# Finite Element Method Questions and Answers – Two Dimensional Problem Modelling and Boundary Conditions

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This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Two Dimensional Problem Modelling and Boundary Conditions”.

1. Finite element method is used for computing _____ and _____
a) Stress and strain
b) Nodes and displacement
c) Nodes and elements
d) Displacement and strain

Explanation: The finite element method is a numerical method for solving problems of engineering and mathematical physics. To solve the problem it subdivides a larger problem into smaller, simpler parts that are called finite elements.

2. In deformation of the body, the symmetry of ______ and symmetry of ____ can be used effectively.
a) Stress and strain
b) Nodes and displacement
c) Geometry and strain

Explanation: Deformation changes in an object’s shape or form due to the application of a force or forces. Deformation proportional to the stress applied within the elastic limits of the material.

3. For a circular pipe under internal or external pressure, by symmetry all points move _____
b) Linearly
c) Circularly
d) Along the pipe

Explanation: The boundary conditions require that points along x and n are constrained normal to the two lines respectively. If a circular pipe under internal or external pressure, by symmetry all the points move radially.

4. Boundary conditions can be easily considered by using _______
a) Rayleigh method
b) Penalty approach method
c) Galerkin approach
d) Potential energy approach

Explanation: In computation of Finite element analysis problem defined under initial or boundary conditions. For implementation of boundary conditions we need a staggered grid.

5. When dividing an area into triangles, avoid large _____
a) Dimensions
c) Aspect ratios
d) Boundary conditions

Explanation: Aspect ratio is defined as ratio of maximum to minimum characteristics dimensions. For this reason we can avoid large aspect ratios when dividing an area into triangles.

6. In dividing the elements a good practice may be to choose corner angles in the range of ____
a) 30-120°
b) 90-180°
c) 25-75°
d) 45-180°

Explanation: The best elements are those that approach an equilateral triangular configuration. Such configurations are usually not possible. A good practice is to choose corner angle in the range of 30-120°.

7. Stresses can be change widely at ____
a) Large circular sections
b) Notches and fillets
c) Corners
d) Crystals

Explanation: In a structure geometrical notches, such as holes cannot be avoided. The notches are causing in a homogeneous stress distribution, as notches fillets are also a cause for in homogenous stress distribution.

8. The Constant strain triangle can give____ stresses on elements.
a) Linear
b) Constant
c) Uniform
d) Parallel

Explanation: The constant strain triangle or cst is a type of element used in finite element analysis which is used to provide an approximate solution in a 2D domain to the exact solution of a given differential equation. By this we get constant stresses on elements.

9. The _____ can be obtained even with coarser meshes by plotting and extrapolating.
a) Minimum stresses
b) Minimum strain
c) Maximum stresses
d) Maximum strain

Explanation: Coarse mesh is more accurate in getting values. The smaller elements will better represent the distribution. Better estimates of maximum stress may be obtained even with coarser meshes. Coarse meshes are recommended for initial trails.

10. Coarser meshes are recommended for _____
b) Notches and fillets
c) Crystals
d) Initial trails

Explanation: The smaller elements will better represent the distribution. Coarse mesh is more accurate in getting values. Better estimates of maximum stress may obtained even with the coarse meshes.

11. Increasing the number of nodes in coarse mesh regions where stress variations are high, should give better results. This method is called _____
a) Divergence
b) Convergence
c) Convergent- divergent
d) Un defined 