then again: Φ.，aΦ 苏，+正n:=m-m: 16.1.3.3 Conditions at the Internal Boundaries The continuity conditions of Section 15.1.2 are verified for uy and u.At an interfacial line ly between two phases i and j,the continuity of uy leads to Φ，=中 The continuity relations in Equation 15.6 lead to the continuity of (Tny+tn) when crossing the lines l,that produces the continuity of c(-,+c(+n 16.1.3.4 Uniqueness of the Function If one superimposes torsion and bending,by using the degrees of freedom for flexure defined in the previous chapter,the displacement component u becomes: dφ+n✉ ux=4-y9+z8,+ The longitudinal displacement u(x)has to respond to its definition (Section 15.1.1),meaning u= E ux ds s-y+y This requires that: Eps=0 JD Then,taking into account the form in Equation 16.2 of and the properties of the elastic center: 2003 by CRC Press LLCthen again: 16.1.3.3 Conditions at the Internal Boundaries The continuity conditions of Section 15.1.2 are verified for uy and uz. At an interfacial line lij between two phases i and j, the continuity of ux leads to Fi = Fj The continuity relations in Equation 15.6 lead to the continuity of (txyny + txz nz) when crossing the lines lij, that produces the continuity of 16.1.3.4 Uniqueness of the Function F If one superimposes torsion and bending, by using the degrees of freedom for flexure defined in the previous chapter, the displacement component ux becomes: The longitudinal displacement u(x) has to respond to its definition (Section 15.1.1), meaning This requires that: Then, taking into account the form in Equation 16.2 of F and the properties of the elastic center: ∂F ∂y -------ny ∂F ∂z + -------nz = zny – ynz Gi ∂Fi ∂y -------- – z Ë ¯ Ê ˆ ny Gi ∂Fi ∂z -------- + y Ë ¯ Ê ˆ + nz ux u y – qz zqy dqx dx = + + --------j h + x u 1 · Ò ES ----------- Eiux dS DÚ = u 1 · Ò ES ----------- u Ei S qz Eiy S qy Eiz dS DÚ d + DÚ d – DÚ Ó Ì = Ï º º dqx dx -------- Eij dS Eihx dS DÚ + DÚ + ˛ ˝ ¸ Eij dS DÚ = 0 EiF dS DÚ = 0 TX846_Frame_C16 Page 310 Monday, November 18, 2002 12:32 PM © 2003 by CRC Press LLC