Finite Elements+

Delauney-based Triangulation with Laplacian Smoothing (Liu and Jeffers, 2018)


My group has done extensive work in the formulation and application of finite element analysis and isogeometric analysis for various solid heat transfer and solid/structural mechanics applications. In addition, I have taught courses on finite element analysis and nonlinear structural analysis for several years. Below are some products from my teaching and research. Details about the numerical models can be found in published papers.

Finite element formulations

  • Fiber heat transfer element for modeling 3D conduction in beams/columns

  • Shell heat transfer elements for modeling 3D conduction in slabs and thin-walled structures

  • Thermo-mechanical shell element for modeling coupled thermomechanical behaviors in nonuniformly heated structures

Isogeometric analysis (IGA)

  • IGA of laminated composites and functionally graded materials

  • Adaptive IGA to capture spread of plasticity in frames

  • Geometrically exact IGA Kirchhoff plate

  • Local refinement techniques

Related algorithms

  • Modified arc-length algorithm for modeling thermal snap-through instabilities

  • Time-averaged subcycling algorithm for bridging differences in time scale between fast- and slow-physics models, e.g., fire dynamics and solid heat transfer

Online Lectures

View a series of tutorials on finite element analysis in Abaqus on Ann Jeffers' YouTube Channel. An introductory lecture is shown below.