GENERALIDADES DEL IMPUESTO

1. What are the different approximate solution methods?

 Finite Element method, Finite difference method and quadrature method.

2. What do you mean by continuum?

 A continuous sequence in which adjacent elements are not perceptibly different from each other, although the extremes are quite distinct.

 A continuous extent, succession, or whole, no part of which can be distinguished from neighboring parts except by arbitrary division.

3. Define term node?

 In the FEM, the structural system is modeled by a set of appropriate finite elements interconnected at points called nodes

 A node is a specific point in the finite element at which the value of the field variable is to be determined.

 Nodes are the selected finite points at which basic unknowns (displacements in elasticity problems) are to be determined in the finite element analysis

4. Define term element?

 In a continuum, unknowns are many. The FE procedure reduces such unknowns to a finite no. by diving the solution regimes into small parts called elements

5. What is convergence?

 Convergence refers to how close the FEM solution is to the exact solution

6. What are the types convergence?

 h – method and p-method

7. What is p-convergence?

 Large elements and complex shape functions are used in p-method problems. In order to increase the accuracy of the solution, the complexity of the shape function must be increased. The mesh does not need to be changed when using the p-method.

Increasing the polynomial order increases the complexity of the shape function. As an initial run, the solution might be solved using a first order polynomial shape function. A solution is obtained. To check the solution the problem will be solved again using a more complicated shape function. For the second run, the solution may be solved using a third order polynomial shape function. A second solution is obtained. The output from the two runs is compared. If there is a large difference between the two solutions, then the solution should be run using a third order polynomial shape function. This process is repeated until the solution is not changing much from run to run.

8. What is h convergence?

 Simple shape functions and many small elements are used in h-method problems. In order to increase the accuracy of the solution, more elements must be added. This means creating a finer mesh.

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As an initial run, a course mesh is used to model the problem. A solution is obtained. To check this solution, a finer mesh is created. The mesh must always be changed if a more accurate solution is desired. The problem is run again to obtain a second solution. If there is a large difference between the two solutions, then the mesh must be made even finer and then solve the solution again. This process is repeated until the solution is not changing much from run to run.

When using an h-method finite element program (such as ANSYS), the user must run two or more solutions to ensure that the solution has converged. The user runs the solution with one mesh and then changes the mesh and reruns the solution.

9. What is higher order elements?

 If the interpolation polynomial is of the order two or more, the element is known as Higher order elements.

10. Give example for higher order elements.

 Quadratic bar element, cubic bar element etc..

11. What do you mean by compatible elements?

 The elements which deform without causing openings, overlaps or discontinuities b/w the adjacent elements are known as compatible elements

12. What is geometric invariance?

 Displacement shapes will not change in local coordinate system. This property is known as geometric invariance.

13. Why do we use Pascal’s triangle in FEA?

 In order to achieve geometric invariance the polynomial should contain terms that do not violate symmetry; this is achieved by the use of Pascal triangle for 2Dcases and Pascal tetrahedron for 3D cases.

14. What are the steps involved in FEA?

 Discretization of the continuum, Selection of displacement models, Deriving element stiffness matrix, assemblage of elemental equations to obtain overall equilibrium equations, Applying boundary conditions, Solution for unknown nodal displacements and Computation of strain, stress and reaction solution.

15. What is stiffness matrix?

 For an element, Stiffness matrix is a matrix such that { f } = [K] {Q}, [K] relates nodal displacements to nodal force of a single element.

16. How to obtain stiffness matrix?

 Using the formula for particular element.

17. What are the properties of stiffness matrix?

 Non negative diagonal elements, Symmetry and sparsity.

57 18. What is displacement function?

 The displacement function, uniquely defines strain within an element in terms of nodal displacements.

19. How to identify order of elements?

 The maximum power of the variable in the interpolation polynomial gives the order or the order can be obtained by no. of nodes present.

20. Mention different types of elements.

 Simplex elements,complex elements and multiplex elements; Based on their geometry they are classified as 1D,2D,3D and axis symmetric elements.

21. Mention some application of FEA.

 Stress analysis of bars, beams, trusses, buckling problems, Heat transfer problems, fluid flow problems, bio medical areas etc.

22. What is connectivity?

 Connectivity is a term used when a matrix or a table connects the stress,reactions ,displacements etc

23. What are the methods to improve problem solution?

 Use of higher order elements in order to get exact solutions

24. Define symmetry in matrix.

 A symmetric matrix is a square matrix that is equal to its transpose

25. What is plane stress?

 Plane stress is defined to be a state of stress in which the normal stress and shear stress directed perpendicular to the plane are assumed to be zero e.g. thin plate with hole 26. What is plane strain?

 Plane strain is defined to be a state of strain in which normal strain and shear strain normal to the XY plane are assumed to be zero.

27. Compare FEA with solid mechanics.

 Finitie element analysis can be applied to any continous matter where you can divide the situation into small elements (usually triangular) and apply a set of edge constraints and then use a computer to solve for the area of concern for whatever the value under investigation is e.g. temperarture, flow rate, stress, shear, bending moment etc.

So Solid mechanics is the study of things as shear, stress, etc. and they use FEA as a tool but FEA can be applied to many other fields e.g fluid mechanics thermodynamics, etc.

28. What are the packages available for FEA?

 STAAD-PRO, GT-STRUDEL, NASTRAN, NISA and ANSYS

58 29. Define potential energy.

 Potential energy is energy which results from position or configuration

30. Define minimum potential energy.

 Deformation and stress analysis of structural systems can be accomplished using the principle of Minimum Potential Energy (MPE), which states that “For conservative structural systems, of all the kinematically admissible deformations, those

corresponding to the equilibrium state extremize (i.e., minimize or maximize) the total potential energy. If the extremum is a minimum, the equilibrium state is stable.

31. Write potential energy equation for cantilever beam.



32. Mention 2 different methods to approach the model of physical system.

 FEM and FDM

33. Difference between global coordinate and local coordinate?



34. What is local coordinate?

 For the convenience of deriving element properties, in FEM many times for each element a separate coordinate system is used known as local coordinate system 35. What is global coordinate?

 The coordinate system used to define the points in the entire structure is called global coordinate system.

36. What is shape function?

 Function which relates the field variable at any point within the element to the field variables of nodal points is called shape function.

37. What are two general natural coordinate?

 Zeta ξ and neta ή

38. Mention the range of natural coordinate.

 -1 to +1

39. Number of shape function in CST

 3

40. Number of shape function in quadrilateral.

 4

41. Explain one point formula and Explain two point formula.

 1 point formula ∫ ( ) w1f(ξ), w1 = 2, ξ= 0

 2 point formula ∫ ( ) w1f(ξ1)+w2f(ξ2), w1= 1,ξ1 = 1/√3, w2= 1, ξ2 = -1/√3

42. Why we are using polynomial equation in FEA?

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 It is easier to formulate and computerize the finite element equations with polynomial-type interpolation functions. Specifically, it is easier to perform differentiation or integration with polynomials.

 It is possible to improve the accuracy of the results by increasing the order of the polynomial.

43. Mention two schemes to represent band width?

 Node numbering along longer edge and shorter edge.

44. What are forces involved in work potential?

 Body forces and traction forces

45. What are anisotropic elements?

 The property of the material is not same along all the directions; such materials are called anisotropic elements.

46. What are isotropic elements?

 The property of the material is same along all the directions; such materials are called isotropic elements.

47. What are the 2 different approaches to study elasticity?

 Elimination and penalty approach method

48. List the properties of shape functions.

 Shape function at a specified point is unity and other than the specified point it is zero.

 Sum of shape functions is unity.

 The differentiation of shape function is a constant

49. Define truss.

 A framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure

50. What is weighted residual methods?

 The weighted residual method is a technique that can be used to obtain approximate solutions to linear and nonlinear differential equations. If we use this method the finite element equations can be derived directly from the governing differential equations of the problem without any need of knowing the “functional.” We first consider the solution of equilibrium, eigenvalue, and propagation problems using the weighted residual method and then derive the finite element equations using the weighted residual approach.

51. Different methods to solve weighed residual problem.

 Galerkin method, Collocation method, Sub domain method

52. Explain the principle of virtual work.

 The principle of virtual work (PVW) states that the stress, body force and traction are in equilibrium if and only if the IVW equals the EVW for every virtual displacement field.

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53. Mention some advantages of FEA over solid mechanics.

 In classical methods exact equations are formed and exact solutions are obtained where as in finite element analysis exact equations are formed but approximate solutions are obtained.

 Solutions have been obtained for few standard cases by classical methods, where as solutions can be obtained for all problems by finite element analysis.

 Whenever the following complexities are faced, classical method makes the drastic assumptions’ and looks for the solutions: Shape, Boundary conditions, Loading

 To get the solution in the above cases, rectangular shapes, same boundary condition along a side and regular equivalent loads are to be assumed. In FEM no such

assumptions are made. The problem is treated as it is.

 When material property is not isotropic, solutions for the problems become very difficult in classicalmethod. Only few simple cases have been tried successfully by researchers.

FEM can handle structures with anisotropic properties also without any difficulty.

 If structure consists of more than one material, it is difficult to use classical method, but finite element can be used without any difficulty.

 Problems with material and geometric non-linearities can not be handled by classical methods.There is no difficulty in FEM.

54. Define Young’s Modulus and Poisson’s Ratio.

 Within the limits of elasticity, the ratio of the linear stress to the linear strain is termed the modulus of elasticity or Young's Modulus and may be written Young's Modulus, or E

=(Stress/Strain) It is this property that determines how much a bar will sag under its own weight or under a loading when used as a beam within its limit of proportionality. For steel, Young's Modulus is of the order of 205000 N/mm2.

 Ratio of decrease in the thickness (lateral contraction) of a body being pulled (under a tensile load) to its increase in length (longitudinal extension). It is constant for

a material, around 0.28 for ordinary steels. Named after its discoverer, the French mathematician Siméon-Davis Poisson (1781-1840).

55. Mention different types of elastic constants.

 (i)Modulus of Elasticity or Young’s Modulus (E)

Modulus of Elasticity is the ratio of direct stress to corresponding linear strain within elastic limit. If p is any direct stress below the elastic limit and e the corresponding linear strain, then E = p / e.

(ii)Modulus of Rigidity or Shear Modulus (G)

Modulus of Rigidity is the ratio of shear stress to shear strain within elastic limit. It is denoted by N,C or G. if q is the shear stress within elastic limit and f the corresponding shear strain, then G = q / f.

(iii) Bulk Modulus (K)

Bulk Modulus is the ratio of volumetric stress to volumetric strain within the elastic limit.

If pv is the volumetric stress within elastic limit and ev the corresponding volumetric strain, we have K = pv / ev.

56. Which is the most accepted form of numerical integration in FEM?

 Gaussian quadrature

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57. List the different approaches to derive integral equation.

 Gaussian quadrature, Simpson’s 1/3 rule etc

58. What are the different types of errors in FEA?

 Modeling Error, User error, bugs, Discretization error, Rounding error, manipulation error, Numerical error

59. Define Beam & Its types.

 A bar subjected to forces and couples that lie in a plane containing its longitudinal axis is called a beam

 Types include Cantilever beam,simply supported beam and over hanging beam

60. Define Conduction, Convection and radiation.

 Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions b/w particles.

 Convection is the mode of heat transfer b/w a solid surface and the adjacent fluid that is in motion and it involves the combined effects of conduction and fluid motion.

 Radiation is the energy emitted by matter in the form of electromagnetic waves as a result of the changes in the electronic configurations of the atoms or molecules.

61. Define Heat flux, Heat flow & Heat generation

 Heat flux is defined as the rate of heat transfer per unit area.\

 Heat flow means transfer of heat energy.

 Heat generation means heat developed in the body.

62. Define adiabatic surfaces.

 Adiabatic surfaces are surfaces which do not allow the flow of heat either into the body or out the body.

63. Define Density, film coefficient.

 Density is defined as mass per unit volume.

 For a fluid confined in a vessel, the rate of flow of heat out of the fluid, per unit area of vessel wall divided by the difference between the temperature in the interior of the fluid and the temperature at the surface of the wall. Also known as convection coefficient.

64. Define Thermal gradient & Thermal conductivity.

 The rate of temperature change with distance

 Thermal conductivity is defined as the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.

62 65. Define Specific heat .

 It is a measure of a material’s ability to store thermal energy

66. Define Dynamic Analysis and its types

 Dynamic analysis is analysis done if loading is of higher frequency or is applied suddenly.

 Types are modal analysis, harmonic analysis etc

67. Define Modal & Harmonic Analysis with its application.

 Modal analysis is the study of the dynamic properties of structures under vibrational excitation

 Harmonic analysis is analysis done when a structure is subjected to cyclic loading

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