 To Linear or to Non-Linear: Which analysis type is suitable for you?
• # To Linear or to Non-Linear: Which analysis type is suitable for you?

When it comes to graduating from a Linear analysis to a Non-Linear analysis, the 3 deciding factors that decide that an analysis is a Non-Linear analysis is:

1. Material Non-Linearities

A. Materials with nonlinear material properties, such as alloys, elastomers, rubbers,         plastics etc.
B. Parts designed to yield and flow in the plasticity region (where the user must use a     model capable of simulating elastoplasticity. 2. Geometric Non-Linearities

B. Large or permanent deformations
C. Stiffness of the structure decreases due to local buckling 3. Boundary Non-Linearities

This class of non-linear behaviour is a result of the changing nature of the boundary           conditions (kinematic/force) of the structures involved in the analysis during motion:

A. Contact Problems
B. Pounding of Structures
C. Fitting Problems
D. Gear-tooth contacts

As such, a non-linear problem cannot be simulated mathematically as a system of linear equations. It can only be formulated as a system of non-linear equations that does not necessarily have a unique solution or even a solution at all.

The solution of non-linear problems requires incremental (step-by-step) techniques and, often, iterations within each increment (step) to ensure equilibrium at the end of each increment (step). This additional control is also available in Non-Linear solvers.

With SOLIDWORKS Simulation Premium, you would be able to tackle all the three factors through its non-linear offerings. For the instance of material non-linearities, it is able to provide the following model calculations for:

1. Elastic Models – which consists of:

A. Linear Elastic
B. Non-Linear Elastic (whereby the stress-strain curve is not defined by a single     Young’s Modulus value but a set of values)
C. Hyper Elastic model, which consists of:

i.   Mooney – Rivlin (examples are compressible rubbers)
ii.  Ogden Model (examples are incompressible rubbers)
iii. Blatz-Ko (for compressible hyper-elastic materials like foam)

2. Plastic Models

This model represents a combination of linear and non-linear range, such as metal being pushed beyond the yield strength, and then being relaxed later, whereby it unloads in a different curve (showing signs of permanent deformations) The Elasto-Plastic models which are included in SOLIDWORKS Simulation Premium are such as:

A. Von Mises
B. Tresca
C. Drucker-Prager (more to simulating behaviour of granular soil materials)

3. Super Elastic Nitinol Model

These materials are a unique class of materials known as shape memory alloys

4. Linear Visco-Elastic Model
5. Creep

When it comes to Geometric Non-Linearities, users are able to tackle these issues with contact control options so as to define how changing contacts interact throughout the analysis. Accuracy is greatly improved with the ability to define the study more concisely to reflect actual operations in real-life.

To get an understanding on how small step increment is important, check out this video:

If you are using the Linear-Static analysis and would like to know how to upgrade your system to a Non-Linear analysis solver, feel free to contact us at +65 6372 1416 or email support@seacadtech.com.