Combing DGS and finite element for stress analysis using inverse boundary method.

Area of Science:

• Solid Mechanics
• Experimental Stress Analysis
• Computational Mechanics

Background:

• Accurate stress analysis is crucial for understanding material behavior and structural integrity, especially in areas of stress concentration.
• Traditional methods often face challenges in precisely defining boundary conditions for local models, limiting accuracy.
• Digital gradient sensing (DGS) offers direct measurement of stress gradients, providing novel experimental data.

Purpose of the Study:

• To propose a novel method combining Digital Gradient Sensing (DGS) with the finite-element method (FEM) for accurate stress solutions.
• To demonstrate the inverse determination of boundary conditions for local FEM models using experimental DGS data.
• To validate the method's effectiveness in calculating individual stress components in stress concentration areas.

Main Methods:

• Direct measurement of Cartesian stress gradient components using the DGS method.
• Inverse determination of nodal forces (boundary conditions) for a local FEM model from DGS experimental values.
• Calculation of the sum of Cartesian stresses using linear least squares on the stress gradient data.
• Application of the direct FEM to compute individual stress components once boundary conditions are established.

Main Results:

• Successfully determined the unknown boundary conditions for a local finite-element model using DGS data.
• Demonstrated the capability to calculate the sum of stresses at various points from the measured stress gradients.
• Validated the proposed DGS-FEM approach on a three-point bending specimen under compression, yielding accurate stress component results.

Conclusions:

• The integration of DGS data with FEM provides an effective approach for stress analysis in critical regions.
• The inverse method allows for accurate determination of boundary conditions, overcoming limitations of traditional approaches.
• This combined methodology enhances the precision of stress component calculations, particularly in areas of high stress concentration.