c++ program and visual studio

this project has 8 steps of fem to solve the problem

The Finite Element Method

Generally, the FEM has eight steps:

1. Idealization

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!

2. Discretization

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

equations.

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

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Projekt ID: #13468334

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