NewmarkImplicitSolver

This component belongs to the category of integration schemes or ODE Solver.

This scheme is an implicit time integrator for dynamic system using the Newmark scheme. To compute the new position or new velocity, the NewmarkImplicitSolver is based on the following equations:

Applied to a mechanical system where , we need to solve the following system:

Sequence diagram

Data

The solver is ruled by several breaking (converging or diverging) conditions:

• gamma is the Newmark scheme gamma coefficient
• beta is the Newmark scheme beta coefficient

Usage

At each simulation step and each Newton Raphson iteration, the NewmarkImplicitSolver requires:

• a LinearSolver to solve the linear system
• and a MechanicalObject to store the state vectors.

Example

This component is used as follows in XML format:

<NewmarkImplicitSolver rayleighMass="0.01" rayleighStiffness="0.01" />

or using SofaPython3:

node.addObject('NewmarkImplicitSolver', rayleighMass='0.01', rayleighStiffness='0.01')  

An example scene involving a NewmarkImplicitSolver is available in examples/Component/ODESolver/Backward/NewmarkImplicitSolver.scn