326 PEEL ACEEHE Jounal of Ni" an University of Technology(2012) Vol. 28 No.3 SCHEMES; 1006-4710(2012)03-0326-04 Het BRE Ty 2 HE JR EE SE OP EE BY TA HE HER, FRR RT AE LARS DE, I HH 710048) HAE: WGA A th TES) he RPE UTA AE RG PB A OT ARE GRRL RPL. AER — RAI AFB RAR KA DIM BARGE HALL, TH TRRPERGAD GHTARPALBDS AME, HAE PRD MAILE Mh EPR TIE RE FED ERA GAA IERR ER AAA: MARY, AAPA; MERB:, RE RGR RM PRS: 0346.1 MRE: A Discussions on the Equivalence of Potential Energy Principle in Elastic Mechanics TANG Anmin, LI Zhihui (Facuby of Civil Engineering and Architecture, Xi" an University of Technology, Xi" an 710048, China) Abstract: ‘The principle of work and energy, equilibrium conditions and geometric equations can be di rived based on the fist law of thermodynamics, and minimum deformation principle and prineiple of ‘mum potential energy ean be derived based on the second law of thermodynamics. ‘These are two elastic deformation conditions with di nt physical properties, and being independent of each other. The mag- nitudes of elastic deformation can be determined by the former, and the distributions law can be deter- mined by the latter. The wordings that principle of minimum potential energy is equivalent to equilibrium conditions and generalized principle of potential energy is equivalent to the basic equations of elasticity are not correct. Key words: clastic deformation; laws of thermodynamics; principle of potential energy; minimum deformation energy principle SAME SE PF DH BEE BPE ETE, FE ME ETE | FB A Sh Di ACS EI) AE AVE fe PEE —— OME, PEE ERS, EET A AEH. DIBA Sh EEE WHI BE We |v Bo EE ES RRR. PR MR REE EIT SE a BE AG AE HA A A Ra SH MUR —“MRE REY AE EF LEP WF ORAS AEE. TES IR SS Ty ok — Ah TE BEFORE MABE MTOR EET AAR eR EAM: 2012-03-20 FEE, REAM A RES: . IP ORE SS REAR , SL BN Os AAA A EE Parkash AY BEV RHA EEN AWE ANE. SF SHEE IERIE KANE A EE, TU SIE SAG AUS 6 PAT — EE. RE SEAR AT St RE IE iL EE BRE PE JSEARAT ROR ARE. PAE ‘ORE AT a 9, EF PS RE PU FATE AB, EP EAR A A HH A EAR RE FRAP AEE OTA TE. 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PORE PIPER AHR AA EG RRA PRELI AY LES SM IAIN HY AE AAS HAIER CEA EASELS EAU AAA ID TID DB BRED ® ASSES ANE EOL TD AEE TE HS EH I, SES. HPA PEER WG, AS HH SH A ERE ARES TBE EEA BE FREI PAV RTS DC WHEL. 12 RNSERBSRTFRARRSLEAE i PERSIE AED 9b Hy CARE aS EI AE ‘Eth _L. Sb SE ETE, AAA a a PYRE AE, BD [Aiade+ [temas = [Foveide (8) ACS) THERA. WTI SF, (5) AT sik: [mae + 3{ Leads =a{ Lede (6) AESCHES” SPATE RT ABLE LIT, BFS Db Fa Bi wT RA A TR ADH BD: [jionde + [nude = [oydeyte (1) (7) HBAS EL. SL AMESEIE EREHEA(e,) = Loyey Hoy = 4A(e,)/d0y Ai: a( [fiu.ae) +8( {p.u,ds) = A([ACe, rao) = ([ Foeydo) (8) BT= o({ Soyeydo - [fu.do — [piuds) = 0 (9) T1= [A(e,)de= [fade ~ [ponds (10) UE i A wy DE EB (8) R45 (6) XA PE BAA HY HELA ABE Wh. (8) CHE SPL EAE TE FA A OSB A FEAR J Aa RE EA ET TLD) ENG RE PE EH BA. AARP HL EAS DFA IEA PE — DRA ADE ATER — BEE MONA EAE, BELA (8) ORR 1) CREE AE Ha (7) EAE AB) (9) RF BIT PEG OT me LS BR LS RE FRA BEE. SABINA Sh Ha AUT LH HR328 BESET ACEI (2012) 95 28 B95 3. SAARI AE Sb DAHA AOE A URAL. ARTE Vs Shy UA A I 9 ABEL ASS ET SEE EN. (7) RAT RL: 8{ [fudo) + { fr.uds) = 6{ foyeyde) (11) 6Tl,=0 tn 1+ [ovevde = [fe [pads HIE: 2: Sh Ay AUR IE AY 9 SP TE EL PA SH WW(7) RAT: [ousude + [oudnds = [Cyexde,do (13) (faut) + (outa) = 8(F[Cwevesde) (a) 4s) 9( 4 foaute) = o{fareyte) (5) 811, =| { (16) th = [ Feyeyte~ [Hynde ~ [Epa Sh i fc ES DGC a 2h a CH By IEE Ds CAA HE LE AHN 5 BOS I MBAR RAL EP RPE RS DT EA GME RTYAH . (12) (16) AIRE AUS LIL BRB STE RHESUS Fh Ha ER A ES Rot FMA INT LAER HH, RE FEARS AY ERIE ESE ETE AB AS A EU BE AB LRA SB DRE, Fit 38 6 LG Oh PF A OBE LAL AE 2 AAFSIERSMERAERERE PAREN RE MERE, AER SEAR ALP ETE Me SETI OU mE 60 Sob AM E MH AS aU = 60 +84 = 604T:8F (17) GE RG YE EL EE.8Q = 0.4 Bl: EAS Ft THERESE EAE, BUS EHBRRER TE BIER. SE — AFORE EIN BAS — A BE OARS ARATE ee LR Clausius RRS: BU - 08S - 7:3 =O (as) FORTE REA TE MEE oy FAHY PRL, HG OU He ‘Talor SBORIF : au, au, u = ese yy Mee, 4 LMS OU BPS * De 36 P08 Bagh TE seansetee (9) (18) soa (35 0)98 + (30 — be, $PU + 30 (20) FAFA LAT s _ au ois aw (2) Pe ae, eUS0 ry a Leas Bs BU = 3 Gp +B 5g, ashe Ee eu > 0 (22) (22) 4 HL AR ASF HE I TE EO TC RAMEE) 5 (17) ei 8 BA BE A A (22) Fe th BS RSE TE MEL PESETE RL EA AR PAR SE AR. SCENE RIED FE Rae FT EE JEL — TR FALE, TE 3H EH ETE RES LTTE EE EE ACSA ARETE A AT I PS — se RFT SBSH LESTE A Avett, ip BFE BEA SA TEAE IG LBW , BUH RE CE 5 An SRPMS Kitt , LAI Sb AE PO FE BE TARA 5 FE AE HE EI Kt, NE ES A AAS Be IL flo BR IL fi es BLP BA SL eS MAS A 38 PAARL SS AB AF TSK AR I Be — ie BOE PME RTE A ERE SOEE ETE 0 5 A BO 5a BO PES — Fi TAT AE SE ETE, SP TE REBURMAO SRE AE a. 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A, 2010,26(4) 403-406. ‘Tang Anmin, Li Zhihui, Mo Xiaoyi, ‘The elastic deforma- tion and stress distribution of circular shaft torsion desived frm eneegy principle [J]. Jounal of Xi” an University of ‘Technology, 2010,26(4) ; 403-406. (5) ieee Pek i. A ART eA RoR Sr RT BELT]. REAL: RE HE, 2009, 34.1) + 36-39, ‘Tang Anmin, Xu Mingda, Zhaolei, New method for elasto- plastic analysis of free-form deformation stricture [J]. Journal of Guangxi University (Natural Science Faition) , 2009 34(1) :36.39, (6) SrA REL FI). SE eH yee CM] [SAPP ARE 1984, 1012-1022, (7) Ee. SERIE LM] ASK AEE BERL 1979. UES EDI)