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FEA Basic Introduction Training By Praveen conducted in 2008

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- 1. Finite Element Analysis Praveen Patil Y Z X
- 2. Contents• Introduction to the Finite Element Method (FEM)• Future Trends
- 3. FEM Applied to Solid Mechanics Problems • A FEM model in solid mechanics can be thought of as a system of assembled springs. When a load is applied, all elements deform until all forces balance. • F = Kd Create elements of the beam • K is dependant upon Young’s modulus and Poisson’s ratio, as well as the geometry. • Equations from discrete elements are assembled together to form Nodal displacement and forces the global stiffness matrix. dxi 1 dxi 2 • Deflections are obtained by solving the assembled set ofdyi 1 1 2 linear equations. dyi 2 • Stresses and strains are 4 3 calculated from the deflections.
- 4. Classification of Solid-Mechanics Problems Analysis of solids Static Dynamics Elementary Advanced Behavior of Solids Stress Stiffening Large Displacement Geometric Instability Linear Nonlinear Fracture Plasticity Material Viscoplasticity Geometric Classification of solidsSkeletal Systems Plates and Shells Solid Blocks 1D Elements 2D Elements 3D ElementsTrusses Plane Stress Brick ElementsCables Plane Strain Tetrahedral ElementsPipes Axisymmetric General Elements Plate Bending Shells with flat elements Shells with curved elements
- 5. Governing Equation for Solid Mechanics Problems• Basic equation for a static analysis is as follows: [K] {u} = {Fapp} + {Fth} + {Fpr} + {Fma} + {Fpl} + {Fcr} + {Fsw} + {Fld} [K] = total stiffness matrix {u} = nodal displacement {Fapp} = applied nodal force load vector {Fth} = applied element thermal load vector {Fpr} = applied element pressure load vector {Fma} = applied element body force vector {Fpl} = element plastic strain load vector {Fcr} = element creep strain load vector {Fsw} = element swelling strain load vector {Fld} = element large deflection load vector
- 6. Six Steps in the Finite Element Method• Step 1 - Discretization: The problem domain is discretized into a collection of simple shapes, or elements.• Step 2 - Develop Element Equations: Developed using the physics of the problem, and typically Galerkin’s Method or variational principles.• Step 3 - Assembly: The element equations for each element in the FEM mesh are assembled into a set of global equations that model the properties of the entire system.• Step 4 - Application of Boundary Conditions: Solution cannot be obtained unless boundary conditions are applied. They reflect the known values for certain primary unknowns. Imposing the boundary conditions modifies the global equations.• Step 5 - Solve for Primary Unknowns: The modified global equations are solved for the primary unknowns at the nodes.• Step 6 - Calculate Derived Variables: Calculated using the nodal values of the primary variables.
- 7. Process Flow in a Typical FEM Analysis Problem Analysis andStart Stop Definition design decisions Processor/Solver Post-processor Pre-processor • Prints or plots • Generates contours of stress • Reads or generates element shape components. nodes and elements functions • Prints or plots (e.g. MD-Patran) • Calculates master contours of • Reads or generates element equations displacements. material property data. • Calculates • Evaluates and • Reads or generates transformation prints error boundary conditions matrices bounds. (loads and • Maps element equations into constraints.) global system Step 6 • Assembles element equations Step 1, Step 4 • Introduces boundary Steps 2, 3, 5 conditions • Performs solution procedures
- 8. Step 1: Discretization - Mesh Generation surface model airfoil geometry (from CAD program e.g CATIA) e.g. MD-PatranET,1,SOLID45N, 1, 183.894081 , -.770218637 , 5.30522740N, 2, 183.893935 , -.838009645 , 5.29452965..TYPE, 1E, 1, 2, 80, 79, 4, 5, 83, 82E, 2, 3, 81, 80, 5, 6, 84, 83... meshed model
- 9. Step 4: Boundary Conditions for a Solid Mechanics Problem • Displacements ⇒ DOF constraints usually specified at model boundaries to define rigid supports. • Forces and Moments ⇒ Concentrated loads on nodes usually specified on the model exterior. • Pressures ⇒ Surface loads usually specified on the model exterior. • Temperatures ⇒ Input at nodes to study the effect of thermal expansion or contraction. • Inertia Loads ⇒ Loads that affect the entire structure (ex: acceleration, rotation).
- 10. Step 4: Applying Boundary Conditions (Thermal Loads) 300 Nodes from 300 275 FE Modeler 275 250 250 bf, 1,temp, 149.77 225 225 bf, 2,temp, 149.78 Temp . 200 .mapper 200 . 175 bf, 1637,temp, 303.64 bf, 1638,temp, 303.63 Thermal 150 Soln Files 150 175
- 11. Step 4: Applying Boundary Conditions (Other Loads) • Speed, temperature and hub fixity applied to sample problem. • FE Modeler used to apply speed and hub constraint. antype,static omega,10400*3.1416/30 d,1,all,0,0,57,1ZY X
- 12. Information Available from Various Types of FEM Analysis• Static analysis • Heat transfer analysis » Deflection »Temperature » Stresses » Heat fluxes » Strains » Thermal gradients » Forces » Heat flow from » Energies convection faces• Dynamic analysis • Fluid analysis » Frequencies » Deflection (mode » Pressures shape) » Gas temperatures » Stresses » Convection coefficients » Strains » Velocities » Forces » Energies
- 13. Example FEM Application Areas• Automotive industry • Aerospace industry » Static analyses » Static analyses » Modal analyses » Modal analyses » Transient dynamics » Aerodynamics » Heat transfer » Transient dynamics » Mechanisms » Heat transfer » Fracture mechanics » Fracture mechanics » Metal forming » Creep and plasticity analyses » Crashworthiness » Composite materials• Architectural » Aeroelasticity » Soil mechanics » Metal forming » Rock mechanics » Crashworthiness » Hydraulics » Fracture mechanics » Hydroelasticity
- 14. Variety of FEM Solutions is Wide and Growing Wider• The FEM has been applied to a richly diverse array of scientific and technological problems.• FEM is increasingly applied to a variety of real-world design and analysis problems.
- 15. Technologies That Compete With the FEM• Other numerical solution methods: – Finite differences » Approximates the derivatives in the differential equation using difference equations. » Useful for solving heat transfer and fluid mechanics problems. » Works well for two-dimensional regions with boundaries parallel to the coordinate axes. » Cumbersome when regions have curved boundaries. – Weighted residual methods (not confined to a small subdomain): » Collocation » Subdomain » Least squares* » Galerkin’s method* – Variational Methods* (not confined to a small subdomain) * Denotes a method that has been used to formulate finite element solutions.
- 16. Technologies that Compete With the FEM (cont.)• Prototype Testing » Reliable. Well-understood. » Trusted by regulatory agencies (FAA, DOT, etc.) » Results are essential for calibration of simulation software. » Results are essential to verify modeled results from simulation. » Non destructive testing (NDT) is lowering costs of testing in general. » Expensive, compared to simulation. » Time consuming. » Development programs that rely too much on testing are increasingly less competitive in today’s market. » Faster product development schedules are pressuring the quality of development test efforts. » Data integrity is more difficult to maintain, compared to simulation.
- 17. Contents• Introduction to the Finite Element Method (FEM)• Future Trends
- 18. Future Trends in the FEM and Simulation• The FEM in particular, and simulation in general, are becomingintegrated with the entire product development process (rather than justanother task in the product development process): – FEM cannot become the bottleneck.• A broader range of people are using the FEM: – Not just hard-core analysts. Future (?? Word excel??)• Increased data sharing between analysis data sources (CAD, testing,FEM software, ERM software.)• FEM software is becoming easier to use: – Improved GUIs, automeshers. – Increased use of sophisticated shellscripts and “wizards.(??)”
- 19. Conflicting Variables . . .with Reduci ng timeNVH & Crash Optimization of Vehicle Body Overnight • Ford body-in-prime (BIP) model of 390K DOF • MSC.Nastran for NVH, 30 design variables • RADIOSS for crash, 20 design variables Achieved overnight • 10 design variables in common BIP optimization on SGI 2800/256, with • Sensitivity based Taylor approx. for NVH equivalent yield of 9 months CPU time • Polynomial response surface for crash
- 20. Future Trends in the FEM and Simulation (cont.)• Enhanced multiphysics capabilities are coming: – Coupling between numerous physical phenomena. » Ex: Fluid-structural interaction is the most common example. » Ex: Semiconductor circuits, EMI and thermal buildup vary with current densities.• Improved life predictors, improved service estimations.• Increasing use of non-deterministic analysis and design methods: – Statistical modeling of material properties, tolerances, and anticipated loads. – Sensitivity analyses.• Faster and more powerful computer hardware. Massively parallel processing.• FEM and simulation software available via Internet subscription.• Decreasing reliance on testing. But (??)
- 21. Economics: Physical prototyping costs continue Increasi ng Engineer more expensive than simulation tools MSC/NASTRAN 1960 2006 Mainframes Simulation Costs $30,000 $0.02 (Source: General Motors) Cost of CAE CAE Engineer Engineer System vs. System Costs $36/hr $1.5/hr Simulation (Source: Detroit Big3) Cost of CAE Engineer Cost of Physical Prototyping Workstations and Servers 1960 Years 2006
- 22. Thanks.

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