Nonlinear Geometric Transformation: Analysis and Approximations

This lecture covers the nonlinear geometric transformation in structural engineering, focusing on the consistent definition of axial deformation and rotation approximations. It explains the differences between linear and nonlinear approximations, emphasizing the importance of accurate integration methods like Gauss quadrature. The lecture also delves into the P-A (or P-Delta) approximation and the linear approximation of displacement-deformation relations. Practical examples of truss and beam elements with uniform and non-uniform cross-sections are provided, showcasing the application of numerical integration techniques. The content highlights the significance of minimizing errors in integration for precise structural analysis.