1. For degenerate four noded quadrilateral element the errors are _____
a) Constant
b) Uniform
c) Higher
d) Lesser
Explanation: A degenerated element is an element whose characteristic face shape is quadrilateral, but is modeled with at least one triangular face. Degenerated elements are often used for modeling transition regions between fine and coarse meshes, or for modeling irregular and warped surfaces.
2. Gauss points are also the points used for numerical evaluation of _____
a) Surfaces
b) ke
c) Elements
d) Planes
Explanation: Stiffness is the rigidity of an object, the extent to which it resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is the less stiff it is. A stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.
3. In the four-node quadrilateral element, the shape functions contained terms _________
a) ξ
b) σ
c) ∅
d) Undefined
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).
4. A _________ element by using nine-node shape function.
a) Load vector
b) Sub parametric
c) Element displacement vector
d) Constant matrix
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.
5. 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)
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.
6. Six node triangular elements is also known as _____
a) Triangle
b) Quadratic triangle
c) Interpolation
d) Shape function
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 ξ2,η2 etc. in the shape functions, this element is also called a quadratic triangle. The isoparametric representation is
u=Nq.
7. 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
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.
8. The nodal temperature load can be evaluated by using _____
a) Uniform energy
b) Strain energy
c) Numerical integration
d) Displacement
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
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.
10. In a nine node quadrilateral, the shape functions can be defined as _______
a) Shape functions
b) Generic shape functions
c) Elements
d) Planes
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.