# Finite Element Analysis of Structures

## Course Description:

The aim of the course is to provide students with a thorough understanding of the fundamental concepts and principles of finite element analysis with a focus on linear elasto-statics. Furthermore, the course provides an introduction on the programming aspects of the method through hands-on programming workshops. Simulation strategies and the implementation of the method on real-life applications are also discussed.

### Prerequisite Knowledge

Knowledge of Mechanics, Structural analysis, Earthquake resistant design, Structures from reinforced concrete and steel

### Course Units

# Title Description Hours
1 Introduction Weak formulation, Principle of minimum total potential energy, FEM discretization, the Galerkin method, strain displacement matrix, stiffness matrix and equivalent load vector 2
2 Uniaxial elements Two and three node truss elements, 2D beam elements, transformation matrices, equivalent loads and boundary conditions 2
3 2D Elasticity Constant Strain Triangle, quadrilateral plane stress/ strain elements, Lagrange and higher order shape functions, Serendipity elements, quadrature rules 4
4 3D Elasticity Tetrahedral and hex elements, linear and higher order shape functions, Lagrange and Serendipity elements 3
5 Isoparametric formulation General description of the isoparametric mapping, Cartesian and natural coordinate systems, isoparametric truss, plane stress and hex element, higher order elements, Numerical quadrature 7
6 Plate Elements Introduction to Plate theories. Kirchhoff Love Plate Element 7
7 Simulation of structures Best practices, error estimation and stress recovery, mesh additivity, kinematic constraints, Connection of different types of elements. Rigid offsets and diaphragms. 2
8 Programming workshops Introduction to the use of finite element programs - troubleshooting. Simulation strategies, implementation on real-life applications. Connection of different types of elements. Rigid offsets and diaphragms. 12

### Learning Objectives

• To develop an understanding of the basic principles of FEM as a method of solving systems of differential equations and its specialization in problems of simulation of mechanical systems and structures.

• To become familiarized with rules of simulation and use of computer tools (commercial programs and source codes).

### Teaching Methods

 Teaching methods Teaching theory and its application with exercises - examples Auxiliary use of slides and other supervisory tools Development of source code for basic solution of quadrilateral elements in Matlab environment. Simulation of constructions with finite elements. Evaluation of results. Software Troubleshooting (MSolve, Abaqus) Series of simple application exercises prepared by students Simulation of constructions with finite elements. Evaluation of results Presentation of the topic by groups of students

### Student Assessment

• Final written exam: 50%
• Assignments (projects, reports): 50%

### Textbooks - Bibliography

Textbooks, Lecture notes on theory and solved examples

## Lecture Time - Place:

• Tuesday, 10:45 – 12:30,
Rooms:
• Ζ. Κτ. 1 Πολ., Αιθ. 4
• Thursday, 09:45 – 11:30,
Rooms:
• Ζ. Κτ. 1 Πολ., Αιθ. 4

© 2017 School of Civil Engineering, ΕΜΠ