• ME-366 Finite Element Methods
• ME-250 Thermodynamics

• Advanced Computational Mechanics of Structures
• Nonlinear Computational Mechanics of Structures

ME-366 FINITE ELEMENT METHODS

• Overview: basic concept, historical background, general applicability of FEM, engineering applications, general description of FEM, comparision with other methods of analysis, FEM packages, problem solving
• Discretization: introduction, basic element shapes, discretization process, node numbering schemem, automatic mesh generation
• Interpolation models: Introduction, polynomial form, simplex, complex and multiplex elements, interpolation polynomial in terms of nodal dof, selection of order of the interpolation polynomial, convergence requirements, linear interpolation polynomials in terms of global coordinates , interpolation polynomials for vector quantities, linear interpolation polynomials interms of local coordinates, problem solving
• Higher order and isoparametric elements: introduction, 1d elements, higher order elements in terms of natural coordinates/classical interpolation polynomials, 2d elements, continuity conditions, comparative study of elements, isoparametric elements, numerical integration
• Derivation of element matrices and vectors: introduction, direct and variational approaches, Using variational (Rayleigh Ritz) Method solution of equilibrium problems, eigenvalue problems, propagation problems. Equivalence of FE and variational methods, derivation of FE equations using variational approach, weighted residual approach, solution of eigen value and propagation problems using weighted residual method, derivation of FE equations using weighted residual (Galerkin) approach, Derivation of FE equations using least squares approach
• Assembly of element matrices and vectors and derivation of system equations: coordinate transformation, assemblage of element equations, computer implementation of the assembly procedure, incorporation of boundary conditions and its use in the computer programs
• Numerical solution of FE equations: Introduction, solution of equilibrium problems, eigenvalue problems, propagation problems, parallel processing in FEM analysis

ME-250 THERMODYNAMICS

• Introduction to thermodynamics, applications, thermodynamic systems, control volume, properties and state of a substance.
• Simple thermodynamic processes and cycles, energy, temperature, pressure and specific volume, properties of a pure substance
• Interpretation and use of thermodynamic tables, problem solving
• Work, heat, first law of thermodynamics, internal energy, Enthalpy & problem solving
• I ^st law of thermodynamics for open and closed loop systems, steady state and transient processes
• 2 ^nd law of thermodynamics, energy equation, reversible processes, carnot cycle
• Irreversibility and availability, power generation systems, rankine cycles
• brayton cycle, otto cycle, problem solving
• Thermodynamic relations, The claperyron equation