Finite element method - tutorial no. 1

Size: px

Start display at page:

Download "Finite element method - tutorial no. 1"

Roderick Hudson
5 years ago
Views:

1 Martin NESLÁDEK Faculty of mechanical engineering, CTU in Prague 11th October / 22

2 Introduction to the tutorials Room no. 622 (6th floor - Dept. of mechanics, biomechanics and mechatronics) Consultations: every Wednesday at 12:30-14:00 Tutorials on FEM I. course: Wednesdays in odd weeks 16:00-17:30 in room no. 405b Lectures on FEM I. course: every Thursday 12:30-14:45 in room no. 259 (Mr. Novotný) 2 / 22

3 Introduction to the tutorials Topics of the tutorials: 1 Introduction to practical applications of the FEM - basic terminology, introduction to ABAQUS software (2 3 lessons) 2 Minimum total potential energy principle (2 lessons) 3 Application of the basic principles of the FEM to simple problems on mechanical response of bars and trusses (2 lessons) 3 / 22

4 Finite element method FEM is a numerical method for solving the partial differential equations (and their systems) on an arbitrary domain By using FEM we are able to solve: Mechanical response of solids - analysis of stress and strain fields of a single part or assembly Heat transfer - calculation of the temperature field Fluid flow - analysis of velocity and pressure fields Fluid-structure interaction... 4 / 22

5 Finite element method / 22

Finite element method http://www.tuvnel.

6 Finite element method solutions finite element analysis 6 / 22

7 Finite element method 7 / 22

8 Finite element method We restrict the FEM I. course to the problems of static mechanical response of solids 8 / 22

9 Simulation procedure by using a FEM-based software 9 / 22

10 Preparation of an FE model 10 / 22

11 Preparation of an FE model F 1 static response of a flexible body? F 2 dσ ij dx j + f i = 0 ε ij = 1 2 ( dui dx j + du ) j dx i σ ij = C ijkl ε kl + boundary cond s 11 / 22

12 Preparation of an FE model CAD model 11 / 22

13 Preparation of an FE model CAD model discretization 11 / 22

14 Preparation of an FE model CAD model discretization nodes 11 / 22

15 Preparation of an FE model elements CAD model discretization nodes 11 / 22

16 Preparation of an FE model F x F y elements F y F x CAD model discretization y x u x = u y = 0 nodes boundary conditions 11 / 22

17 Preparation of an FE model y x F x F y u x = u y = 0 elements nodes boundary conditions F y F x node represents a material point of the body; equations of equilibrium of internal and external forces are assembled and solved in nodes element represents a volumetric subdomain of the body; topology of the elements is given by nodes; many types, regarding the topology, idealization of geometry (continuum el., shells, beams, truss) and physical nature of the problem, exist elements and nodes together form the finite element mesh boundary conditions the kinematic and external load conditions 12 / 22

18 Preparation of an FE model To simulate the material response as real as possible, a proper material model is needed: σ ϕ E = tg(ϕ) ν = ε y ε x ε 13 / 22

19 Preparation of an FE model Basic pre-processing procedure: 1 Create or import CAD geometry of the analysed parts 2 Define and assign material properties to the parts 3 Define the load cycle time distribution (load steps and incrementation) 4 Create assembly from parts 5 Define constraints between parts, loads and kinematic BCs 6 Build the model mesh 14 / 22

20 Preparation of an FE model 15 / 22

21 Preparation of an FE model 16 / 22

22 Solution 17 / 22

23 Solution Solver generates and solves the system of linear algebraic equations Ku = f based on the parameters of the model. K the global stiffness matrix u the global vector of nodal displacements f the global vector of external equivalent nodal forces Displacements are solved primarily u = K 1 f and the other variables are derived from them. 18 / 22

24 Solution 19 / 22

25 Visualization of analysis results 20 / 22

26 Visualization of analysis results 21 / 22

27 Installation of Abaqus Installation files can be downloaded from the website (use the CTU login and password), then switch to software/abaqus directory Abaqus 6.14 is preferable to ensure compatibility with the version installed in the school computer rooms For further instructions on Abaqus installation refer to website 22 / 22

ME 345: Modeling & Simulation. Introduction to Finite Element Method

ME 345: Modeling & Simulation. Introduction to Finite Element Method ME 345: Modeling & Simulation Introduction to Finite Element Method Examples Aircraft 2D plate Crashworthiness 2 Human Heart Gears Structure Human Spine 3 F.T. Fisher, PhD Dissertation, 2002 Fluid Flow