NOC:Variational Methods in Mechanics


Lecture 1 - Classification of optimization problems and the place of Calculus of Variations in it - Part I


Lecture 2 - Classification of optimization problems and the place of Calculus of Variations in it - Part II


Lecture 3 - Genesis of Calculus of Variations - Part I


Lecture 4 - Genesis of Calculus of Variations - Part II


Lecture 5 - Formulation of Calculus of Variations problems in geometry and mechanics and design - Part I


Lecture 6 - Formulation of Calculus of Variations problems in geometry and mechanics and design - Part II


Lecture 7 - Unconstrained minimization in one and many variables - Part I


Lecture 8 - Unconstrained minimization in one and many variables - Part II


Lecture 9 - Constrained minimization KKT conditions - Part I


Lecture 10 - Constrained minimization KKT conditions - Part II


Lecture 11 - Sufficient conditions for constrained minimization - Part I


Lecture 12 - Sufficient conditions for constrained minimization - Part II


Lecture 13 - Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces - Part I


Lecture 14 - Mathematical preliminaries function, functional, metrics and metric space, norm and vector spaces - Part II


Lecture 15 - Function spaces and Gateaux variation


Lecture 16 - First variation of a functional Freche?t differential and variational derivative


Lecture 17 - Fundamental lemma of calculus of variations and Euler Lagrange equations - Part I


Lecture 18 - Fundamental lemma of calculus of variations and Euler Lagrange equations - Part II


Lecture 19 - Extension of Euler-Lagrange equations to multiple derivatives


Lecture 20 - Extension of Euler-Lagrange equations to multiple functions in a functional


Lecture 21 - Global Constraints in calculus of variations - Part I


Lecture 22 - Global Constraints in calculus of variations - Part II


Lecture 23 - Local (finite subsidiary) constrains in calculus of variations - Part I


Lecture 24 - Local (finite subsidiary) constrains in calculus of variations - Part II


Lecture 25 - Size optimization of a bar for maximum stiffness for given volume - Part I


Lecture 26 - Size optimization of a bar for maximum stiffness for given volume - Part II


Lecture 27 - Size optimization of a bar for maximum stiffness for given volume - Part III


Lecture 28 - Calculus of variations in functionals involving two and three independent variables - Part I


Lecture 29 - Calculus of variations in functionals involving two and three independent variables - Part II


Lecture 30 - General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions - Part I


Lecture 31 - General variation of a functional, transversality conditions. Broken extremals, Wierstrass-Erdmann corner conditions - Part II


Lecture 32 - Variational (energy) methods in statics; principles of minimum potential energy and virtual work


Lecture 33 - General framework of optimal structural designs - Part I


Lecture 34 - General framework of optimal structural designs - Part II


Lecture 35 - Optimal structural design of bars and beams using the optimality criteria method


Lecture 36 - Invariants of Euler-Lagrange equations and canonical forms


Lecture 37 - NoetherÂ’s theorem


Lecture 38 - Minimum characterization of Sturm-Liouville problems


Lecture 39 - Rayleigh quotient for natural frequencies and mode shapes of elastic systems


Lecture 40 - Stability analysis and buckling using calculus of variations


Lecture 41 - Strongest (most stable) column


Lecture 42 - Dynamic compliance optimization


Lecture 43 - Electro-thermal-elastic structural optimization


Lecture 44 - Formulating the extremization problem starting from the differential equation, self-adjointness of the differential operator, and methods to deal with conservative and dissipative system