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

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

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

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.

An example for FEM/FEA Source:

Analysis in model space Source:

Short story First application: analysis of structural eleents of airplanes. First application of the phrase ” finite element analysis”: Clough, 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.

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

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.

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

Finite elements Solid Planar One-dimensional MeshElements Shell

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 load Pressure 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.

Analysis of stress on connecting bodies Source:

Analysis of displacement Source:

Analysis of temperature Source:

Dynamic analysis Source:

Application of color code Source:

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. a b c d b a v