304 Random Composites and 00:0: sS6)σ36，) (6.28) -Ejo:l-3Eo.b"o.)a@.) Having computed the first three probabilistic moments of contact stresses (expected values,standard deviations and skewness coefficients),the random field of the limit function g(z;)is to be proposed.Usually,it can be introduced as a difference between allowable and actual stresses o.(z:)induced in the composite as g(zo)=ou(@-o,(2:w) (6.29) Let us underline that allowable stresses are most frequently analysed as random variables in the interior of statistically homogeneous materials,whereas actual stresses are random fields.That is why the computational analysis presented later is carried out for the specific value of the vertical coordinate z.The random variable of allowable stresses o)is specified by the use of the first three probabilistic moments El@),Var((@)and S((@)).Then,the corresponding probabilistic characteristics of the limit function are calculated as 26 (6.30) (6.31) as well as304 Random Composites and ( ) ( ) () () ( ) [] [] ( )} ( )z z z z z n i i i i z i z z i z n i i i z z i z z z z E E S b b b b b b b b S σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ 3 3 2 3 1 3 2 2 3 1 2 2 2 2 2 3 1 3 1 3 2 2 3 − − ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ∂ ∂ ∂ ∂ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ⎪ ⎩ ⎪ ⎨ ⎧ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ∂ ∂ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = + ∑ ∑ = = (6.28) Having computed the first three probabilistic moments of contact stresses (expected values, standard deviations and skewness coefficients), the random field of the limit function g(z;ω) is to be proposed. Usually, it can be introduced as a difference between allowable and actual stresses ) σ z (z;ω induced in the composite as g( ) () ( ) z;ω = σ all ω −σ z z;ω (6.29) Let us underline that allowable stresses are most frequently analysed as random variables in the interior of statistically homogeneous materials, whereas actual stresses are random fields. That is why the computational analysis presented later is carried out for the specific value of the vertical coordinate z. The random variable of allowable stresses σ all ( ) ω is specified by the use of the first three probabilistic moments E[ ] σ all( ) ω , Var( ) σ all( ) ω and S( ) σ all ( ) ω . Then, the corresponding probabilistic characteristics of the limit function are calculated as ∑ ( ) = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = + n i i i b b g E g g 1 2 2 2 2 0 1 [ ] σ (6.30) ( ) ( ) ( ) () () [ ] 2 1 3 2 2 1 2 2 2 0 2 2 2 0 S b b E g b g b g b b g g b g g g n i i i i i n i i i i − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ∂ ∂ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = + ∑ ∑ = = σ σ σ as well as (6.31)