Finite Element Method with Applications in Engineering

EXERCISE PROBLEMS

1. Using the linear interpolation function for line element, find the value of the field variable ɸ and its first derivative at a place x = 0.8 given that x_i = 0, x_j = 5, ɸ_i = 2.5 and ɸ_j = 7.0.
2. Using the integration formula for linear type line element, evaluate
3. Temperature distribution in a steel plate is simulated using the linear type triangular element with the nodal co-ordinates of (x₁ = 1, y₁ = 1), (x₂ = 8, y₂ = 0.5) and (x₃ = 4, y₃ = 5). The nodal values of temperature {ɸ} at different nodes are {25, 27, 23}, respectively. Find the value of temperature ɸ at point (3.5, 3.5).
4. The triangular element is used for ground water ...