The main goal of this course is the introduction of the finite element method for the solution of frames, along with its Matlab implementation. Moreover, structural instability problems will be introduced and discussed as well.
The aim is to help students in developing the ability to build tools to analyze complex problems related to frames, which cannot be solved in an analytical way.
Course Prerequisites
Knowledge of Analytical Mechanics and of Mechanics of Solids and Structures. Matlab programming basics.
Teaching Methods
Blackboard lectures and Matlab-based tutorials.
Assessment Methods
Written examination consisting of exercises (programming) and theoretical questions.
Texts
- Course notes; - T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover. - Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek, Meccanica dei Solidi, 5ed, 2014, McGraw-Hill Education
Contents
1) Introduction to the finite element method: - basics of beam theory; - direct method for planar frames; - finite element method basics: a) axial problem; b) Euler-Bernoulli bending problem; c) Timoshenko bending problem; - finite element method implementation for planar frames; - shear locking problem: a) introduction; b) solution via under-integration and implementation.
2) Introduction to structural instability: - problem introduction; - instability of lumped elasticity systems; - numerical solution of nonlinear equations (Newton's method) and application to instability problems; - Euler's problem; - solution via the finite element method and implementation.
