Define the term finite element. What does discretization mean in the finite elem

Question

Define the term finite element. What does discretization mean in the finite element method? Define the term matrix. List and briefly describe the general steps of the finite element method. What is the displacement method? List four common types of finite elements. Name three commonly used methods for deriving the element stiffness matrix and element equations. Briefly describe each method. To what does the term degrees of freedom refer? List five typical areas of engineering where the finite element method is applied. List five advantages of the finite element method.

Explanation / Answer

1. Finite element term is coined by Clough in 1960. It indicates the smallest element considered to perform analysis to find the solution.

2. Discretization is the process of dividing the structure or object into tiny elements for analysis purpose and detailed analysis.

3. Matrix: In fem we represent the forces and stiffnesses in the form of matrices. Depending on the position in the Matrix each term has a significance with respect to the element and nodes considered.

4. General steps used in Fem:

1. Discretization: Dividing the element into small finite element with nodes.

2.Element analysis: expressing the displacement and then maintaining equilibrium relations.

3. Formulation: writing the corresponding local stiffness matrices and then finding the global stiffness Matrix and substituting into corresponding equilibrium relations.

4. Boundary conditions: apply corresponding boundary conditions like fixed support, no heat transfer etc.,

5. Obtaining global displacement or temperatures

6calculating the stresses or heat flux.

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