Lectures related to Calculus of Variation and Euler's Elastica

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

Calculus of Variations and Euler's Elastica

Explores variational methods, Euler's Elastica, numerical and analytical methods, and the buckling of slender structures.

Calculus of Variations: Euler's Elastica

Covers Euler's Elastica and the equilibrium shape of a bent beam using variational/energy methods.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Calculus of Variations and Euler's Elastica

Explores the calculus of variations and Euler's Elastica in the context of beam equilibrium and inextensible elastic curves under large rotations.

Optimization with Constraints: Theory and Applications

Covers the theory and applications of optimization with constraints, including key concepts and numerical methods.

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Molecular dynamics under constraints

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Elasto-gravitary Bending: Mechanics of Slender Structure

Explores large deformations of inextensible sheets bent under self-weight and their equilibrium shapes under gravity.

Mechanics of Slender Structure: Naturally Curly Hair in 3D

Delves into the mechanics of slender structures using naturally curly hair in 3D as an example.

Mechanics of Slender Structures: Elasticity & Buckling

Explores 3D elasticity, beam bending, and buckling phenomena in slender structures.

Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

Discusses numerical methods, focusing on stopping criteria, SciPy for optimization, and data visualization with Matplotlib.

Numerical Methods: ODE RK Schemes

Covers ODE RK schemes, including explicit RK stages and accuracy computation.

Euler-Lagrange Equation: Convexity and Saddle Point Problems

Explores the Euler-Lagrange equation, convexity, and saddle point problems in variational calculus.

Optimization: Lagrange Multipliers

Covers the method of Lagrange multipliers to find extrema subject to constraints.

Nonlinear Geometric Transformation: Analysis and Approximations

Explores nonlinear geometric transformations in structural engineering, emphasizing accurate integration methods and practical applications.

Optimal Control: OCPs

Covers Optimal Control Problems focusing on necessary conditions, existence of optimal controls, and numerical solutions.

Introduction to Structural Mechanics

Covers beams with distributed and concentrated forces, bending moment, shear force, and internal load diagrams.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.