Q.1
14 Marks(a)
Why FEA gives an approximate solution.
(b)
What do you understand by discretization? What are the factors to be considered for discrediting the domain ?
(c)
Explain step by step procedure for finite element method in detail.
Gujarat Technological UniversitySummer 2026 examination
GTU 3171920 Finite Element Methods Summer 2026 Question Paper & PDF
B.E. · Mechanical Engineering · Semester 7 · Subject code 3171920
- Total
- 70 marks
- To pass
- 23 marks (33%)
- Duration
- 2.5 Hours 2:30 PM – 5:00 PM
- Questions
- 5 with internal choice
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Q.2
14 Marks(a)
Enlist the three key Properties of the Global Stiffness Matrix () when assembled for a general mechanical system.
(b)
Comparison & contrast the Elimination Approach and the Penalty Approach for applying essential boundary conditions. Under what conditions is the Penalty Approach less accurate?
(c)
A 2D truss is to be analyzed. Show the element stiffness matrix in the global coordinate system. Then, detail the procedure for Skyline Assembly of the Global Stiffness Matrix, assuming a specific optimal node numbering scheme
OR
(c)
Compare the solution obtained by Galerkin’s method with exact solution for X= 0.5 and 1 for the following differential equation.
Q.3
14 Marks(a)
Draw different types of 1D, 2D and 3D elements.
(b)
Critically evaluate and justify the importance of using Symmetry and Antisymmetry conditions for FE analysis of frames, specifically focusing on the computational benefits.
(c)
Illustrate the Plane Frames element with neat sketch indicating degree of freedoms. How it is differed from beam element. Write element stiffness matrix K ,transformation matrix L and load vector F.
OR
(a)
What are the ways through which 3D problems can be reduced to a 2D approach?
(b)
Explain Evaluation of eigenvalues in dynamic consideration.
(c)
A stepped shaft is shown in figure. Determine stresses and the deflections in each of the sections. Take E=90GPa and axial force F =50KN.
Q.4
14 Marks(a)
Source of error in FEA.
(b)
For a 3D truss, formulate the modified stiffness equations for an Inclined Support- Plane Constraint (a node can only move in a defined plane). Justify why this constraint requires special treatment.
(c)
Write short notes on:Gaussian quadrature integration technique.
OR
(a)
Define shape function. What are the characteristics of shape function?
(b)
Define Iso-parametric element.
(c)
Give potential energy approach to derive beam element equation
Q.5
14 Marks(a)
Differentiate between the Axisymmetric Formulation and the Plane Stress/Strain Formulation in FEM, specifically regarding the degrees of freedom and the stress components involved.
(b)
How are the thermal effects considered in the analysis of 1 d linear elements.
(c)
Evaluate the deflection at node 2 for the truss element shown in figure.
Take AE/L value as 1000 N/mm.
OR
(a)
What is element connectivity?
(b)
Discuss the applications of Finite Element Method.
(c)
Write properties of stiffness matrix K. Show the general node numbering scheme and the half bandwidth.
Other Semester 7 subjects
BE Mechanical
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About this paper
Official Gujarat Technological University (GTU) examination paper for Finite Element Methods (Summer 2026, B.E. · Mechanical Engineering, Sem 7). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.