Learning Forum

[sumukhsai.peddada]

Hey,nSo I have been using Ansys for a while and I feel I am able to understand and use It fluently.nBut I always have a doubt regarding discretization and Interpolation .nI would like to clear that off before I start working on something big.nnLets Say Structures for example - Whats ansys does is :nWe choose the mathematical model and it's respective governing equationsnThen we apply the weighted function for piece wise polynomial approximation- to make it simplen (Differential equations to linear)nThen define a equation for a node- Which is discretization.nThen we obtain the equations for the other nodes using interpolation.nThen set the boundary conditionsnAfter which we obtain a system of linear equations and solve them.nAfter which any other variable can be found .nnIf non-linearnWe apply guess values , imbalance reduction and so on.nnI know this is a bit lengthy , nBut please correct me , please , nIf I made a mistake while stating the solving steps of ANSYS. nThank You Very Much !

[peteroznewman]

Three types of software are used when doing FEA: Meshing/Pre-processing, Solving and Post-processing.nMeshing 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.nPre-processing allows us to define materials and boundary conditions on the geometry or directly on the nodes.nThe pre-processor writes out an input text file for the solver to read.nThe solver constructs the matrices then solves them and writes an output file with the nodal results and a few discrete points inside each element.nPost-processing allows us to plot the deformation and stress results to visualize the solution. The post-processor 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 post-processor also does averaging of stress extrapolated out to the nodes.n

[sumukhsai.peddada]

Thanks Mr.PeternSo we obtain the nodal equations using interpolation.nUse these set of equations and change it to a matrix.nThen after solving it.nWe obtain the nodal values throughout the surface or 3D model.nAnd once we know those values , we can compute any variable and interpolate to find it at any location right ?n

[peteroznewman]

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}.nSolving 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.nx 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.n

[sumukhsai.peddada]

Thank you ,nI get it now nBasically the {x} matrix consists of all the nodal displacement equations .nUpon solving that matrix , we obtain those nodal values nSo it allows us to calculate any variable such as stress , strain deformations , etcn

[peteroznewman]

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