92 Riccardo Rossi,Vitaliani Renato,and Eugenio Onate where we introduced the symbols g=jTj and G=J-1.Operator g takes, after some calculations,the simple form gE●gEgm·g g= (15) ge●gngm●gm From the definition of he Green Lagrange strain tensor E =(C-I) we obtain immediately E =6C.This allows to write the equation of vir- tual works in compact form as (taking in consideration only body forces and pressure forces) SWint 6Wert 6Wpress (16) 、 6C:S=ho x●b+ p6x●n (17) Internal Work The termC:S describes the work of internal forces during the defor- mation process.Operator G=J-1 is referred to the reference configuration and is therefore strictly constant,follows immediately that C=GTogG (18) The term 6C:S becomes in Einstein's notation 3iC:8-i0u51=06m5m 1 (19) 2 introducing the symbols 6g11 S11 29则→26g}= 6g22 SJ→{S}= S22 (20) 2ǒg12 S12 (G11)2(G12)22G11G12 GuGJ→[Q1T 0 (G22)2 0 (21) 0 G12G22G11G22 it is possible to express the (19)in Voigt form as ic:5-0g1rQrs)-gr母：o=Qrs (22) considering the definition(15),introducing the symbol x)(x)..x and taking in account the isoparametric approximation one obtains Nx·g影=6x {g 2g11= (23) {g}/92 Riccardo Rossi, Vitaliani Renato, and Eugenio Onate where we introduced the symbols g = jT j and G = J−1. Operator g takes, after some calculations, the simple form g =  gξ • gξ gη • gξ gξ • gη gη • gη  (15) From the definition of he Green Lagrange strain tensor E = 1 2 (C − I) we obtain immediately δE = 1 2 δC. This allows to write the equation of vir￾tual works in compact form as (taking in consideration only body forces and pressure forces) δWint = δWext + δWpress (16) h0 2  Ω δC : S = h0  Ω δx • b +  ω pδx • n (17) Internal Work The term h0 2 ) Ω δC : S describes the work of internal forces during the defor￾mation process. Operator G = J−1 is referred to the reference configuration and is therefore strictly constant, follows immediately that δC = GT δgG (18) The term δC : S becomes in Einstein’s notation 1 2 δC : S = 1 2 δCIJ SIJ = 1 2 δgijGiIGjJ SIJ (19) introducing the symbols 1 2 δgij → 1 2 δ {g} = 1 2 ⎛ ⎝ δg11 δg22 2δg12 ⎞ ⎠ ; SIJ → {S} = ⎛ ⎝ S11 S22 S12 ⎞ ⎠ (20) GiIGjJ → [Q] T = ⎛ ⎝ (G11)2 (G12)2 2G11G12 0 (G22)2 0 0 G12G22 G11G22 ⎞ ⎠ (21) it is possible to express the (19) in Voigt form as 1 2 δC : S = 1 2 {δg}T [Q] T {S} = 1 2 {δg}T {s} ; {s} = [Q] T {S} (22) considering the definition(15), introducing the symbol {δx}T=  {δx1} T . . . {δxk} T  and taking in account the isoparametric approximation one obtains 1 2 δg11 = ∂NI ∂ξ δxI • gξ = {δx}T ⎛ ⎝ ∂N1 ∂ξ {gξ} ... ∂Nk ∂ξ {gξ} ⎞ ⎠ (23)