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16.225 is a graduate level course on Computational Mechanics of Materials.
694 years, 4 months
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The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course includes: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms include: variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There is a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science is stressed throughout the course.
Course Currilcum
- Elastic Solids Unlimited
- Vainberg Theorem Unlimited
- Specialized (Simplified) Variational Principles Unlimited
- Weighted – Residuals / Galerkin; Principle of Virtual Work Unlimited
- Sobolev Norms; Global Shape Function; Computation of K and fext; Isoparametric Elements Unlimited
- Higher Order Interpolation; Isoparametric Triangular Elements; Numerical Integration; Gauss Quadrature Unlimited
- Error Estimation, Convergence of Finite Element Approximations Unlimited
- Linear Elasticity; Numerical Integration Errors Unlimited
- Incompressible Elasticity; Hooke’s Law; Governing Equations Unlimited
- Constraints Ratio; Variational Principle of Incompressible Elasticity Unlimited
- Assumed Strain Methods Unlimited
- Finite Elasticity Unlimited
- Newton-Raphson Solution Procedure Unlimited
- Isoparametric Elements Unlimited
- Material Formulation Unlimited
- Time Dependent Problems Unlimited
- Constitutive Relations Unlimited
- Trapezoidal Rule – Heat Conduction Unlimited
- Connection Between Newmark Algorithm and Multistep Methods Unlimited
- Energy Conservation / Dissipation; Abstract Algorithms Unlimited
- Examples: Trapezoidal Rule; Newmark’s Algorithm; Stability Unlimited
- Multidimensional Case Unlimited
- Stability Properties of Trapezoidal Rule; Eigenprojections Unlimited
- Nonlinear Algorithms Unlimited
- Time-stepping Algorithms for Constitutive Relations Unlimited