Description

Theory
1

Laboratory
2

Instructors

Jorge Belinha

Contents

(CP1)-Cartesian tensor calculus. Introduction to Matlab programming.
(CP2)-Theory of computational elasticity. Stress and strain state in tensor notation. Particular states of stress and strain. Generalized Hooke's Law. Principle of virtual work. Fracture, yield and damage criteria.
(CP3)-Finite element method. Isoparametric and Cartesian numerical integration. Jacobian matrix. One-, two- and three-dimensional shape functions. Linear and quadratic finite elements. Interpolation of the displacement field, and calculation of the strain and stress fields. Discrete system of equations. Imposition of essential and natural boundary conditions. Pre- and post-processing.
(CP4)-Nonlinear analysis. Newton-Raphson method and variants. Material non-linearity (plasticity, hyperelasticity and damage). Geometric nonlinearity (large deformations, topological structural optimization and fracture mechanics).
(CP5)-Advanced numerical techniques. Meshless methods.

Learning Outcomes

The student after attending this UC will be able to:
OB1-Operate Cartesian tensors calculus with programming using Matlab language. Identify the advantages and disadvantages of using Matlab as a finite element programming tool.
OB2-Apply the theory of computational elasticity. Develop code capable of calculating stress and strain states (main stress and strain, hydrostatic, deflection and octahedral stress state) and yield, damage and fracture limit states.
OB3-Employ the detailed knowledge of the finite element method to produce autonomously codes with linear formulations and identify their limitations.
OB4-Employ the advanced theoretical knowledge to produce practical computational tools by writing non-linear finite element codes. Apply the developed codes to advanced practical problems in automotive engineering involving material and geometric nonlinearity.
OB5-Identify other advanced discretization techniques, such as meshless methods.