A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry

In an attempt to construct an isogeometric analysis-suited geometry for isogeometric analysis, a new surface parameterization method using the one-step inverse forming (SPIA) is proposed. Initial generation of watertight analysis-suitable geometry (NURBS surfaces) with complex shapes can be a significant bottleneck for isogeometric analysis because computer-aided design models often include ambiguities such as gaps and overlaps. Most of traditional surface parameterization techniques are based on geometric method and limited to finite meshes, while SPIA is a physics-based method using sheet metal forming technique with large elastic-plastic deformation and robust enough and rapid to deal with the finite elements mesh with over 100,000 nodes within 2 min without the necessity to simplify the meshes. Using Coons surface parameterization, global mesh parameterization, and NURBS reconstruction, we can rebuild new computer-aided design models with errors under any tolerance to which isogeometric analysis can be applied. The NURBS surfaces after reconstruction are also used for computer-aided manufacturing.