March 18, 2022 at 2:25 am

peteroznewman

Subscriber

Is this a linear system?

A linear system has only linear contact, such as Bonded or No Separation, or no contact at all.

A linear system has only linear material models.

A linear system has only small deflection.

If you have a linear system then the 30 forces can be applied separately and are additive to the six components of stress at a point.

The sensitivity of each force is immediately known at each of the 3 control points by simply applying a single force.

The same can be said about the 5 forces you want to use to replace the 30 forces.

When you say 30 or 5 forces, are the directions of the forces fixed, so you are only talking about the magnitude of the force, or are there three components for each of the 5 forces?

Max Principal and Min Principal Stress is a nonlinear combination of the six components of stress, so there is an advantage of capturing the six components of stress at the 3 control points, not just the two Principal Stresses to take advantage of the linearity of the system between input forces and output stress components.

The 30 forces will create a target value of the six components of stress at the 3 control points. Then a Least Squares Fit will find magnitude of the 5 forces that minimizes the error of the stress components from the 18 target values.

A linear system has only linear contact, such as Bonded or No Separation, or no contact at all.

A linear system has only linear material models.

A linear system has only small deflection.

If you have a linear system then the 30 forces can be applied separately and are additive to the six components of stress at a point.

The sensitivity of each force is immediately known at each of the 3 control points by simply applying a single force.

The same can be said about the 5 forces you want to use to replace the 30 forces.

When you say 30 or 5 forces, are the directions of the forces fixed, so you are only talking about the magnitude of the force, or are there three components for each of the 5 forces?

Max Principal and Min Principal Stress is a nonlinear combination of the six components of stress, so there is an advantage of capturing the six components of stress at the 3 control points, not just the two Principal Stresses to take advantage of the linearity of the system between input forces and output stress components.

The 30 forces will create a target value of the six components of stress at the 3 control points. Then a Least Squares Fit will find magnitude of the 5 forces that minimizes the error of the stress components from the 18 target values.