JNTU B.Tech III FINITE ELEMENT TECHNIQUES Previous Question Paper (August - 2022 - R16)

For a two-element bar system, the stiffness matrix for each element is given by k = (AE/L). Assuming element 1 has length L1 and element 2 has length L2, the global stiffness matrix K is assembled as:

Given A1 = 200 mm² and A2 = 100 mm², and E = 2 × 10⁵ N/mm², the equilibrium equation is {F} = [K]{u}. Applying the boundary condition u1 = 0 (fixed end), the system reduces to a 2x2 matrix equation. By substituting the specific lengths and nodal forces into the matrix, the nodal displacements u2 and u3 are solved using Cramer's rule or Gaussian elimination based on the applied load of 100N.

Advantages: FEM can handle complex geometries, non-homogeneous materials, and various boundary conditions. It is highly versatile for different physical problems like heat transfer, fluid flow, and structural analysis.

Limitations: It requires significant computational resources for large models, is sensitive to mesh quality, and results are approximate, depending heavily on the choice of element type and discretization.

Applications: Used extensively in automotive and aerospace structural design, stress analysis of pressure vessels, biomechanical modeling, and thermal analysis of electronic components.