A view on stochastic finite element, geostatistics, uncertainty and risk analysis on parameter’s estimation in rock mechanics

Let us consider a reference element wi in the coordinate system s1 s2 s3 and we choose a base (polynomial):

Then the function Z(x) could be presented as a linear combination:

where [P8]−1 is the matrix , whose elements are the polynomials base values at the nodes, {Zs8} is the vector of the distributions of the nodes, while 〈N (s)〉 is the vector of the shape functions, Ni, i = 1, 2 . . . . . . 8.