Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics (eBook)

The Energy-momentum method for flexible multibody dynamics: EM integrators for elastic cosserat points.- EM integrators for rigid body dynamics.- EM integrators for flexible multibody dynamics.- Foundations of time integration methods: basics of time integration in nonlinear system dynamics.- Time integration in industrial multibody system simulation.- Time integration methods for differential equations on manifolds.- Generalized-alpha Lie group time integration.- Spurious oscillations in generalized-alpha time integration.- The Absolute Nodal Coordinate Formulation: Introduction to ANCF.- 2D Bernoulli-Euler (thin) ANC element.- 3D shear and cross section deformable ANC element.- 2D shear and cross section deformable fully parameterized ANCF.- 2D shear and cross section deformable gradient deficient ANCF.- Selection of boundary conditions for 2D ANC elements.- 3D shear and cross section deformable ANC elements.- Variants of the energy-momentum method: Numerical time integration in solid mechanics: the role of dissipation.- The discrete gradient.- High frequency dissipative methods for nonlinear solid dynamics.- Energy decaying, momentum conserving methods.- The Energy-Entropy-Momentum method.- Conservative and dissipative methods in flexible multibody dynamics: Second order time integrators.- Conservative / dissipative time integration schemes.- Lie group formalisms.- A brief course on variational integrators