Substituting to the function (y,2)the function (y,z)such that: Φ0y,=p(0y,2z)+yz-zy (16.2) it becomes: M-6-++s In this expression,it is possible to define an equivalent stiffness in torsion with the form: ∂Φ ∂ +y2+2 (16.3) One obtains then for the constitutive relation: 08 M.=(G) 16.1.3 Determination of the Function (yz) 16.1.3.1 Local Equilibrium Local equilibrium is written as: Otx0 then with the displacement field in Equation 16.1: 72p=0 and with form 16.2 of the functionΦ： 7Φ=0 16.1.3.2 Conditions at the External Boundary The lateral surface being free of stresses,one can write along the external boundary aD: 含7=0. With the displacement field in Equation 16.1: 器-e-l+能+-w=0 2003 by CRC Press LLCSubstituting to the function j(y,z) the function F(y,z) such that: (16.2) it becomes: In this expression, it is possible to define an equivalent stiffness in torsion with the form: (16.3) One obtains then for the constitutive relation: 16.1.3 Determination of the Function F(y,z) 16.1.3.1 Local Equilibrium Local equilibrium is written as: then with the displacement field in Equation 16.1: —2 j =0 and with form 16.2 of the function F: —2 F =0 16.1.3.2 Conditions at the External Boundary The lateral surface being free of stresses, one can write along the external boundary ∂D: . With the displacement field in Equation 16.1: F( ) y, z = j ( ) y, z + yzc – zyc Mx dqx dx -------- Gi y ∂F ∂z ------- z ∂F ∂ y ------- y 2 z2 – + + Ë ¯ Ê ˆ DÚ = ¥ dS · Ò GJ Gi y ∂F ∂z ------- z ∂F ∂ y ------- y 2 z2 – + + Ë ¯ Ê ˆ dS DÚ = Mx · Ò GJ ∂qx ∂ x = ------- ∂txy ∂y --------- ∂txz ∂z + --------- = 0 t . n = 0 ∂f ∂y ------ z z – c – ( ) Ó ˛ Ì ˝ Ï ¸ ny ∂f ∂z ------ y y – c + ( ) Ó ˛ Ì ˝ Ï ¸ + nz = 0 TX846_Frame_C16 Page 309 Monday, November 18, 2002 12:32 PM © 2003 by CRC Press LLC