Numerical Algorithm
Numerical algorithm for solving the equations of motion in a dynamic system involves calculating the state of a model at small time intervals without a matrix inversion. Implementing explicit fea integration provides a way to simulate high speed events like impacts or material failures. The method is restricted to durations short enough that the propagation of stress waves can be captured within stable time steps.
This approach becomes computationally expensive for long duration events where implicit methods are more efficient.
Dynamic Simulation
Implementing this solver requires the definition of a stable time increment based on the smallest element size in the mesh. Rapid changes in velocity are captured by updating the acceleration at every step.
The Solution
The process calculates internal and external forces to find the nodal accelerations at the current time. These values are then integrated to find the new velocities and displacements.
Choosing Stability
Selection of the mass scaling and damping parameters prevents the calculation from diverging during high energy contacts. Stability is maintained when the time step stays below the Courant limit. Careful monitoring of the energy balance ensures that the virtual work done matches the physical reality of the test.
