?30100單元②：(1)(2)(3)↓↓↓123(1)→1??300300+++0000??4(2)→200++1212?3030+×10??(3)→3

8、????0?30100單元③：(1)(2)(3)↓↓↓123(1)→1??60012+++0000??4(2)→200+++2430000×10??(3)→3????030?++00200100??6120?30∴k=×??03240104???????300300提醒：記得加單位。10-11試求圖示剛架的整體剛度矩