General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.

1. General Steps of the
Finite Element Method

2. Step 1: Discretize and Select Element Types
Step 1 involves dividing the body into a finite elements with associated
nodes and choosing the most appropriate element type for the model.
(In this step the geometry is divided in a no. of parts and parts are
known as element. And Elements are interconnected at points called as
Nodes.)
The Process of dividing the geometry into finite no. of elements is
known as discretization.
Element Types:
1D : Bar, Beam, Pipe, Spar (web)
2D: Triangular, Quadrilateral
3D: Tetrahedron, Hexahedron (Brick Element) 2
Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

3. 3
Step 1:
Contd..
Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

4. Additional Knowledge
of Elements
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

5. Step 2: Identify
Primary
Unknown
Quantity
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

6. Step 3: Select a Proper interpolation or
displacement model
Since the displacement solution of a complex structure under any
specified load conditions cannot be predicted exactly, we assume
some suitable solution within an element to approximate the
unknown solution. The assumed solution must be simple from a
computational standpoint, but it should satisfy certain
convergence requirements. In general, the solution or the
interpolation model is taken in the form of a polynomial.
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

7. Step 4: Derive the Element Stiffness Matrix and
Equations
On FEA it is necessary to find out primary unknown at nodal points (nodes)
and this can be done by establishing equation in terms of primary unknown.
From the assumed displacement model, the stiffness matrix and load vector
of element are to be derived by using following method
1. Direct Equilibrium Method (used for 1D Problems)
2. Work Energy Method (Used for 2D and 3D Problems)
3. Method of Weighted Residual. (Used for 1D Problems)
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

8. Step 5: Derive overall Stiffness Equation
(Assemble the Equation)
• The individual element equations generated in step 4 can now be added together using a
method of superposition (called the direct stiffness method).
• This step assembles all individual element equations derived in Step 4 to provide the
“Stiffness equations” for the entire medium.
• Mathematically, this equation has the form:
{F} = [K] {U}
Where,
{F} = Vector of global nodal forces
[K] = Stiffness matrix
{U} = Primary Unknown
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

9. Step 6: Solve Primary Unknowns
{F} = [K] {U}
After introducing Boundary Conditions and Forces, Primary
Unknown (like Displacement) can be solved by using Gaussian
Elimination method or inverse matrix method.
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

10. Step 7 Solve for secondary unknowns
For the structural stress-analysis problem, important
secondary quantities of strain and stress (or moment and
shear force) can be obtained because they can be directly
expressed in terms of the displacements determined in
step 6.
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

11. Step 8 Display and Interpretation of Results
The final goal is to interpret and analyze the results for use in the
design/analysis process. Determination of locations in the
structure where large deformations and large stresses occur is
generally important in making design/analysis decisions.
Postprocessor computer programs help the user to interpret the
results by displaying them in graphical form.
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)

12. Keep in mind that the analyst must make decisions regarding dividing
the structure or continuum into finite elements and selecting the
element type or types to be used in the analysis (step 1), the kinds of
loads to be applied, and the types of boundary conditions or supports
to be applied. The other steps, 2 through 7, are carried out
automatically by a computer program.
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Mr. Mahesh Gaikwad (Mechanical Department SGGSIE&T
Nanded)