this project has 8 steps of fem to solve the problem
The Finite Element Method
Generally, the FEM has eight steps:
The "real" problem is idealized by making assumptions to simplify the problem:
by reducing the dimensions (all real problems are 3D, but may be idealized with 1D,
2D or 3D models),
by idealizing the support conditions,
by suppressing details, such as small holes and fillets, that are insignificant from the
analysis point of view, but which complicate matters during mesh generation.
This step can be dramatically important if the assumptions are not correct!
The problem domain is discretized into a collection of simple shapes, or elements.
3. Choice of the type of element and compute the local stiffness matrices
1D: Truss, beam, frame, and in their higher orders;
2D: Triangular or quadrilateral (or other) elements and in their higher orders
3D: Tetrahedral or hexahedral (or other) elements and in their higher orders
The results can be very different from one type to another. This is due to the theory hidden
behind those elements. After that, compute all stiffness matrices for the discrete elements
(with isoparametric mapping).
4. Assembly of the discrete elements
The element equations for each element in the FEM mesh are assembled into a set of global
equations that model the properties of the entire system.
5. Application of boundary conditions
Solution cannot be obtained unless boundary conditions are applied. They reflect the known
values for certain primary unknowns. Imposing the boundary conditions modifies the global
6. Solve for primary unknowns
The modified global equations are solved for the primary unknowns at the nodes.
7. Calculate derived variables
Calculated using the nodal values of the primary variables