IGA2025

Retaining optimal convergence rates employing a dual static condensation procedure within a mixed isogeometric plate formulation

  • Stammen, Lisa (RPTU Kaiserslautern-Landau)
  • Dornisch, Wolfgang (RPTU Kaiserslautern-Landau)

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Using NURBS basis functions, originating from the geometry representation, as trial functions for the interpolation of unknows during the analysis, the accuracy of results can be increased due to their high continuity and the exact discretization, even for complex geometries. Mixed formulations introduce supplementary variables from different physical fields to the analysis that serve as unknowns in addition to the standard deformation variables. This also enables selecting a distinct discretization for each of the independent fields. Hence, locking phenomena can be alleviated by selecting appropriately reduced approximation orders for the shear-force parameters in a deformation-shear-mixed formulation. As solving the enlarged system of equations goes along with an increased computational effort, performing static condensation is desirable. As this requires the inversion of the sub-matrix related to the additional variables, conducting this procedure is also computationally expensive, especially for large systems of equations. Employing dual basis functions for the interpolation of the supplementary parameters of a mixed formulation ensures the diagonal dominance of the corresponding part of the system matrix. This enables to perform row-sum-lumping for this sub-matrix, while introducing solely a minimal error. Conducting that before performing static condensation increases its efficiency, due to the minimal computational effort required for the comprised matrix inversion. In this contribution, such an efficient static condensation procedure, based on dual lumping, is proposed for a mixed plate formulation. Therefore, the additionally introduced shear force parameters are interpolated employing NURBS and their approximate dual basis functions. The main novelty of our work is to study the effect of points with different types of limited internal continuity within the discretization on the convergence rate. Thus, an adapted interpolation is investigated that enables to retain the optimal convergence rate of a mixed formulation while employing the proposed efficient static condensation procedure.