The ground-structure method is a numerical technique used to find optimal truss layouts. Beginning with a highly redundant truss structure, optimization algorithms are used to eliminate sub-optimal members, resulting in trusses with many of the same properties as the minimum weight analytical solutions, i.e., Michell solutions, calculated by A.G.M. Michell in his 1904 article entitled "Limits of Economy of Material in Frame-structures."

In the links below, learn how the numerical solutions using the plastic formulation in original MATLAB code, GRAND (Zegard and Paulino, 2014), relate to the analytical Michell solutions.

Link to Ground-Structures Educational Page

The PPR potential based cohesive zone model was developed for mixed-mode cohesive fracture and takes into account physical parameters such as fracture energy, cohesive strength, and shape of cohesive interaction.

Learn about the features of the PPR model and how it can be applied for various materials and either intrinsic or extrinsic models. The educational page features:

• Interactive demonstration illustrating the PPR potential and its gradients
• A simple Matlab GUI and user manual available for download
• Abaqus user subroutine (UEL)
• List of related publications

Link to PPR Educational Page

The graph coloring algorithm was developed to alleviate problems associated with the race condition in FEM stiffness matrix assembly.

The educational page features:

• Challenges associated with the race condition
• Interactive demonstration on the graph coloring algorithm on different meshes
• A simple Matlab code implementing the greedy graph coloring algorithm
• List of related publications

Link to Graph Coloring Educational Page

Layout constraints are used in topology optimization of high-rise buildings to develop a lateral bracing system or create a conceptual design for structural members.

Learn about layout constraints applied to topology optimization on the educational page, which features:

• The importance of manufacturing type constraints in building layout optimization
• Interactive demonstration of layout constraints applied to a high-rise building
• Explanations of various layout constraints including projection, symmetry, pattern repetition and gradation
• List of related publications

Link to Layout Constraints Educational Page

The optimal stiffness of a structure is influenced by the size of the domain, given a fixed volume fraction and minimum length scale. The educational page features:

• Interactive demonstration of the influence of domain size of a cantilever beam with a fixed volume fraction and minimum length scale
• Explanations for increased cross bracing with increased length to height ratio

Link to Domain Size Educational Page