Introduction to virtual engineering

1. Budapest Tech John von Neumann Faculty of Informatics Institute of Intelligent Engineering Systems Introduction to virtual engineering Lecture 6. Modeling by finite elements for analysis of engineering objects Finite Element Modeling (FEM). Finite ElementAnalysis (FEA). Shape Optimalization László Horváth www.nik.hu

2. CONTENTS Definition Main features Analysis in model space Short story The FEM/FEA process Finite elements mesh Parameters to be calculated Finite elements Loads and boundary conditions Examples for analysis and visualization of results Optimizing shapes

3. Node Edge Definition Finite Element Modeling (FEM) creates special model forFinite Element Analysis (FEA) Reveals the impact of design variables on the design performance Calculation of location dependent parameters for rods, shells and volumes Analysis is done on a finite number of finite elements

4. Main features The FE analysis is a numerical method for the approximation by finite elements placed in mesh.The values of the analyzed parameters are calculated using mathematical equations built into FEA programs of defined by the users for FEA programs.The FE analysis is a simulation of behaviors of engineering objects.FE analysis is a general purpose problem solving method for arbitrarily complex shape. Any location dependent parameter can be calculated and any load or boundary condition can be considered.

5. An example for FEM/FEA Source: www.catia.com

6. Analysis in model space Source: www.catia.com

7. Short story First application: analysis of structural eleents of airplanes. First application of the phrase ”finite element analysis”: Clough, 1960. First book: Zienkiwiecz and Chung, 1967 End of the 60s: Nonlinear problem solving. Oden, 1972: First book about nonlinear problem solving. 70s: The mathematical basics were established. Recently: product modeling systems include or interfaced to FEM/FEA. FEM/FEA has become a fundamental method for analysis.

8. The FEM/FEA process Creating model for analysis (preprocessing) FEM Preparation of geometric Preparation of FEM model Convert model from Definition of loads and outside source Boundary conditions Postprocessing New geometric model Selection of material Processing of results properties Simplified regions for engineers New entities Checking for consistency Color coding of intervals and correctness for parameter values Mesh generation Construction of data sets and tables Hálógenerálás Controlled by engineer Optimizing the FEM Visualization of variation in time Automatic Automatic correction Graphical visualization of 2D és 3D functions Refining mesh

9. Finite element mesh Finite element entities They describe finite elements connected by common edges and parameters that are calculated by FEA. Libraries are established for finite elements. Nodes Calculation of the analyzed parameters is done at nodes. Degree of edges Straight line edges, or approximation by straight lines (linearization). Quadratic edge is defined by three, cubic edge is defined by four nodes. Exact edge is described as curve of the degree same as of the geometry Mesh, meshing Fixed of varying density. Density varies according to the load on each region. Two-way associatívity between shape model and mesh for automatic change of the mesh in case of changed geometry. Adaptive meshing is an automatic modification of mesh density, element order, and element shape according to accuracy and other specifications.

10. Parameters to be calculated • Stress • Deformation, gradient • Pressure • Internal force • Reaction force • Torque • Deformation energy • Natural frequency • Temperature, gradient • Heat flow • Magnetic field • By layers at composites

11. Finite elements Mesh Elements One-dimensional Planar Shell Solid

12. Loads and boundary conditions Simulation of real operating conditions. Associativity with the shape model. Load model: placing loads and restraints on mesh (at nodes) and shape model (along lines and on surfaces). Loads Concentrated and distributed force. Torque and acceleration ( (gravity, translation, rotation). Inertia and centrifugal forces. Contact loadPressure Temperature on surface Concentrated or distributed heat source. Magnetic Functional variations of loads are handled by mathematical expressions. • Constraints and restraints • Mechanical restraints restrict movements in specified directions and result reaction forces. • Definition of degrees of freedom. Non-restrained nodes have six degrees of freedom. • Automatic contact recognition.

13. Analysis of stress on connecting bodies Source: www.catia.com

14. Analysis of displacement Source: www.catia.com

15. Analysis of temperature Source: www.catia.com

16. Dynamic analysis Source: www.catia.com

17. Application of color code Source: www.catia.com

18. v a b d c b a Design optimization Active application of FEA. Instead of analysis of a proposed shape, design parameters are proposed by analysis. Specification by the engineer (conditions for design optimization): Design parameters to be optimized Design limits (allowable values): Allowable ranges of design parameters, Stress, deformation, natural frequency. Design goals: Minimum, maximum, or optimal values of performance parameters Minimum mass of the part. Maximum utilization of allowable stress and deformation. Design optimization procedure proposes values for design parameters in accordance with design goals and considering design limits.