Relative Entropy Computations for Nonlinear Deformations of the Porous Steel Structures

Area of Science:

• Structural Engineering
• Materials Science
• Computational Mechanics

Background:

• Structural defects in steel elements pose risks at micro- and macro-scales.
• Existing safety assessment methods like First-Order Reliability Method (FORM) rely on specific distribution assumptions (e.g., Gaussian).

Purpose of the Study:

• To investigate the relative entropy framework as a tool for safety assessments of steel elements with structural defects.
• To evaluate relative entropy as a potential alternative to FORM for reliability analysis.
• To present the yield surface of porous materials with random void volume fractions.

Main Methods:

• Application of relative entropy, Bhattacharyya, and Kullback-Leibler (K-L) mathematical theories.
• Hybrid computational technique combining Finite Element Method (FEM) software ABAQUS CAE 2017 with the Gurson-Tvergaard-Needleman (GTN) damage model and MAPLE.
• Iterative generalized stochastic perturbation technique and Weighted Least Squares Method for probabilistic moment determination and response function approximation.

Main Results:

• Relative entropy framework extends beyond FORM by incorporating 3rd- and 4th-order probabilistic moments.
• The approach determines uncertainty in stress, strain, and displacement state functions without assuming distribution types.
• Yield surfaces for porous materials with random void volume fractions were computed.

Conclusions:

• Relative entropy offers a universal and flexible framework for structural safety assessments, overcoming limitations of FORM.
• This method provides a robust alternative for reliability analysis, especially when distribution types are unknown or complex.
• The study demonstrates the viability of relative entropy for analyzing structural integrity under defect conditions.