This set of Finite Element Method Questions and Answers for Freshers focuses on “Assembly of Global Stiffness Matrix for the Banded & Skyline Solutions”.

1. What is a banded matrix?

a) Sparse matrix

b) Rectangular matrix

c) Unit matrix

d) Square matrix

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Explanation: In matrix theory band matrix is a sparse matrix, whose non-zero entities are confined to a diagonal band. Comprising the main diagonal and zero are more diagonals on either side.

2. Skyline matrix storage is in the form of ______

a) Banded matrix

b) Sparse matrix

c) Singular matrix

d) Identity matrix

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Explanation: In scientific computing, skyline matrix storage or SKS or a variable banded matrix storage or envelope storage scheme is form of a sparse matrix storage format matrix that reduces the storage requirement of matrix more than banded storage.

3. Symmetry and sparsity of the global stiffness matrix can be approached by _____ methods.

a) One

b) Three

c) Two

d) Four

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Explanation: In assembly of global stiffness matrix, the solution for finite element equations can take advantage of symmetry and sparsity of global stiffness matrix. There are two methods to identify them. They are banded approach and skyline approach methods.

4. Which of these was one of the methods for determining assembly of global stiffness matrix?

a) Galerkin approach

b) Skyline approach

c) Rayleigh method

d) Assembly method

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Explanation: In assembly of global stiffness matrix, there are two methods to determine the global stiffness matrices. They are banded approach and skyline approach. In which the assembly procedure of the matrix was easy.

5. In banded matrix, elements are _____ placed in stiffness matrix.

a) Singular

b) Determinant values

c) Directly

d) Indirectly

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Explanation: A band matrix is a sparse matrix whose non zero entities are confined to a diagonal band comprising the main diagonal and zero or more diagonals on either side. In the banded approach, the elements of each element stiffness matrix K

^{e}are directly placed in banded matrix S.

6. In Skyline matrix, the elements in a stiffness matrix can be placed in _______

a) Direct values

b) Determinant values

c) Load values

d) Vector form

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Explanation: In skyline matrix storage, or SKS or, variable band matrix storage or, envelope storage scheme is a form of a sparse matrix that reduces the storage requirement of the matrix more than banded storage. In skyline approach, the elements of K

^{e}are placed in a vector form with certain identification pointers.

7. Formula for maximum span or half band width in banded approach is _____

a) m_{e}=[|i-j|+1]

b) \(\frac{y_2-y_1}{l_e}\)

c) q^{‘}=lq

d) m_{e}=[2|i-j|+1]

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Explanation: The matrix has a given band width what we mean is that the band width is at most the quantity, not that it is necessarily exactly equal to that quantity. In a banded approach, half band width is as given

m

_{e}=[2|i-j|+1]

8. The first step of skyline assembly matrix involves evaluation of ____

a) Column height

b) Row height

c) Matrix height

d) Undefined

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Explanation: Skyline assembly matrix scheme of form of a sparse matrix that reduces the storage requirement of a matrix than banded approach. The first step of skyline assembly involves the evaluation of the skyline height or the column height for each diagonal location.

9. The second step in skyline approach is assembling the element stiffness values into _____

a) Row vector

b) Identity vector

c) Column vector

d) Determinant vector

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Explanation: Skyline assembly matrix scheme of form of sparse matrix that reduces the storage requirement of a matrix than banded approach. The second step in skyline approach is assembling the element stiffness values into column vector.

10. The details of a skyline assembly matrix are implemented in a program called ____

a) Boolean program

b) Cholesky program

c) Truss program

d) Trussky program

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Explanation: As this assembly was done to trusses by default all the steps applied in skyline approach were implemented in program TRUSSKY.

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