Integrator

The Integrator class specifies how the StaticAnalysis or DynamicAnalysis is performed. The Integrator class is designed to:

• Compute the state variables, i.e., displacement \(U\), velocity \(V\) and acceleration \(A\)
• Compute the effective stiffness matrix \(\textbf{K}_{\textrm{eff}}\) and effective force vector \(\textrm{F}_{\textrm{eff}}\) required to compute the incremental displacement \(\Delta U\).

The main member function in Integrator are:

• Integrator::ComputeNewStep()
  This function computes the states variables (displacement, velocity and acceleration) once the incremental displacement is obtained.
• Integrator::GetDisplacements()
  This function returns the displacement states variables \(U\) at the current time step.
• Integrator::GetVelocities()
  This function returns the velocity states variables \(V\) at the current time step.
• Integrator::GetAccelerations()
  This function returns the acceleration states variables \(A\) at the current time step.

In general, the Integrator class uses the Assembler class to compute the effective stiffness matrix \(\textbf{K}_{\textrm{eff}}\) and effective force vector \(\textrm{F}_{\textrm{eff}}\) to be provided to the LinearSystem object to compute the displacements \(U\), velocities \(V\) and acceleration \(A\) vector states for the incremental analysis. In the incremental analysis, at each (pseudo) time step \(t_n\), one needs to solve nonlinear systems of equations iteratively until satisfying the given tolerance and convergence criterion. More information regarding the derived integrator classes can be found at:

• QuasiStatic
• CentralDifference
• NewmarkBeta
• ExtendedNewmarkBeta
• CompositeBathe

REFERENCE:

• Forde, B. W. R., Foschi, R. O., & Stiemer, S. F. (1990). "Object-oriented finite element analysis". Computers & Structures, 34(3), 355–374.
• Mackie, R. I. (1992). "Object oriented programming of the finite element method". International Journal for Numerical Methods in Engineering, 35(2), 425–436.