Finite Element Methods January 29, 2019 Vijayan 0 The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics. Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The number of shape function will be equal to the number of Nodes of element Element of the structure Size of the structure Coordinate Heat transfer takes place due to________ Conduction Convection Radiation ∆T LST element contains________nodes. 5 6 3 4 Axis symmetric element is____element 2D 4D 3D 1D Nodal point greater than geometry point is known as____________ Isoparametric Superperametri Subparametric QST Iso-parametric element is_____________element Regular Ir-regular Sub Super Based below condition which is a serendipity triangular element______ Node on element Nodes at centre Nodes at corner None of these __________problems depends on vertical deflection Structural Heat transfer Both are correct None of these A deformable system is in equilibrium, if the first variation in the total P.E of the system is zero refers to theorem of stationary P.E theorem of virtual displacement theorem of virtual work bettis theorem In case of truss member if there are 3 nodes and each nodes 2 DOF, then the order of stiffness matrix is_________. 3x3 6x6 2x3 2x2 In CST element__________is constant. strain stress shape function All of the above If the geometry and field displacement variable of the elements are described by the same shape function, then these element are called ________. Iso Parametric Axis Symmetric Super Parametric Sub Parametric A triangular plane stress elements has____________degree's of freedom 4 2 7 6 On gathering stiffness and loads, the system of equation given by KQ=F KQ≠F K=QF K≠QF What is the value of discrete time signal x(n) at n=0 whose Fourier transform is represented as below? ωc.π -ωc/π ωc/π None of these If cx(n) is the complex cepstrum sequence obtained from the inverse Fourier transform of ln X(ω), then what is the expression for cθ(n)? a b c d The degree of the B-spline with varying knot vectors Increases with knot vectors Decreases with knot vectors Remains constant None of these What is the period of the Fourier transform X(ω) of the signal x(n)? π 1 2π Non-periodic FEA software is categories of_________ 3 4 5 2 Your new question! What are the types of loading acting on the structure? Traction force, shear flow, point load Traction force, point load, bending moment Body force, traction force, point load Bending moment, traction force, shear flow Euler’s Criterion can find the solution to x2 ≡ a (mod n) True False The value ‘n’ in classless addressing is referred to as – prefix length suffix length intermediate length none of the mentioned Which of the following is introduced in the frequency sampling realization of the FIR filter? Poles are more in number on unit circle Zeros are more in number on the unit circle Poles and zeros at equally spaced points on the unit circle None of the mentioned Initial Graphic Exchange Specification (IGES) is: A reference to a surface meshing technique A standard format in which the drawing geometry of a 3D model can be exported for use by other CAD systems A modeling kernel used by several solid modeling CAD packages A way in which data is stored within a CAD database Which of the following is not a modeling kernel used by many solid modeling software packages? CSG ACIS Parasolid Proprietary FEM can not produce exact result as those of___________methods. Analytical Theoritical Logical All of the above What is the average power of the discrete time periodic signal x(n) with period N ? a b c d The Fourier series for the signal x(n)=cos√2πn exists. True False Which of the following 3D modeling methods cannot be shaded to look like a realistic object? Parametric modeling Wireframe modeling Solid modeling Surface modeling The least attractive feature of a physical model/prototype in the refinement phase is: High costs to create the prototype A prototypes lack of flexibility Storing the full-size prototype during the design process Accuracy What are the Fourier series coefficients for the signal x(n)=cosπn/3? c0=c1=c2=c3=c4=c5=0 c0=c1=c2=c3=c4=c5=1/2 c1=c2=c3=c4=0,c1=c5=1/2 None of these Which of the following represents the phase associated with the frequency component of discrete-time Fourier series(DTFS)? ej2πkn/N e-j2πkn/N ej2πknN None of these C” continuity refers to: Common curvature Common point Common tangent Common normal Your new question! Convex hull property is satisfied by the following surface: Bezier B-spline NURBS All of the above FEM gives accurate representation of real geometry real and complex geometry constant geometry complex geometry What is the equation for average power of discrete time periodic signal x(n) with period N in terms of Fourier series coefficient ck? a b c d Finite element method is also called infinite element analysis frequency element analysis finite element analysis partial element analysis A particular class of numerical simulation algorithms for simulation of physical phenomena which was developed by combining mesh free methods with finite element method is XFEM SFEM hpk-FEM hp-FEM FEM that combines adaptively, elements with variable size h, polynomial degree of local approximations p and global differentiability of local approximations (k-1) in order to achieve best convergence rates is XFEM SFEM hpk-FEM hp-FEM Numerical algorithms are based on FEM and FDTD FEM and IFEM TD and FD FEM and FD To solve FEM problem, it subdivides a large problem into smaller, simpler parts that are called infinite elements finite elements dynamic elements static elements A type of finite element method in which extra independent variables are introduced as nodal variables during discretization of a partial differential equation problem is called mixed FEM SFEM hpk-FEM hp-FEM The fixed support displacement are equal to____________ 1 3 4 0 The higher order element are also called as complex element compound element linear element none of these Number of displacement polynomial used for an element depends on______ nature of element type of element degree's of freedom nodes In weighted residual technique, the method adopted are________ point collocation methods least square's methods galerkin's method all of the above Finite element method formulation of problem results in a system of logical equations algebraic equations Arthimatic equations flow equations The eight node quadrilateral elements belongs to___________family of elemets. interdipity Serendipity sardipity none Range of poisson's ratio for metal is 0.25-0.33 0.25-0.50 0.22-0.44 0.42-0.44 FEM also operates the parameters like Heat transfer Temperature Both are correct None of these What is the Fourier transform X(ω) of a finite energy discrete time signal x(n) a b c none of these At fixed support the displacement are equal to_________ 2 5 0 1 Sum of all shape function is equal to__________ 0 2 1 -1 The geometrical and other parameter of an element in term of only one spatial coordinate then element is__________. one dimensional two dimensional three dimensioal none of these In choosing the right modeling method, which of the following is a key consideration? Accuracy Software capabalities Time to model part All of the above Which of the following is the least likely to benefit from solid modeling? Civil mapping Finite Element Analysis Machine design Product design Wireframe modeling software has the following advantage over solid modeling software: Low-cost Modeling complex shapes Visualization Surface area and volume calculation Which of the following is not a basic method to create a surface model? Spline approximations Extrusion Meshes Boolean operations

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