Theory and formulations

This section includes some material on formulations and general theoretical backgrounds for Exudyn. Note that the formulation of nodes, objects, markers, etc. is presented right at the subsection of each object, see Items reference manual. Furthermore, the general notations are described in Notation and an overview on the system assembly and system equations of motion is given in Notation, solvers are described in Solvers.

• Introduction to multibody systems
  • Historical development
  • Simulation tools in computational engineering
  • Components of a multibody system
  • Kinematics basics
  • Euler’s and Chasles’s theorems
  • Degree of freedom – DOF
  • Non-holonomic constraints
  • Dependent and independent coordinates
  • Chebychev-Grübler-Kutzbach criterion
  • Generalized coordinates
  • Reference and current coordinates
• Dynamics: mechanical principles
  • Newton’s basic principles
  • The Lagrange-d’Alembert principle
  • Generalized principle of virtual work
  • Virtual displacements
  • Generalized forces
  • Lagrange’s equations of motion
  • Multibody formulations: redundant and minimal coordinates
• Frames, rotations and coordinate systems
  • Reference points and reference frames
  • Coordinate systems of frames
  • Homogeneous transformations
  • Rotations
  • Rotation tensor: axis-angle representation
  • Euler angles: Tait-Bryan angles
  • Euler parameters and unit quaternions
• Finite elements
  • Integration points
• Model order reduction and component mode synthesis
  • Import of flexible bodies
  • Eigenmodes
  • Hurty-Craig-Bampton modes
  • Computation of stresses and strains for CMS modes
  • Interfaces and boundaries
  • Node weighting
  • Reference conditions
• Modeling of contact in Exudyn
  • Contact of meshed rigid bodies
  • Regularized friction
  • Sphere-sphere contact: equations
  • Sphere-triangle contact: equations
  • Contact relations for ANCF cable \(g_i\) (marker \(m0\)) and sphere \(g_j\) (marker \(m1\))