VARIATIONALLY CONSISTENT INERTIA TEMPLATES FOR B-SPLINE- AND NURBS-BASED FEM: INERTIA SCALING AND CUSTOMIZATION

Abstract eng:
The primal goal of this contribution is the investigation of variationally scaled consistent masses and reciprocal masses for B-Spline- and NURBS-based FEM. These technologies can be applied both for higher order low-frequency accuracy, as well as for high speed-up due to larger critical time steps for explicit dynamics. The derivation for selectively scaled consistent and reciprocal masses is based on a unified variational template based on a three-field parametrized functional with independent displacement, velocity and massspecific linear momentum fields. Usage of a mass-specific linear momentum field allows for mass preservation in case of non-constant density and the formulation is thus an enhancement to the one presented in [1]. Introduction of the mass scaling parameters by a free-parameter template in the style of [2] enables customization of the method to optimal low-frequency accuracy, optimal speed-up or non-negative dispersion by means of analytical dispersion analyses. To allow for the direct construction of inverse (reciprocal) masses without matrix inversion, biorthogonal bases for them momentum field are used. For higher order spline-based finite elements, the construction of dual bases is not unique and different constructions are discussed. When Diriclet boundary conditions are imposed by elimination, modifications of the biorthogonal ansatz space are required, their realization and influence on the results is investigated. By the proposed methods, significant reduction of the maximum eigenfrequencies are obtained and higher order accuracy then for consistent and lumped masses can be obtained. The variational methods are as well compared with existing higher-order masses ([3]) and algebraic mass-scaling methods ([4]) for eigenvalue analyses and transient benchmarks.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket