Ansys Solcing Methods
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 nonlinear
We apply guess values , imbalance reduction and so on.
I know this is a bit lengthy ,
But please correct me , please ,
If I made a mistake while stating the solving steps of ANSYS.
Thank You Very Much !
Best Answer

peteroznewman Member
Three types of software are used when doing FEA: Meshing/Preprocessing, Solving and Postprocessing.
Meshing software performs the discretization. It takes solid or surface geometry and divides it into elements connected to nodes. The elements might be linear or quadratic, depending on the setting made by default or overridden by the user.
Preprocessing allows us to define materials and boundary conditions on the geometry or directly on the nodes.
The preprocessor writes out an input text file for the solver to read.
The solver constructs the matrices then solves them and writes an output file with the nodal results and a few discrete points inside each element.
Postprocessing allows us to plot the deformation and stress results to visualize the solution. The postprocessor uses interpolation to show results anywhere inside the elements since the solver only returned nodal values, and a few discrete points in the element. The interpolation will be linear for linear elements and quadratic for quadratic elements. The postprocessor also does averaging of stress extrapolated out to the nodes.
Answers
Three types of software are used when doing FEA: Meshing/Preprocessing, Solving and Postprocessing.
Meshing software performs the discretization. It takes solid or surface geometry and divides it into elements connected to nodes. The elements might be linear or quadratic, depending on the setting made by default or overridden by the user.
Preprocessing allows us to define materials and boundary conditions on the geometry or directly on the nodes.
The preprocessor writes out an input text file for the solver to read.
The solver constructs the matrices then solves them and writes an output file with the nodal results and a few discrete points inside each element.
Postprocessing allows us to plot the deformation and stress results to visualize the solution. The postprocessor uses interpolation to show results anywhere inside the elements since the solver only returned nodal values, and a few discrete points in the element. The interpolation will be linear for linear elements and quadratic for quadratic elements. The postprocessor also does averaging of stress extrapolated out to the nodes.
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 ?
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 postprocessor 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.
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
Exactly. Some textbooks call the displacement vector {U} to avoid using x which is a component on one nodal displacement.