Deformation and Energy Formulation — Lesson 3

This lesson covers the concept of deformation and energy formulation in structural analysis. It begins with the evaluation of deformation by integral methods and then moves on to the differential equation of deformation. The lesson further explains the energy formulation approach to solving structural problems, highlighting its advantages over the force formulation approach. It also introduces the concept of energy formulation for static and dynamic problems. The lesson then delves into the principle of virtual work and how it is applied to get energy formulation. It also explains the concept of holonomic and non-holonomic constraints in the system. The lesson concludes with the application of these concepts in solving problems related to wing deformation and beam bending.

Video Highlights

03:48 - Introduction to the energy formulation as another approach to solving the structural problem.
5:26 - Discussion on the principle of minimum potential energy and the principle of virtual work.
14:09 - Discussion on the principle of virtual work for static equilibrium of the rigid body.
39:00 - Explanation of the Rayleigh-Ritz approach and the principle of virtual work applied to continuous systems.
68:03 - Discussion on the constraints in the system and the concept of holonomic and non-holonomic constraints.

Key Takeaways

- Deformation can be evaluated using integral methods and differential equations.
- Energy formulation is an approach to solving structural problems that deals with scalar quantities and is coordinate independent.
- The principle of virtual work is a fundamental concept in energy formulation.
- Holonomic and non-holonomic constraints play a crucial role in the system.
- The concepts of deformation and energy formulation can be applied to solve problems related to wing deformation and beam bending.