# Finite Element Method Questions and Answers – Three Dimensional Problems – Hexa Hedral Elements and Higher Order Elements

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Three Dimensional Problems – Hexa Hedral Elements and Higher Order Elements”.

1. Usage of higher order elements complicates a given finite element method problem.
a) True
b) False

Explanation: The given statement is false. Usage of higher order elements actually simplifies a given finite element method problem. These elements are capable of capturing more complex data and reduce the number of elements required to solve a given problem.

2. Which of the following is an advantage of using higher order elements?
a) Cleaner geometric interpolations
b) More complex software
c) Pre and post processing issues
d) Probable issues with parallel solution methodologies

Explanation: Cleaner geometric interpolations is one of the many advantages of using higher order elements in finite element analysis. Some other advantages include – continuous shape function derivatives, rapid convergence and natural means of mesh refinement.

3. How can a lower order element be converted into a higher order one?
a) Adding a node in the end of each side of the linear element
b) Subtracting a node in the middle of each side of the linear element
c) Multiplying a node in the middle of each side of the linear element
d) Adding a node in the middle of each side of the linear element

Explanation: Lower order or linear elements can be converted into higher order ones. This can be achieved by adding a node in the middle of each side of the linear element. For a 4 noded quadrilateral, terms like 1, ξ, η, ξη are added; whereas, for an 8 noded higher order element ξ2η, ξη2 are added for higher accuracy.

4. Which of the following is an example of a higher order element?
a) Eight noded rectangle
b) Cantilever beam
c) Shell
d) 1D Truss

Explanation: The Eight noded rectangle is an example of a higher order element. It clearly has higher number of nodes, which makes it is a higher order element. All the other elements – Beam, Shell and the 1D Truss are examples of linear or lower order elements.

5. Which of the following defines a hexahedral element?
a) Element with 8 corners, 12 edges and 6 faces
b) Element with 4 corners, 12 edges and 6 faces
c) Element with 8 corners, 5 edges and 6 faces
d) Element with 8 corners, 12 edges and 10 faces

Explanation: A hexahedral element is one which has 8 corners, 12 edges and 6 faces. It is used to obtain refined mesh and better results in the finite element method. The hexahedral element can also be classified into a higher order element.
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6. Which of the following are limitations of using higher order elements?
a) Cost of computation, time taken for calculation
b) Accuracy of results
c) Increase in the number of elements used
d) Decrease in the number of elements used

Explanation: Even though higher order elements have a lot of advantages over their linear counterparts, they have some limitations as well. Cost of computation of such elements is on the higher side as the infrastructure today doesn’t have scope for the same. Time taken for calculation is going to be more, due to the complex nature of such elements.

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