Important RGPV Question
ME-504(C), Finite Element Method
V Sem, ME
UNIT 1- Introduction
Q.1) What is structural analysis? What are its objectives?
Q.2) Differentiate between static, dynamic, and kinematic analyses.
Q.3) Distinguish between skeletal and continuum structures. Give examples.
Q.4) Explain the concept of degrees of freedom (DOF) in structural analysis.
Q.5) How can an infinite DOF system be modeled into a finite DOF system?
Q.6) Outline the basic steps involved in the finite element method.
Q.7) What are the advantages and limitations of the finite element method?
Q.8) Explain the concept of discretization in the finite element method.
Q.9) What is the role of shape functions in the finite element method?
Q.10) Discuss the concept of element stiffness matrix and global stiffness matrix.
Q.11) What are the various engineering fields where the finite element method is widely used?
Q.12) How can the finite element method be used to analyze complex structures with irregular geometries and loading conditions?
Q.13) Discuss the role of boundary conditions in finite element analysis.
Q.14) Explain the concept of convergence and accuracy in finite element solutions.
Q.15) How can the finite element method be used to analyze nonlinear problems?
UNIT 2- Element Types and Characteristics
Q.1) What is meant by discretization of a domain?
Q.2) Explain the concept of meshing in finite element analysis.
Q.3) Discuss the factors influencing mesh quality.
Q.4) What are the advantages and disadvantages of different meshing techniques (e.g., structured, unstructured)?
Q.5) Describe the different types of 1D, 2D, and 3D elements used in FEA.
Q.6) Explain the concept of parent element and physical element.
Q.7) Discuss the advantages and disadvantages of different element shapes (e.g., triangular vs. quadrilateral).
Q.8) What is aspect ratio, and why is it important in FEA?
Q.9) How does aspect ratio affect the accuracy and convergence of FEA solutions?
Q.10) What are the guidelines for choosing appropriate aspect ratios for different element types?
UNIT 3- Assembly of Elements and Matrices
Q.1) What is the concept of element assembly in the Finite Element Method?
Q.2) Explain the difference between local and global coordinate systems.
Q.3) How are the element stiffness matrices and load vectors assembled into global matrices?
Q.4) Describe the process of imposing boundary conditions on the global system of equations.
Q.5) Define local and global coordinate systems.
Q.6) How are local coordinates transformed to global coordinates?
Q.7) Explain the role of transformation matrices in element assembly.
Q.8) What is the significance of coordinate transformation in finite element analysis?
Q.9) Define bandwidth in the context of finite element analysis.
Q.10) How does bandwidth affect the efficiency of solving the system of equations?
Q.11) Discuss techniques to reduce bandwidth, such as nodal renumbering.
Q.12) Explain the impact of bandwidth on computational cost and storage requirements.
Q.13) What is banded and skyline storage?
Q.14) How are banded and skyline matrices formed during element assembly?
Q.15) Explain the advantages of using banded and skyline storage over full matrix storage.
Q.16) Discuss the implementation of banded and skyline solvers.
Q.17) Describe the finite element formulation for one-dimensional problems (e.g., bar element, beam element).
Q.18) Explain the finite element formulation for two-dimensional problems (e.g., plane stress, plane strain, axisymmetric problems).
UNIT 4- Higher Order and Isoparametric Elements
Q.1) Explain the concept of natural coordinate systems and their significance in finite element analysis.
Q.2) Derive the shape functions for a one-dimensional quadratic element and a two-dimensional quadratic triangular element using natural coordinates.
Q.3) What is isoparametric formulation? How does it differ from subparametric and superparametric formulations?
Q.4) Explain the concept of Jacobian matrix and its role in isoparametric mapping.
Q.5) Discuss the various numerical integration techniques (Gauss quadrature, etc.) used in finite element analysis.
Q.6) Explain how numerical integration is applied to evaluate element stiffness and mass matrices.
Q.7) What are the necessary conditions for convergence in finite element analysis?
Q.8) Explain the role of mesh refinement and element order in achieving accurate solutions.
Q.9) Compare and contrast the advantages and disadvantages of using higher-order elements over lower-order elements.
Q.10) Derive the shape functions for a one-dimensional cubic element and a two-dimensional cubic triangular element.
Q.11) Explain the concept of serendipity elements and their application in 2D analysis.
Q.12) Derive the shape functions for a four-node quadrilateral element and an eight-node quadrilateral element.
Q.13) Explain the concept of Lagrange elements and their application in 2D analysis.
Q.14) What are the continuity requirements (C0, C1, etc.) for different types of elements?
Q.15) Explain the concept of compatible elements and their importance in finite element analysis.
Q.16) Discuss the practical applications of higher-order and isoparametric elements in structural analysis, heat transfer, and fluid mechanics.
Q.17) How can you choose the appropriate element type and order for a given problem?
Q.18) Explain the sources of error in finite element analysis, including discretization error and numerical integration error.
Q.19) How can error analysis be used to improve the accuracy of finite element solutions?
Q.20) Derive the shape functions for a three-node triangular element and a six-node triangular element.
UNIT 5- Static & Dynamic Analysis
Q.1) Explain the method of joints and method of sections for analyzing trusses.
Q.2) Discuss the concept of static indeterminacy and its implications in structural analysis.
Q.3) Describe the finite element method (FEM) and its application in analyzing complex structures.
Q.4) How can commercial software packages like ANSYS or ABAQUS be used to analyze trusses and frames? What are their advantages and limitations?
Q.5) Derive the equation of motion for a single degree of freedom (SDOF) system using Newton’s second law of motion.
Q.6) Explain the concept of natural frequency and mode shape for a vibrating system.
Q.7) What is Rayleigh’s quotient, and how can it be used to estimate the fundamental frequency of a vibrating system?
Q.8) Describe the finite element formulation for dynamic analysis, including the derivation of mass and stiffness matrices.
Q.9) How can modal analysis be used to predict the dynamic response of a structure to external excitations?
Q.10) Discuss the application of commercial software packages like ANSYS or MATLAB in solving dynamic analysis problems.
— Best of Luck for Exam —
