Semester-wise syllabus outline for an M.Tech in Computational Mechanics

Semester 1:

Foundational Core

1. Advanced Numerical Methods

   - Finite difference/element/volume methods, linear algebra solvers (direct/iterative), error analysis. 

2. Computational Solid Mechanics 

   - Stress-strain modeling, elasticity, plasticity, hyperelasticity, and constitutive laws. 

3. Finite Element Analysis (FEA) 

   - Static/dynamic analysis, isoparametric elements, meshing techniques, validation. 

4. Programming for Mechanics 

   - Python/Matlab for scientific computing, introduction to C++/Fortran for high-performance computing (HPC). 

5. Lab 1: Basic FEM & Coding 

   - Implementing simple FEM codes (e.g., beam/plate bending), using open-source tools (FEniCS, CalculiX). 

Semester 2:

Advanced Modeling & Applications

1. Nonlinear Finite Element Analysis 

   - Geometric/material nonlinearities, contact mechanics, solution algorithms (Newton-Raphson). 

2. Computational Fluid Mechanics (CFD) (Optional Core) 

   - Navier-Stokes equations, turbulence modeling (RANS, LES), finite volume methods. 

3. Multiphysics & Coupled Systems 

   - Thermo-mechanical, fluid-structure interaction (FSI), piezoelectric systems. 

4. Elective 1 (e.g., Fracture Mechanics or Computational Heat Transfer) 

5. Lab 2: Advanced FEM & Commercial Tools 

   - ANSYS/ABAQUS/COMSOL projects, validation against analytical solutions, HPC basics (parallel computing). 

Semester 3:

Specialization & Research 

1. Elective 2 (e.g., Multiscale Modeling or Topology Optimization) 

2. Elective 3 (e.g., Machine Learning in Mechanics or Biomechanics) 

3. Probabilistic & Stochastic Mechanics 

   - Uncertainty quantification, Monte Carlo methods, reliability-based design. 

4. Project Work Part 1 

   - Research proposal, literature review, preliminary simulations (e.g., crash analysis, composite modeling). 

5. Workshops/Professional Skills 

   - Industry-standard software training (LS-DYNA, OpenFOAM), data visualization (Paraview, Tecplot). 

Semester 4:

Thesis/Dissertation 

- Independent Research Thesis 

  - Focus on cutting-edge topics (e.g., AI-driven simulations, additive manufacturing modeling, multiscale FEA). 

  - Dissertation submission and defense. 

Elective Options (Semesters 2–3): 

- Advanced CFD & Turbulence Modeling 

- Computational Geomechanics 

- Material Modeling (Metals, Composites, Polymers) 

- High-Performance Computing (HPC) in Mechanics 

- Inverse Problems & Optimization 

- Digital Twin Technology for Structural Systems 

Lab Focus Areas: 

1. Code Development: Writing custom FEM/CFD solvers for niche problems. 

2. Validation & Verification: Benchmarking simulations against experiments/theory. 

3. Industry Applications:

   - Automotive crash analysis, 

   - Aerospace component optimization, 

   - Biomedical device modeling (e.g., stent deployment).