Jacobian in FEA
In the Finite Element Method, an element's Jacobian Matrix relates the quantities wrote in the natural coordinate space and the real space. The bigger the element is distorted in comparison…
What is the difference between serendipity family elements and isoparametric elements in finite element analysis?
In the Finite Element Method we use several types of elements. These elements can be classified based upon the dimensionality ( ID, II D and III D Elements) or on…
Springs and Elements
We already discussed, that “spring equations” are “coupled”. You can’t simply say that a single “spring equation” describes the force/displacement relation between 2 nodes. Take a look at this drawing:…
What are Nodes and Elements in Finite Element Analysis?
Nodes and Elements are the very backbones of Finite Element Analysis. You will use them in every analysis you will perform in FEA, so learning about them seems like a…
Isoparametric Elements
As mentioned above, to form a mesh over a general region the elements must be allowed to take more general shapes. This is done by using the parent elements and…
Lagrange Interpolation Method:
In FEM, Lagrange interpolation method is used for the polynomial interpolation. The formula was named after Joseph Louis Lagrange who published it in 1795, though it was first published by…
Natural Coordinates
Natural coordinate system is basically a local coordinate system which allows the specification of a point within the element by a set of dimensionless numbers whose magnitude never exceeds unity.…
Shape Function
The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned,…
Completeness
The elements must have enough approximation power to capture the analytical solution in the limit of a mesh refinement process. The element shape functions must represent exactly all polynomial terms…
