Finite Element Method (ME-504 (C)) - Important Questions

Discuss the steps involved in the finite element formulation of a physical system and its major advantages and limitations.

Discuss the principle of minimum potential energy, the meaning of displacement function, and define geometric invariance.

Describe the use of skeletal and continuum structures in the Finite Element Method.

Describe the Galerkin approach and its use in FEM analysis, and explain the features of Hermitian interpolation function with an example.

What is the difference between the finite element method and the classical method? Write the element stiffness matrix for the 2D beam element.

Derive the shape functions for a 4-node rectangular element using the Lagrange method.

What is the stiffness matrix? Write the stiffness matrix for the beam element.

Describe 2D rectangular and triangular elements in finite element problem formulation.

For a steel rod in compression modeled by two bar elements, determine the nodal displacements and the axial stress in each element and state what other concern should be examined.

Differentiate between local coordinates, global coordinates and natural coordinates in the Finite Element Method (FEM).

Derive the Jacobian for a four-node rectangular element with coordinates (0,0), (4,0), (4,2) and (0,2).

Derive the isoparametric representation for Constant Strain Triangle (CST) element modeling.

Discuss the errors involved in finite element solution with example of a model second-order differential equation in one dimension.

Write a detailed note on Derivation of mass matrices for 1D elements with the help of a related examples.

A composite plane wall consists of three materials with conduction and convective coefficient given as $(k_1, k_2, k_3)$ and $(h_1, h_2, h_3)$ with cross sectional area 'A' each. Find the effective resistance with an analogy to thermal circuit. Develop global matrix for temperature change from $400^{\circ}C$ to $100^{\circ}C$ from one side of wall to other side.

State Kirchhoff's theory and Mindlin theory for plate bending problem. Using four corner nodes plate, explain displacement, rotation, strain force and moments for both.