  This paper presents a steady-state and transient heat conduction analysis
framework using the polygonal scaled boundary finite element method (PSBFEM)
with polygon/quadtree meshes. The PSBFEM is implemented with commercial finite
element code Abaqus by the User Element Sub-routine (UEL) feature. The detailed
implementation of the framework, defining the UEL element, and solving the
stiffness/mass matrix by the eigenvalue decomposition are presented. Several
benchmark problems from heat conduction are solved to validate the proposed
implementation. Results show that the PSBFEM is reliable and accurate for
solving heat conduction problems. Not only can the proposed implementation help
engineering practitioners analyze the heat conduction problem using polygonal
mesh in Abaqus, but it also provides a reference for developing the UEL to
solve other problems using the scaled boundary finite element method.
