IUPUI School of Engineering and Technology

IUPUI School of Engineering and Technology

Topology Optimization

ME 59700 / 3 Cr. (3 Class)

This graduate-level course focuses on theoretical and practical aspects of numerical methods utilized in the solution of structural optimization with emphasis on topology optimization problems. This course presents fundamental aspects of finite element analysis and mathematical programming methods with applications on discrete and continuum topology optimization problems. Applications include designing lightweight structures, compliant mechanisms, heat transfer, and energy harvesting systems.


Christensen, P.W. and A. Klarbring, An Introduction to Structural Optimization, Springer, 2009


In this course students will understanding the complexity behind finite element-based design optimization methods and develop programming skills to apply this knowledge to the solution of structural engineering design problems.

  1. Apply state-of-the art optimization algorithms, particularly finite element-based methods. [a,e]
  2. State and parameterize a topology optimization problem. [a,e]
  3. Perform sensitivity analysis and derive sensitivity coefficients using direct and adjoint methods. [a,e]
  4. Implement specialized algorithms optimization algorithm including: SQP, MMA, OC, ESO, HCA/CBO, and explore the use of state-of-the art methods. [a,e,k]
  5. Understand and address computational issues such as uniqueness, checkerboards, and mesh dependency. [a,e]
  6. Apply topology optimization methods to solve problem involving non-compliant structures, compliant mechanisms, energy absorbing structures and energy harvesting systems. [a,c,e,k]

Note: The letters within the brackets indicate the Program Outcomes of Mechanical Engineering.