QUIZ 2_Finite Element Method

What is the primary purpose of the Finite Element Method (FEM) in engineering?

• To provide exact solutions to differential equations

• To approximate solutions for complex engineering problems

• To replace experimental testing in all cases

• To eliminate the need for boundary conditions

How does FEM simplify the analysis of complex structures?

• By solving equations directly without any approximations

• By discretizing structures into smaller elements connected at nodes

• By assuming that all materials behave linearly

• By using only one type of element for all problems

Which of the following is NOT a category of FEM elements?

• Line elements

• Surface elements

• Volume elements

• Fluid elements

Why are quadrilateral (QUAD) and hexahedral (HEX) elements preferred over triangular (TRI) and tetrahedral (TET) elements?

• They require fewer nodes and provide more accurate results

• They are easier to generate for complex geometries

• They are always computationally cheaper

• They allow for infinite refinement

What is the difference between ‘plane stress’ and ‘plane strain’ elements in FEM?

• Plane stress elements are used in 3D modeling, while plane strain elements are for 2D modeling

• Plane stress assumes zero stress in one direction, while plane strain assumes zero strain in one direction

• Plane stress is only used for static problems, while plane strain is for dynamic problems

• There is no difference between the two

Why is discretization an essential step in FEM?

• It helps in reducing computational cost

• It transforms complex differential equations into solvable algebraic equations

• It ensures that all materials behave elastically

• It removes the need for boundary conditions

What is the primary role of boundary conditions in an FEM simulation?

• They determine the type of element used

• They define constraints like supports, forces, and temperatures

• They are only necessary for nonlinear problems

• They automatically refine the mesh

What is the main disadvantage of using linear tetrahedral (TET4) elements?

• They require too many nodes

• They are overly stiff and can lead to inaccurate results

• They do not work with complex geometries

• They cannot be used in structural analysis

Which of the following numerical methods is commonly used to solve FEM equations?

• Euler’s Method

• Gaussian Elimination

• Newton’s Law

• Simpson’s Rule

Why are quadratic (second-order) elements preferred over linear (first-order) elements in FEM?

• They are computationally cheaper

• They have fewer degrees of freedom

• They provide more accurate solutions by including mid-side nodes

• They do not require meshing