This course covers the intricate concept of the calculus of variation and its application in structural mechanics. It begins with a generalization of the maximum or minimum problem of ordinary calculus, moving on to its application in determining the deformed shape of a system. The course introduces the Euler Lagrange equation as the governing differential equation and explains its use in extremizing a functional. The course also provides practical examples such as a simply supported beam with uniformly distributed load and a simply supported column subjected to axial loading. The course further delves into the Brachistochrone problem, a classic problem that led to the growth of calculus of variation.
This course has been developed by Prof. Sarat Kumar Panda from IIT-ISM for NPTEL. It is now accessible through Ansys Innovation Space courtesy of the partnership between Ansys and NPTEL, under the CC BY-SA license. For more details, visit https://nptel.ac.in/courses/105105217.
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Cost: FREE
- Course Duration: 4-6 HOURS
- Skill Level: Intermediate
- Skills Gained: Euler Lagrange Equation, Variational Method, Brachistochrone Problem, Rayleigh-Ritz Method
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