# Finite Element Method Questions and Answers – Finite Element Equations – Treatment of Boundary Conditions

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Finite Element Equations – Treatment of Boundary Conditions”.

1. Types of Boundary conditions are ______
a) Potential- Energy approach
b) Penalty approach
c) Elimination approach
d) Both penalty approach and elimination approach

Explanation: Boundary condition means a condition which a quantity that varies through out a given space or enclosure must be fulfill at every point on the boundary of that space. In fem, Boundary conditions are basically two types they are Penalty approach and elimination approach.

2. Potential energy, π = _________
a) $$\frac{1}{2}$$QTKQ-QTF
b) QKQ-QF
c) $$\frac{1}{2}$$KQ-QF
d) $$\frac{1}{2}$$QF

Explanation: Minimum potential energy theorem states that “Of all possible displacements that satisfy the boundary conditions of a structural system, those corresponding to equilibrium configurations make the total potential energy assume a minimum value.”
Potential energy π=$$\frac{1}{2}$$QTKQ-QTF

3. Equilibrium conditions are obtained by minimizing ______
a) Kinetic energy
b) Force
c) Potential energy

Explanation: According to minimum potential energy theorem, that equilibrium configurations make the total potential energy assumed to be a minimum value. Therefore, Equilibrium conditions are obtained by minimizing Potential energy.

4. In elimination approach, which elements are eliminated from a matrix ____
a) Force
c) Rows and columns
d) Undefined

Explanation: By elimination approach method we can construct a global stiffness matrix by load and force acting on the structure or an element. Then reduced stiffness matrix can be obtained by eliminating no of rows and columns of a global stiffness matrix of an element.

5. In elimination approach method, extract the displacement vector q from the Q vector. By using ___
a) Potential energy
c) Force
d) Element connectivity

Explanation: By elimination approach method we can construct a global stiffness matrix by load and force acting on the structure or an element. Then we extract the displacement vector q from the Q vector. By using Element connectivity, and determine the element stresses.
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6. Penalty approach method is easy to implement in a ______
a) Stiffness matrix
b) Iterative equations
c) Computer program
d) Cg solving

Explanation: Penalty approach is the second approach for handling boundary conditions. This method is used to derive boundary conditions. This approach is easy to implement in a computer program and retains it simplicity even when considering general boundary conditions.

7. If Q1=a1 then a1is _________
a) Displacement
b) Symmetric
c) Non symmetric
d) Specified displacement

Explanation: In penalty approach method a1 is known as specified displacement of 1. This is used to model the boundary conditions.

8. The first step of penalty approach is, adding a number C to the diagonal elements of the stiffness matrix. Here C is a __________
a) Large number
b) Positive number
c) Real number
d) Zero

Explanation: Penalty approach is one of the method to derive boundary conditions of an element or a structure. The first step is adding a large number C to the diagonal elements of the stiffness matrix. Here C is a large number.

9. In penalty approach evaluate _______ at each support.
b) Degrees of freedom
c) Force vector
d) Reaction force

Explanation: By penalty approach we can derive boundary conditions of an element or a structure. The first step of this approach is to add a large number to the diagonal elements. Second step is to extract element displacement vector. Third step is to evaluate reaction force at each point.

10. For modeling of inclined roller or rigid connections, the method used is ___
a) Elimination approach
b) Multiple constraints
c) Penalty approach
d) Minimum potential energy theorem

Explanation: Multiple constraints is one of the method for boundary conditions it is generally used in problems for modeling inclined rollers or rigid connections.

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