Assumptions / Limitations in COSMOS

When learning about a game, the first step is to understand the rules. Once we understand rules, learning curve is smooth and less time consuming.

Linear Static Analysis / COSMOS Designer / COSMOS Professional

There are three major assumptions for Linear Static Analysis.

• Linear:  The assumption here is, material properties are linear. That is Hooke’s Law is always being followed.  

Objects that quickly regain their original shape after being deformed by a stress, with the molecules or atoms of material returning to initial state of stable equilibrium, often obey Hooke’s law.

Materials which follow Hooke’s law are known as linear-elastic or Hookean Materials. Upto the elastic limit this is true for most metals. If considering a stress strain diagram the linear region (red) is where we work in.

• Static: Boundary conditions do not change with respect to space and time.

This means that magnitude, orientation, distribution of  loads / restraints  never change during solution.

• Small Deformation: Deformation or displacements are so small that final shape is very similar to the initial shape; thus stiffness or strength of material is not affected by changing stresses/forces. Usually, plastics, rubber materials are an anomaly to this small deformation rule.

Non-Linear Analysis / SolidWorks Simulation Premium

Looking at the assumptions/limitations of  Linear static analysis, one can guess the realms of  Non-Linear Analysis.

Material Non-Linearity

There are several types of material nonlinearity in structural analysis.

• Nonlinear Elastic
• Elasto-Plastic
• Bi-linear
• Multi-Linear
• Hyperelastic
• Viscoelastic

There are significant differences between linear and non linear material responses. For many materials, reviewing the stress-strain curve is the best way to understand nonlinearity of problem.  A linear material model can provide valid data at low strains, and predict the onset of yield. On the other hand a plastic material model, can predict onset of fracture. Once these limits are exceeded, the correlation between stresses and strains become complex and need to be better defined.

Geometric Nonlinearity  

Geometric nonlinearity becomes a concern when parts deform so much that initial model assumptions are no longer valid.  The areas where these assumptions no longer count or are invalid are

• Stress Stiffening / Softening: When loads add to the strength of a component stress stiffening is observed in the plane on which loads are applied.  Similarly when loads reduce the strength of a component stress softening is observed.  For example: blades of a fan under constant angular velocity will experience an outward centripetal force. This force will add to the strength (stress stiffening) of the fan.
• Snap -  Thru
• Buckling
• Large Strain

Boundary Nonlinearity

A model exhibits boundary nonlinearity when the loads, restraints or load path change throughout the course of the solution. Common examples of such cases are Contact analysis or Follower force.