# Ansys Solcing Methods

Member
edited August 23

Hey,

So I have been using Ansys for a while and I feel I am able to understand and use It fluently.

But I always have a doubt regarding discretization and Interpolation .

I would like to clear that off before I start working on something big.

Lets Say Structures for example - Whats ansys does is :

We choose the mathematical model and it's respective governing equations

Then we apply the weighted function for piece wise polynomial approximation- to make it simple

(Differential equations to linear)

Then define a equation for a node- Which is discretization.

Then we obtain the equations for the other nodes using interpolation.

Then set the boundary conditions

After which we obtain a system of linear equations and solve them.

After which any other variable can be found .

If non-linear

We apply guess values , imbalance reduction and so on.

I know this is a bit lengthy ,

If I made a mistake while stating the solving steps of ANSYS.

Thank You Very Much !

• Member
edited August 29

Thanks Mr.Peter

So we obtain the nodal equations using interpolation.

Use these set of equations and change it to a matrix.

Then after solving it.

We obtain the nodal values throughout the surface or 3D model.

And once we know those values , we can compute any variable and interpolate to find it at any location right ?

• Member
edited August 30

The nodes are connected to elements. Elements define stiffness between nodes. The element stiffness values are assembled into a matrix [K] that has rows and columns. The unknown nodal displacements are assembled into a vector {x} and the applied forces are assembled into another vector {F}. The matrix equation is [K]{x} = {F}.

Solving the matrix calculates a solution for each unknown value of x. Once the post-processor knows the values of x at all the nodes, the element shape function allows it to interpolate the displacement of any point inside the element.

x means a displacement Degree of Freedom (DOF). A node might have 3 DOF, in the X, Y and Z directions so there are three cells in the {x} vector for each node.

• Member

Thank you ,

I get it now

Basically the {x} matrix consists of all the nodal displacement equations .

Upon solving that matrix , we obtain those nodal values

So it allows us to calculate any variable such as stress , strain deformations , etc

• Member
edited August 31

Exactly. Some textbooks call the displacement vector {U} to avoid using x which is a component on one nodal displacement.