美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes131

The finite element Metnod Overcome limitations of Rita Simple basis functions( ow order polyuouisls) Basisfonctians supported in sdo domains(fuite elemnet Basis functions constructed to provide interpolant of proximate soluton Undetermined beraweters represent vales of dead varlables(solution at suo dowiBin boundaries. ite eleven Mesh: 7777A8

2 A6,E Mode problew EA4+9)=00xL BC: A"specified: u(o=o EA du speCked: EAdu=p ormuleron o generic elene: A A B seek variation approxi wetion in tois dow ain ()xu闪)=艺9Q<x<x 0: nuwber of nodes in elemnet n=2: A B (n= us U2

Note: choosing undetermined parameters the V of the option at the he nodes en totes Continuity of the sol tion acoss elements A ebec e+1C UB U e+1 e1 This imposes conditions。p 人(飞 y)=9?喻=9 9+m+9(9+啊 ?(3) corange bolyhowiais

9()= x)的为 3)(x x)= Ayy减时pr址w或 Satisfy Is slDw Soltions exact 从闪=C=90 Asx<×1 B 公CC z9=4 E ∩=2 2=m X-X

=× 4-X2 2- (023 de(X-Xi(-xs de(X-X4)(-X3 2x)(x12 d=(x-×nx-×) ( x3-×) ②2 N atural Coordinate sy≤lw he functions loo& simpler when exe ressed in terms o the local coorotunete system 3 b the transformtion feom""toxis X=A-×A+1+×B 2

02)4x=4当+-4 A圳L2 ⅪA-新-5 A-X8 2 2 2 吗-1(1+5 m)h-455+ +1 在15(- g。3(什+9