1)Lagrange multiplier for friction When the force at the tip is P¼25 N, calculate the tip displacement of the beam and determine if a stick of slip occurs using the Lagrange multiplier method

1)Lagrange multiplier for friction When the force at the tip is P¼25 N, calculate the tip displacement of the beam and determine if a stick of slip occurs using the Lagrange multiplier method.

2)Penalty method for beam contact Using the potential energy and the penalty method, calculate the deflection curve for the cantilever beam example in Sect. 5.2.1 with different values of penalty parameter. Assume the following form of beam deflection curve v(x)=a₂x² + a₃x³ + a₄x⁴ and calculate unknown coefficients.