Finite Element Method Questions and Answers – Four Node Quadrilateral for Axis Symmetric Problems

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This set of Finite Element Method Questions and Answers for Experienced people focuses on “Four Node Quadrilateral for Axis Symmetric Problems”.

1. In the four-node quadrilateral element, the shape functions contained terms _________
a) ξ
b) σ
c) ∅
d) Undefined
View Answer

Answer: a
Explanation: FourNodeQuad is a four-node plane-strain element using bilinear isoparametric formulation. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot’s theory of porous medium. Each element node has 3 degrees-of-freedom (DOF): DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p).
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2. A _________ element by using nine-node shape function.
a) Load vector
b) Sub parametric
c) Element displacement vector
d) Constant matrix
View Answer

Answer: b
Explanation: The Nine-Node Biquadratic Quadrilateral This element is often abbreviated to Quad9 in the FEM literature. This element has three types of shape functions, which are associated with corner nodes, midside nodes and center node, respectively.

3. Eight-Node Quadrilateral. This element belongs to the ________ family of elements.
a) Serendipity
b) Constant matrix
c) Load vector
d) Master element
View Answer

Answer: a
Explanation: The Eight-Node “Serendipity” Quadrilateral. This element is often abbreviated to Quad8 in the FEM literature. It is an eight-node quadrilateral element that results when the center node 9 of the biquadratic quadrilateral (Quad9) is eliminated by kinematic constraints.
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4. N1, is of the form ____
a) Co-ordinates
b) N1=c(1-ξ)(1-η)(1+ξ+η)
c) N1=(1-ξ)(1-η)
d) N1=(1-ξ)
View Answer

Answer: b
Explanation: The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions. In this work linear shape functions are used.

5. Six node triangular elements is also known as _____
a) Triangle
b) Quadratic triangle
c) Interpolation
d) Shape function
View Answer

Answer: b
Explanation: The six-node triangle is shown in Figs. 7.8a and b. By referring to the master element where ϛ=1-ξ-η. Because of terms ξ22 etc. in the shape functions, this element is also called a quadratic triangle. The isoparametric representation is
u=Nq.
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6. In six node triangular element, the gauss points of a triangular element can be defined by ____
a) Two point rule
b) Three point rule
c) One point rule
d) Undefined
View Answer

Answer: c
Explanation: In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration.

7. The mid node should not be outside of the triangular element this condition should ensures that det J does not attain a value ____
a) Constant
b) Zero
c) Unity
d) Infinite
View Answer

Answer: b
Explanation: The Mid-Node Admissible Spaces (MAS) [1,2] for two-dimensional quadratic triangular finite elements are extended to three-dimensional quadratic tetrahedral finite elements (3DQTE). The MAS concept for 3DQTE postulates a bounded region within which a mid-side node of a curved edge of the 3DQTE can be placed to ensure maintaining a specified minimum and maximum Jacobian determinant value at any point of the element.
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8. The nodal temperature load can be evaluated by using _____
a) Uniform energy
b) Strain energy
c) Numerical integration
d) Displacement
View Answer

Answer: c
Explanation: A temperature can be applied to nodes, surfaces, or parts in a model. A surface temperature applies nodal temperatures to each node on the surface, and a part temperature applies nodal temperatures to each node in the part. A temperature is used for a thermal stress analysis.

9. The gauss points for a triangular region differ from the _____ region.
a) Rectangular
b) Triangular
c) Square
d) Temperature
View Answer

Answer: c
Explanation: In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration.
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10. In a nine node quadrilateral, the shape functions can be defined as _______
a) Shape functions
b) Generic shape functions
c) Elements
d) Planes
View Answer

Answer: b
Explanation: The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions. In this work linear shape functions are used.

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