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L3-1 Introduction to Analysis tools.pdf
The document provides an introduction to finite element analysis (FEA) and its role in solving structural analysis problems in engineering. It outlines various analysis methods including experimental, analytical, and numerical methods, with a focus on FEA as a numerical technique that divides structures into finite elements. Additionally, it details the general steps and considerations involved in the FEA process, such as mesh generation, load applications, and boundary conditions.
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L3-1 Introduction to Analysis tools.pdf
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- 2. Learning objectives • Explainthe basic principles of Finite Element Analysis, including discretization, elements, nodes, and degrees of freedom • Solve basic structural analysis problems using FEA tools to predict stress, strain, and deformation • Outline the key steps involved in performing FEA
- 3. 1. Introduction toAnalysis Tools 1.1 Introduction • There are a great number of analysis tools used in engineering applications to predict the behavior of mechanical components
- 4. • The threebasic methods commonly applied to provide solutions to various engineering problems includes:- Experimental methods Analytical methods Numerical methods (or) Approximate methods 1. Cont…
- 5. • Prototype arephysically created in labs • Time consuming and costly process • Needs man power and material 1. Cont… 1) Experimental methods t is one of the most reliable methods and widely used
- 6. • Problems areexpressed using mathematical differential equations to obtain solutions • It is used only for simple geometries and loading conditions 1. Cont… 2) Analytical methods It is a classical approach which gives 100 % accurate results
- 7. • This methodprovide solutions to problems involving complex material properties and boundary conditions 1. Cont… 3) Numerical methods (or) Approximate methods It uses computational techniques through simulation software’s & large infrastructures The results obtained are approximate
- 8. • There arefour common numerical methods used to solve engineering problems are:- Finite Element Analysis (FEA) Boundary Element Method (BEM) Finite Difference Method (FDM) Finite Volume Method (FVM) 1. Cont… 1.2 Numerical methods (or) Approximate methods
- 9. • FEA isa numerical technique that discretizes domain of continuous structure In this method, a body or structure in which the analysis to be carried out is subdivided into smaller elements of finite dimensions called finite elements Then the body is considered as an assembly of these elements connected at a finite number of joints called Nodes 1. Cont… i. Finite Element Analysis FEA method
- 10. • Based onapplication, finite element problems are classified as follows: Structural Problems Stress and Strain in each element can be calculated Non-structural Problems Temperature (or) Fluid pressure at each nodal point is obtained 1. Cont…
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- 12. 1. Cont… General Stepsof the Finite Element Analysis • The following two general methods are associated with the FEA:- Force Method: Internal forces are considered as the unknowns of the problem Displacement or stiffness method: Displacement of the nodes are considered as the unknowns of the problem
- 13. 1. Cont… Finite-Element AnalysisSolution Process Idealized model Finite-element model Step 1: Discretization of the Geometry
- 14. • Smaller elementsare classified as follows – One dimensional elements – Two dimensional elements – Three dimensional elements 1. Cont… Element Geometries Categories
- 15. 1. Cont… One dimensionalelements • A bar and beam elements are considered as one dimensional elements
- 16. • Triangular andrectangular elements are considered as two dimensional elements 1. Cont… Two dimensional elements
- 17. • The mostcommon three dimensional elements are tetrahedral and hexahedral (Brick) elements 1. Cont… Three dimensional/Solid elements
- 18. • Consider atruss element modeled as a spring element (e) of spring rate ke, with nodes i and j 1. Cont… Solution Process spring rate:
- 19. • Taking allforces f and displacements u directed toward the right as positive, the forces at each node can be written as; 1. Cont… Solution Process In matrix form:
- 20. • Consider atwo-spring system as shown; 1. Cont… Solution Process The internal forces can be analyzed as shown;
- 21. • From eachfree body diagram; 1. Cont… Solution Process The total force at each node is the external force, F1 = f1,1, F2 = f2,1 + f2,2, and F3 = f3,2
- 22. • Network ofelements and nodes is called a mesh • Mesh density increases as more elements are placed within a given region • Mesh refinement is when the mesh is modified from one analysis to the next to yield improved results 1. Cont… Mesh Generation
- 23. • Results generallyimprove when mesh density is increased in areas of high stress gradients • Mesh generation techniques includes; – Manual – Semiautomatic – Fully automated 1. Cont… Mesh Generation
- 24. • When stressconcentrations are present, it is necessary to have a very fine mesh at the stress- concentration region in order to get realistic results; 1. Cont… Mesh Generation
- 25. • Loads areapplied at the nodes • Element loads such as weight, thermal effects, surface pressure, etc. are automatically converted to equivalent nodal loads • The results very near the nodal forces may be unrealistic 1. Cont… Load Application
- 26. 1.1 Cont… Boundary Conditions •Constraints at the nodes can be placed to model boundary conditions • Typical boundary conditions include fixed, simply supported, and constrained in one direction
- 27. 1. Cont… • CADpackages and automatic mesh generators make model creation relatively painless • Computing speeds are sufficient to allow for dense meshes • The model only needs to be as detailed as needed • For example, five beam elements can provide deflections and slopes at the nodes of the shaft shown. Modeling Techniques
- 28. 1. Cont… • Forexample, five beam elements can provide deflections and slopes at the nodes of the shaft shown; Modeling Techniques
- 29. 1. Cont… 1. Performa numerical analysis on an I-shaped beam under the constricted transfer loading P shown Numerical Examples
- 30. 1. Cont… 1. Performa static analysis of the flat plate shown subjected to a tensile force of 5 kN is shown in Figure below. The plate material is grey cast iron FG 200. The thickness of the plate is 9 mm. Numerical Examples
- 31. Acknowledgements 2. R.L. Mott(2007), Machine Elements in Design, Fourth Edition 3. J.E Shigley & C.R. Mischke, Mechanical Engineering Design, 6th Edition, Tata McGraw-Hill, New Delhi, India, 2003, ISBN: 0-07-049462-2 1. V. B. Bhandari (1994), Design of Machine Elements, third Edition
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