Finite Element Methods — Winter 2023

Differentiate between Plane stress and plane strain.

What do you understand by Discretization? What are the factors to be considered for discrediting the domain?

Explain general steps of the Finite element method in detail

State various application of FEM in different field of Engineering.

What are the convergence requirements?

Give the derivation of the stiffness matrix for a bar element in local coordinate.

Explain the Galerkin’s residual method and its use to derive the one dimensional bar element equations.

Explain Different types of elements used in FEA.

Explain in brief: CST & LST

Classify the different boundary condition & explain it in detail.

Explain symmetric banded matrices and skyline matrices.

Explain the properties of stiffness matrices.

Illustrate the Plane Frames element with neat sketch indicating degree of freedoms. How it is differed from beam element. Write element stiffness matrix K ,transformation matrix Land load vector F.

Enlist three examples of practical application of axisymmetric element.

What are the conditions necessary to be followed for considering a problem as axisymmetric?

Give potential energy approach to derive beam element equation

What are the ways through which 3D problems can be reduced to a 2D approach?

Aconstant stain triangular element is defined by three nodes 1(1.5,2),2(7,3.5) and 3(4,7).Evaluate the shape functions N1,N2, and N3 at the interior point P (3.85,4.8).

Give the derivation of the linear strain triangular element stiffness matrix and equation.

Explain the different types of nonlinearity.

Define Isoparametric element.

Establish the shape functions and derive the strain displacement matrix for axisymmetric triangular element.1

Differentiate between Spring, Bar and beam elements from general and application point of view.

Explain Evaluation of eigenvalues in dynamic consideration.

Write short note on FEM convergence requirements.