Finite element method - tutorial no. 1

Transcription

1 Martin NESLÁDEK Faculty of mechanical engineering, CTU in Prague 13th October / 17

2 Introduction to the tutorials Room no. 622 (6th floor - Dept. of mechanics, biomechanics and mechatronics) Consultations: every Tuesday at 10:45-12:15 Tutorials to the FEM I. course: every even week at 16:00-17:30 in room no. 405b Lectures to the FEM I. course: every Friday from 10:45 in lecture room no. 366 (Mr. Španiel) 2 / 17

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 / 17

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... We restrict the FEM I. course to problems of the mechanical response of solids 4 / 17

5 Simulation procedure by using a FEM-based software 5 / 17

6 Preparation of an FE model 6 / 17

7 Preparation of an FE model F 1 F 2 7 / 17

8 Preparation of an FE model F 1 CAD model F 2 discretization 7 / 17

9 Preparation of an FE model F 1 CAD model F 2 discretization nodes 7 / 17

10 Preparation of an FE model F 1 CAD model elements F 2 discretization nodes 7 / 17

11 Preparation of an FE model F 1 F 1 elements F 2 F2 discretization nodes boundary conditions 7 / 17

12 Preparation of an FE model F 1 elements nodes boundary conditions F2 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 8 / 17

13 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 9 / 17

14 Preparation of an FE model 10 / 17

15 Preparation of an FE model 11 / 17

16 Solution 12 / 17

17 Solution Solver generates and solves the system of linear 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. 13 / 17

18 Solution 14 / 17

19 Visualization of analysis results 15 / 17

20 Visaulization of analysis results 16 / 17

21 Installation of Abaqus Installation files can be downloaded from the website (use the same login as to the other school systems), then switch to software/abaqus directory At first, install the Abaqus documentation When installing the program, refer to elic.fsid.cvut.cz license server and port no Windows 8+ is compatible only with Abaqus versions 17 / 17