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Python FEM: Plate with Circular Hole or Elastic Inclusion, Parametric Stress Concentration Study
• Compared stress concentration locations and magnitudes for hole vs stiffness-contrast inclusion
• Parametric studies over defect radius with automated simulation runs (radius sweep / DOE-ready)
• Implemented sparse global stiffness assembly and solution using SciPy sparse solvers
• Generated automated post-processing and visualization of von Mises stress fields
2D Finite Element Implementation – Plane Stress Q4
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)
Maximum von Mises stress converged toward theoretical SCF = 3 with mesh refinement.
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
3D Thermo-Mechanical Simulation: Hot Sphere Heating a Cold Plate (Python FEM / FDM)
Thermal contact between a hot spherical body and a cold metallic plate, heat propagation.
Explicit time-integration scheme with stability-controlled timestep based on thermal diffusivity.
Boundary conditions:
Cold plate base (Dirichlet temperature condition)
Insulated lateral boundaries (Neumann condition)
Localized hot contact patch beneath the sphere
Real-time temperature field evolution visualized using rotating 3D animations.
Thermo-Mechanical Simulation of Localized Electronic Hotspot
Thermo-Mechanical Simulation of Localized Electronic Hotspot
Steady-state conduction with Gaussian internal heat generation
Fully coupled plane-stress thermoelastic response
Sparse FEM implementation (Q4, 2×2 Gauss)
Automated stress recovery & visualization
Temperature:
Localized Electronic Hotspot — Steady-State Thermal Field (FEM)
Displacement:
Thermal Expansion–Driven Warpage Under Constrained Boundary Conditions
Stress:
Thermally Induced Stress Concentration from Confined Expansion
Thermo-Mechanical Finite Element Solver with Gaussian Hotspot
Thermo-Mechanical Finite Element Solver with Gaussian Hotspot
Class-Based Python Implementation (Q4 FEM, Thermoelastic Coupling).
Semiconductor packaging, Battery thermal management, Electronic device hotspot analysis
Implemented a modular thermo-mechanical FEM engine in Python with sparse matrix assembly, strategy-based boundary conditions, and deformed-configuration scalar visualization, demonstrating CAE automation.
Steady-state conduction with Gaussian internal heat generation
Fully coupled plane-stress thermoelastic response
Sparse FEM implementation (Q4, 2×2 Gauss)
Automated stress recovery & visualization
Temperature:
Peak temperature at hotspot center, Symmetric heat diffusion, Boundary cooling
Displacement:
Outward expansion from the heated center, Constraint-induced stress near boundaries, Smooth displacement gradients consistent with thermoelastic theory
Stress:
Peak stresses near hotspot region, Elevated stress concentrations near constrained edges, Stress redistribution consistent with thermoelastic theory
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