The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

Zusammenfassung

In this thesis, several approaches are discussed in order to further enhance the performance of the finite cell method (FCM). Thereby, novel moment fitting quadrature schemes are introduced that allow to reduce the effort of the numerical integration process significantly. Further, a basis function removal scheme is proposed to improve the conditioning behavior of the resulting equation system. Finally, an innovative remeshing strategy is presented that overcomes the problem of severely distorted elements for simulations with large deformations.

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Goal and scope of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Basic elements of continuum mechanics 6

2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Motion and deformation . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Strain measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Equilibrium and stress measures . . . . . . . . ....