Documentation of NL_2D_FEM

This Matlab code presents a novel method for simulating the nonlinear dynamics of highly flexible beam structures based on a finite element discretization of the geometrically exact beam model. The finite element model, currently limited to capturing in-plane motion, is solved in the frequency domain using a combination of harmonic balance and numerical continuation. The solving scheme is automated with the solver MANLAB, freely available to download at (the MANLAB website). Several different computations are available to the user with this code, notably classical forced response simulations, but also computation of the nonlinear modes (i.e. the backbone curves).

Contents

• Installation
  • Virtual environment
• Example
  • Set the Matlab Path
  • Create a new FE model
  • Input definition
  • Matrices and force vector initialization
  • Static solution
  • Modal analysis
  • Linear forced analysis
  • MANLAB analysis
  • Quick launch of a computation
• Initial value problems
  • Attributes
  • Methods
• Integration methods
  • Finite element model (FEM) of geometrically exact beam structures
  • Searching for periodic response
  • Frequency domain resolution with MANLAB
• Code
  • MANLAB Graphical User Interface (GUI)
• Useful functions folder
• Description of the inputs
  • Input by defining a model data base