1. For a four noded quadrilateral elements, In uT=[u.v]T the displacement elements can be represented as u=N1q1+N2q3+ N3q5+ N4q7
v= N1q2+N2q4+ N3q6+ N4q8
then the shape function can be represented as _____
a) \(N=\left[\begin{array}{ |c c c c}q_1 & q_5 \\ q_2 &q_6\\q_3 &q_7\\q_4 & q_8\end{array}\right]\)
b) \(N=\begin{bmatrix}q_1 &q_3 &q_5 &q_7 \\ q_2 &q_4&q_6&q_8\end{bmatrix}\)
c) \(N=\begin{bmatrix}q_1 \\ q_2\end{bmatrix}\)
d) \(N=\begin{bmatrix}N_1 & 0 & N_3 & 0&N_5&0&N_7 & 0 \\ 0 & N_2 &0 &N_4&0&N_6&0&N_8\end{bmatrix}\)
Explanation: Displacement function in FEM. When the nodes displace, they will drag the elements along in a certain manner dictated by the element formulation. In other words, displacements of any points in the element will be interpolated from the nodal displacements, and this is the main reason for the approximate nature of the solution.
2. The stiffness matrix from the quadrilateral element can be derived from _____
a) Uniform energy
b) Strain energy
c) Stress
d) Displacement
Explanation: In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to as certain an approximate solution to the differential equation.
3. For four noded quadrilateral element, the global load vector can be determined by considering the body force term in _____
a) Kinetic energy
b) Potential energy
c) Kinematic energy
d) Temperature
Explanation: A body force that is distributed force per unit volume, a vector, many people probably call up Vector’s definition (from Despicable Me). He says: It’s a mathematical term. A quantity represented by an arrow with both direction and magnitude. … Vector: a quantity with more than one element (more than one piece of information).
4. Shape functions are linear functions along the _____
a) Surfaces
b) Edges
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.
5. Which method of approach is useful for evaluating four noded quadratic elements?
a) Numerical integration
b) Penality approach method
c) Gaussian quadrature approach
d) Rayleighs method
Explanation: Gaussian quadrature is to select the n Gauss points and n weights such that provides an exact answer for polynomials f(ξ) of as large ∼ degree as possible. In other words, the Idea is that if the n-point integration formula is exact for all polynomials up to as high a degree as possible, then the formula will work well even if f is not a polynomial.
6. One point formula in quadratic approach is ____
a) w1f(ξ1)
b) σ=εD
c) Nt=(1-ξ)(1-η)
d) Constant matrix
Explanation: In elementary algebra, the quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing. This is seen to be the familiar midpoint rule.
7. The extension of Gaussian quadrature to two-dimensional integrals of the form of _____
a) I≈\(\sum_{i=1}^{n}\sum_{j=1}^{n}\)wiwjf(ξi,ηj)
b) Natural co-ordinates
c) w1f(ξ1)+w2f(ξ2)
d) w1f(ξ1)
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. An n-point Gaussian quadrature rule, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the points xi and weights wi for i=1,…, n. The domain of integration for such a rule is conventionally taken as [−1, 1].
8. The stresses in the quadratic element are not ______
a) Linear
b) Uniform
c) Constant
d) Undefined
Explanation:The stress applied to a material is the force per unit area applied to the material. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress. Tensile means the material is under tension. The forces acting on it are trying to stretch the material.
9. The stresses are evaluated at the __________
a) Nodal points
b) Nodal displacements
c) Gauss points
d) Elements
Explanation: The stress applied to a material is the force per unit area applied to the material. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress. The forces acting on it are trying to stretch the material. 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. For quadrilateral with 2X2 integration gives _____ sets of stress values.
a) One
b) Two
c) Three
d) Four
Explanation: The stress applied to a material is the force per unit area applied to the material. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress. Tensile means the material is under tension. The forces acting on it are trying to stretch the material.