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Last updated:

September 21, 2022

Duration:

Unlimited Duration

FREE

This course includes:

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Description

16.225 is a graduate level course on Computational Mechanics of Materials.

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 Curriculum

  • 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

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Massachusetts Institute of Technology
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