2D Finite Element Implementation – Plane Stress Q4

Implemented a 2D plane stress finite element solver from scratch in Python using bilinear Q4 elements with 2×2 Gauss integration.

Investigated stress concentration around a circular hole under uniaxial tension.

• Sparse global stiffness assembly
• Stress recovery at Gauss points
• von Mises contour visualization
• Mesh refinement study
• Achieved SCF ≈ 3.0 (consistent with theoretical solution)

2D Nonlinear Finite Element Solver – J2 Plasticity (Plane Strain)

Implemented small-strain elastoplasticity with isotropic hardening using return mapping, load stepping, and global Newton iteration. 

• Bilinear Q4 elements (2×2 Gauss integration)

• Backward Euler radial return mapping for J2 plasticity

• Isotropic hardening model

• Global modified Newton iteration

• Damped displacement updates for nonlinear stability

• Sparse stiffness assembly

• Load stepping procedure

• Stress redistribution after yielding