美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes133

The finite element method In FEMi we derale finite element equations fro PVD swe- SWe and obtained: K0=R:=4…n waere n:number of element nodal p Ue: elenent nodal displace ents EA doi dx: dement stiffness 2“94dxP(: demet nodal forcer e year Eκ erase; derive Q JiNi Dr lineer a vaare interpolation for He case of unifor w Cross sesion CA) Youngs Modals() and distrbuted load (9 02)=%o)

2 Finite element assembl Each finite element is conneted to ts neighbors st its end nodes DC a ge nodes 已1 Ue Dr iwer Meats 41(2=V2≠ 3 eU(° en Conceot question: Expression for the locel-globsl nodal M中 pins for te pusdratc clement we=n he assembly of the element equi sions is based on the satisfaction of Hhe varitional principle for he whole systeM

st> a sU_ 1 where t is the sum of the element valves ir over the mesh elements. Exawple, Mesh wilh two linear elements C=4 2 strein end e-1 2 1 xn nxn nx1 se=U-v 0= EE, U 1E(e- L Ue A Le ve- AsL E Us-Ue)=A EEue-Ug 2 e 2L l We hed obtained ke as ke AEEE1-4 1

{呼要吗号[= U. U Aeee ue-Ue Ue-ue, A Ee 0S-0 e e Replacing loca with globe numbering tovA{「kK ery 2 3=1 4{1V203「K:o{ K O lo o oU 24502(23KKb1 2 =4{「000「0

G UToTAL= U+U =4{01423[KK O UA 2 bhe论meS%4 sign has a special lenin assel which involves proper placement of the element stiffness metrix coefficiet io the bel matrIX Rewar ks on assemby oed watrix Lo Diagonal element corresponding to gbb dd node ,"i ets contributions frown d he eeents writine bo it Trusses, bows lane elastic 2⑦ ,1 ao 1k③+<+:

e Kij=o if node iand j are in di fferent dements Ki preserves the symmetry of the elemenT AsseM ably of 8 Lobe torce year Given R e E Find:R+=2 R e=1 ‖E×awpk ④2②2 R∈L 42 2 2 R=R+R cg「o12 42 ♀ R三早{+ 2