1、WU EAlPlPWU2212PPlEAdxxNdVEudVdU2)(222llEAdxxNdUU2)(2EAdxxNdU2)(2PGIlmmWU2212m22222)(2PGIdAdxxTdVGudVdUlPlGIdxxTdUU2)(2Gu2212mEIlmmWU221222222)(2EIdAdxyxMdVEudVdUllEIdxxMdUU2)(2EIdxxMdU2)(2m0EImlmEAlPlPWU2212PGIlTTWU2212cPyWU21PWU21TPccyPlmEIlmmWU2212.2121212144332211PPPPU321PPP扭矩横向力轴向力CBAByl,;CBA3P
2、1P2PCBABPyPlPWU321212121变形能1P3P2P4PAB21344433221121212121PPPPU1P2PAB123422112121PPUa3P4PAB341244332121PPUb1P2PAB221144332211121212121PPPPPPU3P4P34123412443344332211221212121PPPPPPU21UU44332211PPPP44332211PPPP等于零时和当42PP3311PPm12Pymm12PymEIaB2122EImamy22213311PP时等于当31PP31而引起的位移方向因作用作用点沿于而引起的位移等方向因作用作用
3、点沿133311PPPPPPm12Pym时当1 Pm12ysin2PNPctgNNcos21222211212221EAlNEAlNPyc222112)sin(22)(21PEAlEAlPctgPycPEAlEAlctgyc)sin1()(222112PEALEALctgyc)sin1(cos)(2212?xyAPxPyFyF?Ay?x?AyAPxyFM?BMAPByFM?BXAyBXAPBPyFxX?MAy?Bx iiPPPP321321位移作用下具有相应的广义在广义力无刚性位移的弹性结构 iiPPPPU21212121332211 iiiPP321起相应的位移将引力一个增量设此时仅给 ii
4、iiPPPPU221121 iiiiPPPPU221121 iiPPPU2211 iPPP21iPUPPPPiiii 2211iiPUiiPUiiiiPPPU作用方向的位移作用点沿于的偏导数等对任一载荷结构变形能iiPUilliiidxxxMEIxMEIdxxMPPU)()(2)(2njnjijjjjjjjiiiPNEAlNEAlNPPU1122iiFVP221)(qxPxxMPABlqillAdxxqxPxEIdxPxMEIxMf)(21(1)()(2)83(143qlPlEIfA方向一致和为正值表示方向PfA221)(qxPxmxMillmAdxqxPxmEIdxmxMEIxM02)1)(
5、21(1)()(iAqlPlEI)62(132方向相反和为负值表示方向mAmPABlqAxEIMVld22EIlF632PPFVwA xxEIFld2022P)(33PEIlFwA)2()2(PxlxEIFxlxxEIFFxxEIFxxEIFllllllld)2(2d)2(d2d22222P222P2022PxEIMVld22EIlFEIlFFEIlF2P484856323P3)20(PlxxFMEIlFwPB48530FBFVw?PFV?PFV?PFVPFPP21PPFPPVFPPVFV2211PPPFPPVFPPVFV2211PPPFPPVFV)()(11PFP21?qV?PFV12012
6、)20181121(2208342)22(21215252054322222EIlqEIlqxxlxlEIqdxxqxqlEIdxMEIUlllEIqlqU1205)2(24433xlxxlEIqvEIqlEIqldxxlxxlEIqvdxll120)512121(24)2(2455433qdxPidxPUqPPUqUiiiliqdxP?qUqL ildxxvxqvPvPvPW)()(332211外力虚功QdMdlNddW)(内力虚功dQdMldNW)(内力总虚功 ildxxvxqvPvPvPW)()(332211外力虚功dQdMldNW)(内力总虚功 ildxxvxqvPvPvP)()(33
7、2211dQdMldN)( 211332211)()(mmdxxvxqvPvPvPilTddQdMldN)(dxQdxMldxN)()()()(1在这里看作虚位移是外力作用下的位移和与式中ddl的内力方程是单位载荷下式中)()()(xQxMxNdxMl)()()(ldxNldxTl)(方向和单位力方向一致为正值表示dxEIxMdxdxvddxdxdvdxdd)(22EANll dxGIxTdP)(dxEIxMxMl)()(niiiiiEAlNN1dxEIxTxTlP)()()2)(2(116)()(12202dxlxxlPdxlxPxEIEIPldxEIxMxMlllBlARBR1mABxlx
8、M1)(PARBRABx2l)(2)(2xlPxMxPxM2)(1P)(xMx1m)(xMxtgxM)(ccllMxtgdxxxMtgdxxMXM)()()(ccxtgMccllMxtgdxxxMtgdxxMXM)()()(1mxP)(xM)(xMxtgxM)(EIMxEItgxdxxMEItgdxEIxtgxMdxEIxMxMcclll)()()()(xP)(xM)(xM1mxtgxM)(EIPllPlEI16212412EIMc矩值矩图形心位置对应的弯弯是单位载荷下与外载荷cM积是外载荷下的弯矩图面)(线位移或角位移是广义位移和轴向拉压情况式可以推广应用于扭转EIMc 221qxPxmxM
9、PABlqm 221qxPxmxMPl221qlmMPABlqml8321432131322214322qlPlmlEIllqlllPllmlEIyA62211213121322qlPlmlEIlqllPlmlEIAqlElqqqElq21)(1FssVqdsdrqqdsdr表面表面 qFlFVqFVFlE21WPPPPU.2121212144332211WU PS SS P PjjiiFFiiPUdxxMxMEIl)()(1cMEI1UMUFU?FMUUUsin2PNPctgNNcos21222211212221EAlNEAlNPyc222112)sin(22)(21PEAlEAlPctgP
10、ycPEAlEAlctgyc)sin1()(222112PEALEALctgyc)sin1(cos)(2212百分表百分表qlElqqqElq21)(1FssVqdsdrqqdsdr表面表面 qFlFVqFVFlE21?xyAPxPyFyF?Ay?x?AyAPxyFM?BMAPByFM?BXAyBXAPBPyFxX?MAy?Bx)2)(2(116)()(12202dxlxxlPdxlxPxEIEIPldxEIxMxMlllBlARBR1mABxlxM1)(PARBRABx2l)(2)(2xlPxMxPxM2)(1ili zi zi ziABxEIMMd31)2,()(P2RxRECRxRFM)
11、0 ,(01RxCAM)20 ,()sin1 (P3GERFMxM11xM12)sin2(3RMiliziziziABxEIMMd31)2,()(P2RxRECRxRFM)0 ,(01RxCAM)20 ,()sin1 (P3GERFMxM 11xM 12)sin2(3 RM253233PEIRFAB)sin2()sin1 ()(022020RdEIRRFdxEIxRxFdxEIxPRRPRAB加什么单位力？加什么单位力？加在哪里？加在哪里？加在什么方向？加在什么方向？怎样建立坐标系？怎样建立坐标系？11)(4825)4816131(44EIqlEIqlEIllql32212 21iiciiBI
12、EMAMEIllql228322EIllql232212EAlql12021NNiiCiiAEFAFEAql2221NiiCiiIEFA21iiCiiBIEMAEIql44825EAql222N2524)()(AlIMF22N2522524)()(lhAlIMFDCiMDCiM3EIFl3321iiCiiIEMAEIllFl342221EIllFl3221P32GIFlP)(2GIllFl21PiixCiiIGMA0)(23P3321P21GIFlEIFlIGMAIEMAiiCixiiiCiiBP32GIFlP)(2GIllFl21PiixCiiIGMA0EIFl33EIllFl342221EIllFl322121iiCiiIEMA0EIFl2221iiCiiIEMAEIlFl121P) 1(2GIlFl21PiixCiiIGMA0P22GIFl0EIFl2221iiCiiIEMAEIlFl121P) 1(2GIlFl21PiixCiiIGMA0P22GIFlP222121P22GIFlEIFlIEMAIGMAiiCiiiixCiiA.2121212144332211PPPPUWU PS SS P PjjiiFFiiPUdxxMxMEIl)()(1cMEI1
