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STRUCTURAL
ANALYSIS
FINITE ELEMENT
The Finite element approach:
I is actually a numerical method for solving differential equations generated by
theories of mechanics such as elasticity theory and strength of materials.

depends heavily on the processing power of computers and is more applicable
to structures of arbitrary size and complexity.
an assembly of elements or components with various forms of connection
between them.
Thus, a continuous system such as a plate or shell is modeled as a discrete
system with a finite number of elements interconnected at finite number of nodes.
The behaviour of individual elements is characterised by the element's
stiffness or flexibility relation, which altogether leads to the system's stiffness
or flexibility relation.
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we can use the mechanics of
materials approach for simple
one-dimensional bar elements,
and the elasticity approach for
more complex two- and three-
dimensional elements.
Forms element
two-dimensional:
Three-dimensional:
prismatic elements:
one-dimensional
tetrahedral element:

most elements quadratic element cubic element




most elements quadratic element cubic element




most elements quadratic element cubic element


most elements quadratic element cubic element
A program including:
Read input data:
-mechanical parameters of materials
-the geometric parameters of the structure
-network parameters conditions
-load effects
-pairing information elements
-boundary conditions
information element stiffness matrix K
information element node force vector F
determine the stiffness matrix K & vector force F
impose boundary conditions
(transformation matrix vector K & F)
solve simultaneous equations KQ = F

(determining the overall node displacement vector Q)
calculation of other quantities
(calculation of stresses, deformation, strength test, etc.)
results in:
-in the results
- Drawing diagrams, graphs