## LINEAR STATIC ANALYSIS.

What is linear static analysis and a quick demonstration in SolidWorks.

First let’s understand how SolidWorks understands the effects of forces applied in real-world.

Real-World forces, for example heat, Flow of Fluid, and other physical effects are taken into consideration.

There is a computerized method to solve such problems, predicting how our fabricated part will react to real world forces.

This method is known as Finite-element-method.

This method shows whether the fabricated part will bend, break away, or work exactly as it was supposed to, when the above defined forces are applied on it.

LINEAR FINITE ELEMENT ANALYSIS

Finite element analysis is based on principle that a body’s geometry is divided into a set of finite elements then partial equations based on boundary conditions are solved to get various parameters.

We are splitting the model down into finite number of elements from there, we are calculating the displacements that are applied because of the action of various forces.

To understand this better, let’s take a path:

Next, we will divide this path into elements.

Let’s call these points as nodes. We will join these nodes together:

So these elements will move when we will apply forces at different points, and the forces will be measured by calculating the displacement of these elements before and after the application of forces.

The difference between the points before and after the application of force is strain then this strain can be used to work out the young’s modulus.

This is a mathematical concept, this method is used in SolidWorks to check whether the designed model will work exactly as it is supposed to, when real-World forces are applied to it.

Let’s discuss linear static.

This is the universal equation of motion, [m] is the inertia matrix.

[C] is damping matrix
[K] is stiffness matrix

Assumptions in static study are:

Therefore inertia matrix and damping matrix coefficients get cancelled off because they are time dependent. That leaves us with [K]x=F(t).

Before you start static analysis just check:
Is the system dynamic?
Are dynamic loads are being applied slowly?

Let’s discuss the ‘linear’ part of linear static analysis

Linear means that the analysis complies with Hooke’s law (there is a linear relationship between applied loads and induced responses.

As shown in the graph, there is a point beyond which static analysis will be inaccurate, therefore if force displacement relation goes beyond this point, one should consider using non-linear analysis.

This assumes that we do not reach yield point of materials and that deflections are small such that stress stiffness/softening does not occur.

Let’s take an example of static analysis of a spanner just to understand the theoretical part of static linear simulation step by step example will be discussed later:

What we are going to do is load the model and then we will remove anything that is not important. Because when we run the study it will be easier.

Let’s create a flowchart representing the steps that we will perform:

Cad initial geometry -> idealization/Defeature/clean-up -> simplified model -> mathematical model (type of analysis-static/materials/loads/restraints) -> FEA model (meshing) -> FEA results.

In mathematical model we define the type of analysis in this case it is static because all forces applied are static in nature and dynamic forces are extremely slow we assume these as static.

Next, we define the material in mathematical model.

Different materials give different results so make sure that defined material is the same as fabricated material.

Then loads are given to the model. These are faces which will be under stress.

Restraints are given to faces which are obstructed to have any motion the play an important role in this study as if obstruction is present then force is applied to the object as well, as indicated by newton’s 3rd law of motion.

Blue arrows indicate forces applied whereas green arrows indicate restraints present.

Now we will divide this model into a finite no. of elements. This process is called meshing.

By doing that we can see that the model is broken down into very small elements as required by finite element analysis method.

Elements look like they are on the surface, but actually they go all the way through the surface.

As you can see there is a noticeable displacement. Different colors show different parameters.

In next tutorial we will take a step by step example to understand this type of simulation in SolidWorks.

Contact us for more information and help on linear static analysis and a quick demonstration in SolidWorks at support@nccs.com.au or call 03 86770871