Variationally consistent inertia templates for B-spline- and NURBS-based FEM: Inertia scaling and customization

With the focus on B-spline and NURBS-based finite elements, the proposed template provides alternatives to the row-sum-lumped mass matrix, which is only 2nd order accurate independent of the polynomial order. Earlier proposed algebraically constructed higher order masses from the literature can be reconstructed in the variational setting described here as special instances. Furthermore, higher-order reciprocal masses can be constructed from the template. They are especially attractive for explicit dynamics as there is no extra expense per time step compared with lumped mass for linear problems. For non-linear problems only small overhead is expected, but this paper focuses on linear problems only and mainly undistorted meshes. Tuning the method towards inertia scaling, a reduction of the maximum eigenfrequency by 25%-40% is obtained in the examples herein, whereas the accuracy is higher than for lumped or consistent mass.