美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes152

cmaulenon o isoparametRic elemets (Bathes book Consider the uadriltersd denat shown in the 8oc nodd coordinates 12}- nodal displacements le need to generai e our interpolation for the lineor square, Consider the Mepping from Hhe following- Master elee e4(4 2 (-1)g

le interpola le dlisplecewat ela as betore H-「4(+s(+45)0 2 O4(4+54+分 儿 从(5 But we need expression for Ou,.-- le follow Hhe fo lowie procedure 。EeHe ntexpoleton-Hoow He weser I element fo the quadrilateral k()=%513=H」X (11 wnere xlis the vedor of nodal coordinates 「=对…XX

3 I. Link der'ivatives fhrough choin role a3x1+2 十 9X190×,1 4 af 3x2 OXA+0X 9328×1a32 2 I In vecor form e)「a×2E 9X1 2 Whet we really hee ed is the inverse X1 olet]-3x, x ax. 52 l. Now we can derive the interpolation of strains

E-E a是 E22}=0/×1 /x+。u2/x OU 8x4(丁 sowe br l2 eu The strain vedor can then be written as: A ouA/afi wnere 9认a 3 2 4x4 A=4|J2-00|and J00 -1JJ工 [6]{},!9+w*k ere ves Ms 4×88x1

3x1 3x44x88×4 把2}=][G]{0 B 3×8 The fina s+ cowpat stion of the std地e etrix r the element ik- bcb dy B'CBJds, ds 2 1 Element force vedor R3=[时咖+时时的