A numerical algorithm for Karhunen-Loeve expansion is proposed based on the theory of numerical analysis.The algorithm is embedded into the computational kernel of Abaqus through a hybrid coding approach using Python and Fortran.The key elements in the development of the program are analyzed,and an error analysis is conducted.The results show that the developed program is feasible,the random field expansion is reasonable,and the numerical algorithm has high precision.The calculated eigenvalues,eigenfunctions,and covariance functions are consistent with the theoretical solutions.
random fieldAbaqusKarhunen-Loeve expansioncovariance functionFredholm integral equation of the second kind
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