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Detailing the Enumerating Steps taken in FEA Procedure inside Software

Finite element analysis (FEA) involves solution of engineering problems using computers. Engineering structures that have complex geometry and loads, are either very difficult to analyze or have no theoretical solution. However, in FEA, a structure of this type can be easily analyzed. Commercial FEA programs are written so that a user can solve complex engineering problems without knowing the governing equations or the mathematics; the user is required only to know the geometry of the structure and its boundary conditions. FEA software provides a complete solution including deflections, stresses, reactions, etc.

In order to become a skillful FEA user, a thorough understanding of techniques for modeling a structure, the boundary conditions and, the limitations of the procedure, are very crucial. Engineering structures, e.g., bridge, aircraft wing, high-rise buildings, etc., are examples of complex structures that are extremely difficult to analyze by classical theory. But FEA technique facilitates an easier and a more accurate analysis. In this technique the structure is divided into very small but finite size elements (hence the name finite element analysis). Individual behavior of these elements is known and, based on this knowledge; behavior of the entire structure is determined.

Let us now look at the steps taken in FEA procedure inside the software:

  • Using the user's input, the given structure is graphically divided into small elements (sections or regions) so that each and every element's mechanical behavior can be defined by a set of differential equations.
  • The differential equations are converted into algebraic equation, and then into matrix equations, suitable for a computer-aided solution.
  • The element equations are combined and a global structural equation is obtained.
  • Appropriate load and boundary conditions, supplied by the user, are incorporated into the structural matrix.
  • The structural matrix is solved and deflections of all nodes are calculated
  • A node can be shared by several elements and the deflection at the shared node represents deflection of the sharing elements at the location of the node
  • Deflection at any other point in the element is calculated by interpolation of all node points in the element
  • An element can have a linear or higher order interpolation function
  • The individual element matrix equations are assembled into a combined structure equation of the form {F}=[k]{u}.

Where, {F} = Column matrix of the externally applied loads. [k]= Stiffness matrix of the structure, which is always a symmetric matrix. This matrix is analogues to an equivalent spring constant of several connected springs. {u} = Column matrix representing the deflection of all the node points, that results when the load {F} is applied.

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