美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes122

n计门2 The Ritz Method (covt /a) d(E4)=43 0<×< Model problein 0 Potential: =1 AE udx-(f u dx fo boundar conditions (o) EAul=P (essenti Ritz Approx imotion: u w C: p: Ta m(cB)=m(a Eowilibrom: STT-OT &c=o -NxN system of epusthons rex mwe

-lEA F4×-4c E4以C-(+ aci K R Sdve for C:: [kI[c]=RT R oximate soltion from obtined Coe Alternative for mnulohion usine PVD pVD:「qAd×=「-+dx+ admissible Sc =E以,中xwee从C U S=8c9,+c SE- Sc: 8

3 EA Ci 供引的=A以 EA4“以C;-(中Sc:=0 t ScU {}={8 as before ondiTions on ①+ee+ as WT ②Watd,s+ Conditons of pD ore sensti'ed ant system [K]]=R] to have unigue sownon( lineorw indebev de Stions sowe continuity such thot intends be velveted '(exist,<oo satisfy the esseut ial boundary canditions

计+从=从0 a sowe per we satisfy His by rewiring 的2(x)= ers ne boonda the se ot tunatons ipo] MUst be Compe Renerotig the toncnons S∪Wowe a towil ot Simple functons (polynomials, trigonometric funchions) sohstyiug the requirements above x =订 note Hnat o. sin lix wold give U(2) =x多

Conver pence could be very sl a poor Choice of basts tumcnons soution is two piecewise Cubic tonowas Pi= sin Tix gives very slow over& emarks hor well-dnoseu bs the process converges proot o wiTted for increasing N"Hhe prevously computed c:s donlt change. Ki is symmetric for linear elastics strains ana stresses are general Governing euston end neuro boundary con osition satisfied in the variation (integra)sense. the remore the aquation of oquilil ilibriomn is not sstistiedl pointwise tee convo Syste wfor degrees ef freedow) ce number s fromn Pare/ pproxiete sotion Minimizes emergy within subspace of funchions=> hot the red winiwuin energy is higher sysTew is stather