Finite Element Method with Applications in Engineering

EXERCISE PROBLEMS

1. Using the direct approach, develop element stiffness matrix for a cantilever beam of length L subjected to a concentrated load W at the free end and find the expression for the deflection and slope at the free end.
2. Using FEM based on the variational approach develop element property matrix for the following differential equation. Use one-dimensional linear elements for discretization. ɸ″− ɸ = x² with boundary conditions ɸ(x = 0) = 0 and ɸ(x = 1) = 0.
3. Using FEM based on the weighted residual approach (Galerkin's method), develop element property matrix for the following differential equation. Use one-dimensional linear elements for discretization. in the range 0 ≤ x ≤ 1, with the boundary conditions y (x = 0) = 0 and y (x