ME6603 - FINITE ELEMENT ANALYSIS UNIT - IV NOTES AND QUESTION BANKASHOK KUMAR RAJENDRAN
This document contains a collection of practice problems related to finite element analysis of two-dimensional vector variable problems, including axisymmetric problems. The problems cover derivation of element stiffness matrices and strain-displacement matrices for various element types under different conditions, calculation of element stresses and displacements, modeling of cylinders under pressure, and determination of global stiffness matrices for structures. The elements and conditions include constant strain triangles, linear strain triangles, axisymmetric triangles, plane stress, plane strain, and shells.
This document provides a question bank for the Finite Element Analysis course ME6603 taught at R.M.K College of Engineering and Technology. It contains 180 questions divided into two parts - Part A (short questions) and Part B (long questions). The questions cover the main topics of the course including the basic concepts and procedure of finite element analysis, discretization, element types, weighted residual methods, potential energy approach, and boundary conditions. Commercial FEA software packages and steps to use them are also discussed. The document aims to help students prepare for exams by providing a variety of questions related to the finite element method and its applications in engineering problems.
This document contains formulas and equations related to finite element analysis (FEA) for one-dimensional structural and heat transfer problems. It includes formulas for weighted residual methods, Ritz method, beam deflection and stress, springs, one-dimensional bars and frames, and one-dimensional heat transfer through walls and fins. Displacement functions, stiffness matrices, thermal loads, and conduction/convection equations are provided for linear and quadratic elements undergoing static structural and thermal analysis.
The document discusses isoparametric finite elements. It defines isoparametric, superparametric, and subparametric elements. It provides examples of shape functions for 4-noded rectangular, 6-noded triangular, and 8-noded rectangular isoparametric elements. It also discusses coordinate transformation from the natural to global coordinate system using these shape functions and calculating the Jacobian.
This document discusses two-dimensional vector variable problems in structural mechanics. It describes plane stress, plane strain and axisymmetric problems, and provides the stress-strain relations for materials under these conditions. It also discusses thin structures like disks and long prismatic shafts. Additionally, it covers dynamic analysis and vibration of structures, describing free vibration, forced vibration and types of vibration. Equations of motion are developed using Lagrange's approach and the weak form method. Mass and stiffness matrices for axial rod and beam elements are also presented.
ME6603 - FINITE ELEMENT ANALYSIS UNIT - IV NOTES AND QUESTION BANKASHOK KUMAR RAJENDRAN
This document contains a collection of practice problems related to finite element analysis of two-dimensional vector variable problems, including axisymmetric problems. The problems cover derivation of element stiffness matrices and strain-displacement matrices for various element types under different conditions, calculation of element stresses and displacements, modeling of cylinders under pressure, and determination of global stiffness matrices for structures. The elements and conditions include constant strain triangles, linear strain triangles, axisymmetric triangles, plane stress, plane strain, and shells.
This document provides a question bank for the Finite Element Analysis course ME6603 taught at R.M.K College of Engineering and Technology. It contains 180 questions divided into two parts - Part A (short questions) and Part B (long questions). The questions cover the main topics of the course including the basic concepts and procedure of finite element analysis, discretization, element types, weighted residual methods, potential energy approach, and boundary conditions. Commercial FEA software packages and steps to use them are also discussed. The document aims to help students prepare for exams by providing a variety of questions related to the finite element method and its applications in engineering problems.
This document contains formulas and equations related to finite element analysis (FEA) for one-dimensional structural and heat transfer problems. It includes formulas for weighted residual methods, Ritz method, beam deflection and stress, springs, one-dimensional bars and frames, and one-dimensional heat transfer through walls and fins. Displacement functions, stiffness matrices, thermal loads, and conduction/convection equations are provided for linear and quadratic elements undergoing static structural and thermal analysis.
The document discusses isoparametric finite elements. It defines isoparametric, superparametric, and subparametric elements. It provides examples of shape functions for 4-noded rectangular, 6-noded triangular, and 8-noded rectangular isoparametric elements. It also discusses coordinate transformation from the natural to global coordinate system using these shape functions and calculating the Jacobian.
This document discusses two-dimensional vector variable problems in structural mechanics. It describes plane stress, plane strain and axisymmetric problems, and provides the stress-strain relations for materials under these conditions. It also discusses thin structures like disks and long prismatic shafts. Additionally, it covers dynamic analysis and vibration of structures, describing free vibration, forced vibration and types of vibration. Equations of motion are developed using Lagrange's approach and the weak form method. Mass and stiffness matrices for axial rod and beam elements are also presented.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
ME6601 - DESIGN OF TRANSMISSION SYSTEM NOTES AND QUESTION BANK ASHOK KUMAR RAJENDRAN
This document contains the question bank for the subject ME6601 - Design of Transmission Systems for the sixth semester Mechanical Engineering students of RMK College of Engineering and Technology. It is prepared by R. Ashok Kumar and S. Arunkumar, faculty of the Mechanical Engineering department.
The question bank contains 190 questions divided into two parts: Part A containing conceptual questions and Part B containing design/numerical problems. The questions cover the five units of the subject - Design of Flexible Elements, Spur Gears and Parallel Axis Helical Gears, Bevel, Worm and Cross Helical Gears, Gear Boxes, and Cams, Clutches and Brakes. Most questions are related
The document contains 38 questions related to machine design. The questions cover topics such as standardization of sizes, tolerances, fits, design of joints, shafts, levers, frames and other machine elements. Design calculations are required to determine dimensions that satisfy given loading and stress criteria. Materials, their properties and appropriate factors of safety are provided. References for solutions and examples are given from standard machine design textbooks.
The document discusses stress concentration and fatigue failure in machine elements. It defines stress concentration as the localization of high stresses due to irregularities or abrupt changes in cross-section. Stress concentration can be reduced by avoiding sharp changes in cross-section and providing fillets and chamfers. Fatigue failure occurs when fluctuating stresses cause cracks over numerous load cycles. The endurance limit is the maximum stress amplitude that causes failure after an infinite number of cycles. Factors like stress concentration, surface finish, size, and mean stress affect the endurance limit. Designs should minimize stress raisers and protect against corrosion to prevent fatigue failures.
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This presentation discusses the shape function of axisymmetric elements used in finite element analysis. Axisymmetric elements are 2D elements that can model objects that are symmetric about an axis, like pressure vessels. They have advantages over full 3D modeling like smaller model size, faster computation, and easier post-processing. The presentation covers how axisymmetric elements are defined based on the radial, circumferential and longitudinal directions. It also derives the element stiffness matrix which relates displacements to forces and describes the shape functions which define element deformation based on node positions. Examples of applying axisymmetric elements to problems like pressure vessels and engine parts are provided.
The finite element method is used to solve engineering problems involving stress analysis, heat transfer, and other fields. It involves dividing a structure into small pieces called finite elements and deriving the governing equations for each element. The element equations are assembled into a global stiffness matrix and force vector. Boundary conditions are applied and the system is solved for the unknown displacements at nodes. Results like stresses, strains, and temperatures are then determined. Key steps are discretization, deriving the element stiffness matrix, assembling the global matrix, applying boundary conditions, and solving for nodal displacements.
The document discusses two-dimensional finite element analysis. It describes triangular and quadrilateral elements used for 2D problems. The derivation of the stiffness matrix is shown for a three-noded triangular element. Shape functions are presented for triangular and quadrilateral elements. Examples are provided to calculate strains for a triangular element and to determine temperatures at interior points using shape functions.
This document provides an overview of finite element analysis (FEA). It defines FEA as a numerical method for solving governing equations over the domain of a continuous physical system that is discretized into simple shapes. It lists several common structural and non-structural applications of FEA, such as stress analysis, buckling problems, vibration analysis, and heat transfer. Finally, it provides the course outline, textbooks, references, and some common FEA software packages.
Finite Element analysis -Plate ,shell skew plate S.DHARANI KUMAR
This document provides an overview of plate and shell theory and finite element analysis for plates and shells. It discusses the assumptions and applications of thin plate theory, thick plate theory, and shell theory. It also describes different types of finite elements that can be used to model plates and shells, including plate, shell, solid shell, curved shell, and degenerated shell elements. Additionally, it covers skew plates and different discretization methods that can be used for finite element analysis of skew plates.
The document discusses numerical methods for solving structural mechanics problems, specifically the Rayleigh Ritz method. It provides an overview of the Rayleigh Ritz method, indicating that it is an integral approach that is useful for solving structural mechanics problems. The document then provides a step-by-step example of using the Rayleigh Ritz method to determine the bending moment and deflection at the mid-span of a simply supported beam subjected to a uniformly distributed load over the entire span.
This document contains a question bank for the Design of Machine Elements course covering various topics in 5 units. It includes over 180 questions related to steady and variable stresses in machine members, shafts and couplings, joints, energy storing elements, and bearings. The questions cover topics such as stress analysis, materials selection, fits and tolerances, failure theories, stress concentration, fatigue design, and design of common machine components. The document also lists the textbook and references used for the course.
INTRODUCTION TO FINITE ELEMENT ANALYSISAchyuth Peri
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a system into small elements and solving for variables within each element. This allows for analysis of complex geometries, loadings, and materials. The FEM process includes discretizing the system, selecting functions to approximate the solution, assembling element equations into a global system, applying boundary conditions, and calculating displacements, stresses, and strains. FEA offers advantages like analyzing irregular shapes and nonlinear problems, reducing testing costs, and optimizing designs.
ME6503 - DESIGN OF MACHINE ELEMENTS TWO MARKS QUESTIONS WITH ANSWERS ASHOK KUMAR RAJENDRAN
This document contains a question bank with multiple choice questions and answers related to the Design of Machine Elements course. It covers topics from the first unit on steady and variable stresses in machine elements. The questions are about materials selection factors, mechanical properties, common engineering materials, classification of machine designs, definitions of terms like loads, stresses, strains and more. The document is prepared by R. Ashok Kumar for the RMK College of Engineering and Technology.
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
One of the most Simple and Interesting topics in Engineering is FEA. My work will guide average students to score good marks. I have given you full package which includes 2 Marks and Question Banks of previous year. All the Best
For Guidance : Comment Below Happy to Teach and Learn along with you guys
This document contains a question bank for the course CE6451 - Fluid Mechanics and Machinery. It includes 80 questions related to fluid properties and flow characteristics that cover topics like fluid classification, density, viscosity, vapor pressure, compressibility, and flow concepts. The questions are multiple choice or short answer and are intended to assess students' understanding of key concepts in fluid mechanics.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
ME6601 - DESIGN OF TRANSMISSION SYSTEM NOTES AND QUESTION BANK ASHOK KUMAR RAJENDRAN
This document contains the question bank for the subject ME6601 - Design of Transmission Systems for the sixth semester Mechanical Engineering students of RMK College of Engineering and Technology. It is prepared by R. Ashok Kumar and S. Arunkumar, faculty of the Mechanical Engineering department.
The question bank contains 190 questions divided into two parts: Part A containing conceptual questions and Part B containing design/numerical problems. The questions cover the five units of the subject - Design of Flexible Elements, Spur Gears and Parallel Axis Helical Gears, Bevel, Worm and Cross Helical Gears, Gear Boxes, and Cams, Clutches and Brakes. Most questions are related
The document contains 38 questions related to machine design. The questions cover topics such as standardization of sizes, tolerances, fits, design of joints, shafts, levers, frames and other machine elements. Design calculations are required to determine dimensions that satisfy given loading and stress criteria. Materials, their properties and appropriate factors of safety are provided. References for solutions and examples are given from standard machine design textbooks.
The document discusses stress concentration and fatigue failure in machine elements. It defines stress concentration as the localization of high stresses due to irregularities or abrupt changes in cross-section. Stress concentration can be reduced by avoiding sharp changes in cross-section and providing fillets and chamfers. Fatigue failure occurs when fluctuating stresses cause cracks over numerous load cycles. The endurance limit is the maximum stress amplitude that causes failure after an infinite number of cycles. Factors like stress concentration, surface finish, size, and mean stress affect the endurance limit. Designs should minimize stress raisers and protect against corrosion to prevent fatigue failures.
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This presentation discusses the shape function of axisymmetric elements used in finite element analysis. Axisymmetric elements are 2D elements that can model objects that are symmetric about an axis, like pressure vessels. They have advantages over full 3D modeling like smaller model size, faster computation, and easier post-processing. The presentation covers how axisymmetric elements are defined based on the radial, circumferential and longitudinal directions. It also derives the element stiffness matrix which relates displacements to forces and describes the shape functions which define element deformation based on node positions. Examples of applying axisymmetric elements to problems like pressure vessels and engine parts are provided.
The finite element method is used to solve engineering problems involving stress analysis, heat transfer, and other fields. It involves dividing a structure into small pieces called finite elements and deriving the governing equations for each element. The element equations are assembled into a global stiffness matrix and force vector. Boundary conditions are applied and the system is solved for the unknown displacements at nodes. Results like stresses, strains, and temperatures are then determined. Key steps are discretization, deriving the element stiffness matrix, assembling the global matrix, applying boundary conditions, and solving for nodal displacements.
The document discusses two-dimensional finite element analysis. It describes triangular and quadrilateral elements used for 2D problems. The derivation of the stiffness matrix is shown for a three-noded triangular element. Shape functions are presented for triangular and quadrilateral elements. Examples are provided to calculate strains for a triangular element and to determine temperatures at interior points using shape functions.
This document provides an overview of finite element analysis (FEA). It defines FEA as a numerical method for solving governing equations over the domain of a continuous physical system that is discretized into simple shapes. It lists several common structural and non-structural applications of FEA, such as stress analysis, buckling problems, vibration analysis, and heat transfer. Finally, it provides the course outline, textbooks, references, and some common FEA software packages.
Finite Element analysis -Plate ,shell skew plate S.DHARANI KUMAR
This document provides an overview of plate and shell theory and finite element analysis for plates and shells. It discusses the assumptions and applications of thin plate theory, thick plate theory, and shell theory. It also describes different types of finite elements that can be used to model plates and shells, including plate, shell, solid shell, curved shell, and degenerated shell elements. Additionally, it covers skew plates and different discretization methods that can be used for finite element analysis of skew plates.
The document discusses numerical methods for solving structural mechanics problems, specifically the Rayleigh Ritz method. It provides an overview of the Rayleigh Ritz method, indicating that it is an integral approach that is useful for solving structural mechanics problems. The document then provides a step-by-step example of using the Rayleigh Ritz method to determine the bending moment and deflection at the mid-span of a simply supported beam subjected to a uniformly distributed load over the entire span.
This document contains a question bank for the Design of Machine Elements course covering various topics in 5 units. It includes over 180 questions related to steady and variable stresses in machine members, shafts and couplings, joints, energy storing elements, and bearings. The questions cover topics such as stress analysis, materials selection, fits and tolerances, failure theories, stress concentration, fatigue design, and design of common machine components. The document also lists the textbook and references used for the course.
INTRODUCTION TO FINITE ELEMENT ANALYSISAchyuth Peri
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a system into small elements and solving for variables within each element. This allows for analysis of complex geometries, loadings, and materials. The FEM process includes discretizing the system, selecting functions to approximate the solution, assembling element equations into a global system, applying boundary conditions, and calculating displacements, stresses, and strains. FEA offers advantages like analyzing irregular shapes and nonlinear problems, reducing testing costs, and optimizing designs.
ME6503 - DESIGN OF MACHINE ELEMENTS TWO MARKS QUESTIONS WITH ANSWERS ASHOK KUMAR RAJENDRAN
This document contains a question bank with multiple choice questions and answers related to the Design of Machine Elements course. It covers topics from the first unit on steady and variable stresses in machine elements. The questions are about materials selection factors, mechanical properties, common engineering materials, classification of machine designs, definitions of terms like loads, stresses, strains and more. The document is prepared by R. Ashok Kumar for the RMK College of Engineering and Technology.
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
One of the most Simple and Interesting topics in Engineering is FEA. My work will guide average students to score good marks. I have given you full package which includes 2 Marks and Question Banks of previous year. All the Best
For Guidance : Comment Below Happy to Teach and Learn along with you guys
This document contains a question bank for the course CE6451 - Fluid Mechanics and Machinery. It includes 80 questions related to fluid properties and flow characteristics that cover topics like fluid classification, density, viscosity, vapor pressure, compressibility, and flow concepts. The questions are multiple choice or short answer and are intended to assess students' understanding of key concepts in fluid mechanics.
This document contains a question bank for the Design of Transmission Systems course with 70 multiple choice questions covering various topics in Unit 1 on the design of flexible elements such as belts, chains, and wire ropes. The questions assess students' understanding of key concepts like the different types of belts and their materials, belt ratings, tension ratio calculations, crowning of pulleys, V-belt specifications and advantages over flat belts, chain drive components, and chordal action. Examples of applications and limitations of different flexible elements are also provided. The question bank is intended to help students prepare for exams in this subject.
ANNA UNIVERSITY TWO MARK QUSTIONS WITH ANSWERS FOR FLUID MECHANICS AND MACHIN...ASHOK KUMAR RAJENDRAN
This document contains 33 two-mark questions and answers related to fluid properties and flow characteristics from the subject CE6451 – Fluid Mechanics and Machinery. The questions cover topics like definitions of fluid, classification of fluids, properties of ideal and real fluids, Newtonian and non-Newtonian fluids, viscosity, density, specific gravity, kinematic viscosity and more. The answers to each question are brief and provide the key details to help understand the concepts being asked about. This appears to be a study material document compiled by faculty to help students prepare for their exams on this subject.
This document contains questions related to manufacturing technology and processes such as metal casting, welding, and fabrication. It begins with 75 multiple choice and short answer questions on metal casting processes including defining casting, listing common metals and pattern materials used, types of patterns, cores, moulds, and furnaces. It then continues with 58 similar questions on welding and fabrication processes such as defining welding types, listing equipment, classifying welding processes like arc, gas, resistance and more, as well as questions on brazing, soldering and adhesive bonding. The document concludes with 15 longer answer/essay questions requiring explanations and comparisons of various casting, welding and fabrication topics.
This document contains a question bank for the Finite Element Analysis course ME6603 at Sri Eshwar College of Engineering. It includes 33 questions in Part A and 13 multi-part questions in Part B related to Unit 1 on introductions to FEA. The questions cover topics like the basis of FEA, weighted residual methods, discretization, degrees of freedom, potential energy, boundary conditions, interpolation functions, refinement, and solving sample problems using techniques like Galerkin's method and Rayleigh-Ritz method. The document provides the question number, topic covered, cognitive level, and month/year when the question can be asked.
This document contains questions from past exams on the topic of unconventional machining processes. It is divided into 5 units which cover various unconventional processes like ultrasonic machining, abrasive jet machining, electrical discharge machining, electrochemical machining, plasma arc machining and laser beam machining. The questions range from short definitions and explanations to longer discussions of specific processes and comparisons of different unconventional processes. The document serves as a study guide for students by providing examples of question types that may appear on exams for this subject.
This document proposes an analytical framework called FESM for evaluating and comparing elastic similarity measures for time series pattern recognition. FESM has three main components: 1) It classifies elastic similarity measures into two approaches - those based on Lp norms and those based on matching thresholds. 2) It evaluates the classified similarity measures using proposed qualitative criteria. 3) It determines the appropriate application scopes for the classified similarity measures. FESM is intended to help users quickly understand and select the best existing elastic similarity measure for a given time series pattern recognition task.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
1. The document analyzes the vibration of beams subjected to moving point loads using finite element analysis and the Newmark numerical time integration method.
2. It investigates the effect of load speed on the dynamic magnification factor, defined as the ratio of maximum dynamic displacement to static displacement.
3. The effect of spring stiffness at beam-column junctions is also evaluated. Computer codes in Matlab are developed to calculate dynamic responses and critical load velocities.
Acoustical modeling of urban building designNisha Verma
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Vibration analysis and response characteristics of a half car model subjected...editorijrei
This document summarizes the modeling and analysis of a half car model subjected to sinusoidal road excitation. It describes:
1) Developing a two degree-of-freedom half car model considering bounce and pitch motions, with driver body coupled to vehicle body.
2) Deriving the governing equations of motion using Lagrange's equations and kinetic and potential energies.
3) Setting up and solving the matrix equation of motion for the half car model parameters and excitation inputs.
This document contains questions from past exams on the topic of production planning and control. It is divided into 5 units which cover introductory concepts, work study, production planning and process planning, production scheduling, and inventory control. The questions range from definitions and short explanations to longer discussions requiring analyses. The document serves as a study guide for students, with questions at different levels of difficulty in each unit to test comprehension of key production planning and control topics.
This document discusses forecasting Indian monsoon rainfall using artificial neural networks (ANN). It summarizes previous research using statistical and dynamical models to forecast Indian monsoon rainfall, noting limitations. The document then proposes a new ANN model to forecast southwest monsoon (SWM) rainfall that incorporates within-year seasonal variability from pre-monsoon and northeast monsoon rainfall, in addition to year-to-year variability. It presents rainfall data from all India as well as two regions and one subdivision for modeling and validation of the new ANN approach.
Acoustic Emission Education Program by Boris Muravinmboria
The document proposes an academic program for training acoustic emission specialists. The 494-hour program covers AE fundamentals, materials science, AE equipment and applications, and data analysis methods through 12 courses over one academic year. It aims to systematically develop students' knowledge in the theoretical and technological aspects of the multidisciplinary field of acoustic emission.
This document presents a mathematical model and analysis of the vibration response characteristics of a half car model subjected to different sinusoidal road excitations. The half car model is modeled as a two degree of freedom system, considering bounce and pitch motions. Lagrange's equations are used to derive the governing equations of motion. The natural frequencies of the system are calculated. MATLAB is used to simulate the dynamic response of the vehicle for different road bump amplitudes and vehicle velocities. The results show that vibration amplitude increases with bump amplitude and velocity up to a point, after which amplitude decreases with further increases in velocity.
Instance Space Analysis for Search Based Software EngineeringAldeida Aleti
Search-Based Software Engineering is now a mature area with numerous techniques developed to tackle some of the most challenging software engineering problems, from requirements to design, testing, fault localisation, and automated program repair. SBSE techniques have shown promising results, giving us hope that one day it will be possible for the tedious and labour intensive parts of software development to be completely automated, or at least semi-automated. In this talk, I will focus on the problem of objective performance evaluation of SBSE techniques. To this end, I will introduce Instance Space Analysis (ISA), which is an approach to identify features of SBSE problems that explain why a particular instance is difficult for an SBSE technique. ISA can be used to examine the diversity and quality of the benchmark datasets used by most researchers, and analyse the strengths and weaknesses of existing SBSE techniques. The instance space is constructed to reveal areas of hard and easy problems, and enables the strengths and weaknesses of the different SBSE techniques to be identified. I will present on how ISA enabled us to identify the strengths and weaknesses of SBSE techniques in two areas: Search-Based Software Testing and Automated Program Repair. Finally, I will end my talk with future directions of the objective assessment of SBSE techniques.
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The document discusses the Computer Aided Machine Drawing Lab Manual of R.M.K College of Engineering and Technology. It includes information about the drawing standards, welding symbols, and types of joints used in machine drawings. The objectives of the lab are also mentioned which involve studying drawing standards, limits, fits and tolerances. The document lists various assembly drawings exercises like couplings, screw jack, tailstock etc. that will be covered in the lab along with the syllabus.
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The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
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Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
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geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
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china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
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governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
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ME6603 - FINITE ELEMENT ANALYSIS UNIT - I NOTES AND QUESTION BANK
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73. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 3
UNIT – I – INTRODUCTION
PART – A
1.1) What is the finite element method?
1.2) How does the finite element method work?
1.3) What are the main steps involved in FEA. [AU, April / May – 2011]
1.4) Write the steps involved in developing finite element model.
1.5) What are the basic approaches to improve a finite element model?
[AU, Nov / Dec – 2010]
1.6) What are the methods generally associated with the finite element analysis?
[AU, May / June – 2016]
1.7) Write any two advantages of FEM Analysis. [AU, Nov / Dec – 2012]
1.8) What are the methods generally associated with finite element analysis?
1.9) List any four advantages of finite element method. [AU, April / May – 2008]
1.10) What are the applications of FEA? [AU, April / May – 2011]
1.11) Define finite difference method.
1.12) What is the limitation of using a finite difference method? [AU, April / May – 2010]
1.13) Define finite volume method.
1.14) Differentiate finite element method from finite difference method.
1.15) Differentiate finite element method from finite volume method.
1.16) What do you mean by discretization in finite element method?
1.17) What is discretization? [AU, Nov / Dec – 2010, 2015]
1.18) What is meant by node or joint? [AU, May / June – 2014]
1.19) What is meant by node? [AU, Nov / Dec – 2015, 2016]
1.20) List the types of nodes. [AU, May / June – 2012]
1.21) Define degree of freedom.
1.22) What is meant by degrees of freedom? [AU, Nov / Dec – 2012]
74. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 4
1.23) State the advantage of finite element method over other numerical analysis
methods.
1.24) State the fields to which FEA solving procedure is applicable.
1.25) What is a structural and non-structural problem?
1.26) Distinguish between 1D bar element and 1D beam element.
[AU, Nov / Dec – 2009, May / June – 2011]
1.27) Write the equilibrium equation for an elemental volume in 3D including the body
force.
1.28) How to write the equilibrium equation for a finite element? [AU, Nov / Dec – 2012]
1.29) Classify boundary conditions. [AU, Nov / Dec – 2011]
1.30) What are the types of boundary conditions?
1.31) What do you mean by boundary condition and boundary value problem?
1.32) Write the difference between initial value problem and boundary value problem.
1.33) What are the different types of boundary conditions? Give examples.
[AU, May / June – 2012]
1.34) List the various methods of solving boundary value problems.
[AU, April / May – 2010, Nov / Dec – 2016]
1.35) Write down the boundary conditions of a cantilever beam AB of span L fixed at A
and free at B subjected to a uniformly distributed load of P throughout the span.
[AU, May / June – 2009, 2011]
1.36) Briefly explain force method and stiffness method.
1.37) What is aspect ratio?
1.38) Write a short note on stress – strain relation.
1.39) Write down the stress strain relationship for a three dimensional stress field.
[AU, April / May – 2011]
75. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 5
1.40) If a displacement field in x direction is given by 𝑢 = 2𝑥2
+ 4𝑦2
+ 6𝑥𝑦 Determine
the strain in x direction. [AU, May / June – 2016]
1.41) State the effect of Poisson’s ratio.
1.42) Define total potential energy of an elastic body.
1.43) What is the stationary property of total potential energy? [AU, May / June – 2016]
1.44) Write the potential energy for beam of span L simply supported at ends, subjected
to a concentrated load P at mid span. Assume EI constant.
[AU, April / May, Nov / Dec – 2008]
1.45) State the principle of minimum potential energy.
[AU, Nov / Dec – 2007, 2013, April / May – 2009]
1.46) State the principle of minimum potential energy theorem. [AU, May / June – 2016]
1.47) How will you obtain total potential energy of a structural system?
[AU, April / May – 2011, May / June – 2012]
1.48) Write down the potential energy function for a three dimensional deformable body
in terms of strain and displacements. [AU, May / June – 2009]
1.49) What should be considered during piecewise trial functions?
[AU, April / May – 2011]
1.50) What do you understand by the term “piecewise continuous function”?
[AU, Nov / Dec – 2013]
1.51) Write about weighted residual method. [AU, May / June – 2016]
1.52) Distinguish between the error in solution and Residual. [AU, April / May – 2015]
1.53) Name the weighted residual methods. [AU, Nov / Dec – 2011]
1.54) List the various weighted residual methods. [AU, Nov / Dec – 2014]
1.55) What is the use of Ritz method? [AU, Nov / Dec – 2011]
1.56) What is Rayleigh – Ritz method?
[AU, May / June – 2014, Nov / Dec – 2015, 2016]
76. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 6
1.57) Mention the basic steps of Rayleigh-Ritz method. [AU, April / May – 2011]
1.58) Highlight the equivalence and the difference between Rayleigh Ritz method and the
finite element method. [AU, Nov / Dec – 2012]
1.59) Distinguish between Rayleigh Ritz method and finite element method.
[AU, Nov / Dec – 2013]
1.60) Distinguish between Rayleigh Ritz method and finite element method with regard
to choosing displacement function. [AU, Nov / Dec – 2010]
1.61) Compare the Ritz technique with the nodal approximation method.
[AU, Nov / Dec – 2014]
1.62) Why are polynomial types of interpolation functions preferred over trigonometric
functions? [AU, April / May – 2009, May / June – 2013]
1.63) What is meant by weak formulation? [AU, May / June – 2013]
1.64) What are the advantage of weak formulation? [AU, April / May – 2015]
1.65) Define the principle of virtual work.
1.66) Differentiate Von Mises stress and principle stress.
1.67) What do you mean by constitutive law?[AU, Nov / Dec – 2007, April / May – 2009]
1.68) What are h and p versions of finite element method?
1.69) What is the difference between static and dynamic analysis?
1.70) Mention two situations where Galerkin’s method is preferable to Rayleigh – Ritz
method. [AU, Nov / Dec – 2013]
1.71) What is Galerkin method of approximation? [AU, Nov / Dec – 2009]
1.72) What is a weighted resuidal method? [AU, Nov / Dec – 2010]
1.73) Distinguish between potential energy and potential energy functional.
1.74) What are the types of Eigen value problems? [AU, May / June – 2012]
1.75) Name a few FEA packages. [AU, Nov / Dec – 2014]
1.76) Name any four FEA software
77. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 7
PART – B
1.77) Explain the step by step procedure of FEA. [AU, Nov / Dec – 2010]
1.78) Explain the general procedure of finite element analysis. [AU, Nov / Dec – 2011]
1.79) List and briefly describe the general steps of the finite element method.
[AU, May / June – 2014]
1.80) Briefly explain the stages involved in FEA.
1.81) Explain the step by step procedure of FEM. [AU, Nov / Dec – 2011]
1.82) List out the general procedure for FEA problems. [AU, May / June – 2012]
1.83) Compare FEM with other methods of analysis. [AU, Nov / Dec – 2010]
1.84) Define discretization. Explain mesh refinement. [AU, Nov / Dec – 2010]
1.85) Explain the various aspects pertaining to discretization, process in finite element
modeling analysis. [AU, Nov / Dec – 2013]
1.86) Explain the process of discretization of a structure in finite element method in
detail, with suitable illustrations for each aspect being & discussed.
[AU, Nov / Dec – 2012]
1.87) Discuss procedure using the commercial package (P.C. Programs) available today
for solving problems of FEM. Take a structural problem to explain the same.
[AU, Nov / Dec – 2011]
1.88) State the importance of locating nodes in finite element model.
[AU, Nov / Dec – 2011]
1.89) Write briefly about weighted residual methods. [AU, Nov / Dec – 2015]
1.90) Write a brief note on the following.
(a) isotropic material
(b) orthotropic material
(c) anisotropic material
78. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 8
1.91) What are initial and final boundary value problems? Explain.
[AU, Nov / Dec – 2010]
1.92) Explain the Potential Energy Approach [AU, Nov / Dec – 2010]
1.93) Explain the principle of minimization of potential energy. [AU, Nov / Dec – 2011]
1.94) Explain the four weighted residual methods. [AU, Nov / Dec – 2011]
1.95) Explain Ritz method with an example. [AU, April / May – 2011]
1.96) Explain Rayleigh Ritz and Galerkin formulation with example.
[AU, May / June – 2012]
1.97) Write short notes on Galerkin method? [AU, April / May – 2009]
1.98) Discuss stresses and equilibrium of a three dimensional body.
[AU, May / June – 2012]
1.99) Derive the element level equation for one dimensional bar element based on the
station- of a functional. [AU, May / June – 2012]
1.100) Derive the characteristic equations for the one dimensional bar element by using
piece-wise defined interpolations and weak form of the weighted residual method?
[AU, May / June – 2012]
1.101) Develop the weak form and determine the displacement field for a cantilever beam
subjected to a uniformly distributed load and a point load acting at the free end.
[AU, Nov / Dec – 2013]
1.102) Explain Gaussian elimination method of solving equations.
[AU, April / May – 2011]
1.103) Write briefly about Gaussian elimination? [AU, April / May – 2009]
1.104) The following differential equation is available for a physical phenomenon.
𝑑
𝑑𝑥
(𝑥
𝑑𝑢
𝑑𝑥
) −
2
𝑥2
= 0, 1 ≤ 𝑥 ≤ 2
Boundary conditions are, x = 1 u = 2
79. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 9
x = 2 𝑥
𝑑𝑢
𝑑𝑥
= −
1
2
Find the value of the parameter a, by the following methods.
(i) Collocation (ii) Sub – Domain (iii) Least Square
(iv) Galerkin
1.105) The following differential equation is available for a physical phenomenon.
𝑑2
𝑦
𝑑𝑥2
+ 50 = 0, 0 ≤ 𝑥 ≤ 10
Trial function is 𝑦 = 𝑎1 𝑥(10 − 𝑥)
Boundary conditions are, y (0) = 0 y (10) = 0
Find the value of the parameter a, by the following methods.
(i) Collocation (ii) Sub – Domain (iii) Least Square
(iv) Galerkin
1.106) Discuss the following methods to solve the given differential equation :
𝐸𝐼
𝑑
2
𝑦
𝑑𝑥2
𝑀( 𝑥) = 0
with the boundary condition y(0) = 0 and y(H) = 0
(i) Variant method (ii) Collocation method. [AU, April / May – 2010]
1.107) The differential equation of a physical phenomenon is given by
𝑑2
𝑦
𝑑𝑥2
+ 𝑦 = 4𝑥, 0 ≤ 𝑥 ≤ 1
The boundary conditions are: y(0)=0; y(1)=1; Obtain one term approximate solution
by using Galerkin's method of weighted residuals.
[AU, May / June – 2014, 2016, Nov / Dec – 2016]
80. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 10
1.108) Find the approximate deflection of a simply supported beam under a uniformly
distributed load ‘P‘ throughout its span. Using Galerkin and Least square residual
method. [AU, May / June – 2011]
1.109) Solve the differential equation for a physical problem expressed as
𝑑2 𝑦
𝑑𝑥2 + 100 =
0, 0 ≤ 𝑥 ≤ 10 with boundary conditions as y (0) = 0 and y (10) = 0 using
(i) Point collocation method
(ii) Sub domain collocation method
(iii) Least squares method and
(iv) Galerkin method. [AU, May / June – 2013]
1.110) Solve the differential equation for a physical problem expressed as
𝑑2 𝑦
𝑑𝑥2 + 50 =
0, 0 ≤ 𝑥 ≤ 10 with boundary conditions as y (0) = 0 and y (10) = 0 using the
trail function 𝑦 = 𝑎1 𝑥 (10 − 𝑥) Find the value of the parameters a1 by the
following methods.
(i) Point collocation method
(ii) Sub domain collocation method
(iii) Least squares method and
(iv) Galerkin method. [AU, Nov / Dec – 2011]
1.111) Solve the following equation using a two – parameter trial solution by the
(a) Collocation method (𝑅 𝑑 = 0 𝑎𝑡 𝑥 =
1
3
𝑎𝑛𝑑 𝑥 =
2
3
)
(b) Galerkin method.
Then, compare the two solutions with the exact solution
𝑑𝑦
𝑑𝑥
+ 𝑦 = 0, 0 ≤ 𝑥 ≤ 1
y (0) = 1
1.112) Determine the Galerkin approximation solution of the differential equation
81. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 11
𝐴
𝑑2 𝑢
𝑑𝑥2 + 𝐵
𝑑𝑢
𝑑𝑥
+ 𝐶 = 0, 𝑢(0) = 𝑢( 𝑙) = 0
1.113) Solve the following differential equation using Galerkin’s method.
D
𝑑2 𝜑
𝑑𝑥2 + 𝑄 = 0, 0 ≤ 𝑥 ≤ 𝐿
subjected to 𝜑(0) = 𝜑0 𝑎𝑛𝑑 𝜑( 𝐿) = 𝜑1 [AU, April / May – 2011]
1.114) A physical phenomenon is governed by the differential equation
𝑑2 𝑤
𝑑𝑥2 − 10𝑥2
= 5 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 1 The boundary conditions are given by
𝑤(0) = 𝑤(1) = 0. By taking two-term trial solution as 𝑤( 𝑥) = 𝑐1 𝑓1( 𝑥) +
𝑐2 𝑓2(𝑥) with, 𝑓1( 𝑥) = 𝑥 ( 𝑥 − 1) 𝑎𝑛𝑑 𝑓2 = 𝑥2
(𝑥 − 1) find the solution of
the problem using the Galerkin method. [AU, Nov / Dec – 2009]
1.115) Determine the two parameter solution of the following using Galerkin method.
𝑑2 𝑦
𝑑𝑥2 = − cos 𝜋𝑥 , 0 ≤ 𝑥 ≤ 1, 𝑢(0) = 𝑢(1) = 0 [AU, Nov / Dec – 2012]
1.116) The following differential equation is available for a physical phenomenon.
𝑑2
𝑦
𝑑𝑥2
− 10𝑥2
= 5, 0 ≤ 𝑥 ≤ 1
With boundary conditions y (0) = 0, y (l) = 1. Find an approximate solution of the
above differential equation by using Galerkin's method of weighted residuals and
also compare with exact solution [AU, May / June – 2016]
1.117) A physical phenomenon is governed by the differential equation
𝑑2 𝑤
𝑑𝑥2 − 10𝑥2
=
5 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 1. The boundary conditions are given by w (0) = w (1) = 0.
Assuming a trail function 𝑤(𝑥) = 𝑎0 + 𝑎1 𝑥 + 𝑎2 𝑥2
+ 𝑎3 𝑥3
. Determine using
Garlerkin method the variation of “w” with respect to “x”. [AU, Nov / Dec – 2016]
1.118) Using Collocation method, find the maximum displacement of the tapered rod as
shown in Fig. E = 2 *107
N/cm2
ρ = 0.075N/cm3
[AU, Nov / Dec – 2014]
82. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 12
1.119) A cantilever beam of length L is loaded with a point load at the free end. Find the
maximum deflection and maximum bending moment using Rayleigh-Ritz method
using the function 𝑦 = 𝐴{ 1 − cos (
𝜋𝑥
2𝐿
)} Given: EI is constant.
[AU, April / May – 2008]
1.120) Compute the slope deflection and reaction forces for the cantilever beam of length
L carrying uniformly distributed load of intensity 'fo'. [AU, Nov / Dec – 2014]
1.121) A simply supported beam carries uniformly distributed load over the entire span.
Calculate the bending moment and deflection. Assume EI is constant and compare
the results with other solution. [AU, Nov / Dec – 2012]
1.122) Determine the expression for deflection and bending moment in a simply supported
beam subjected to uniformly distributed load over entire span. Find the deflection
and moment at midspan and compare with exact solution using Rayleigh-Ritz
method. Use 𝑦 = 𝑎1 sin (
𝜋𝑥
𝑙
) + 𝑎2 sin (
3𝜋𝑥
𝑙
) [AU, Nov / Dec – 2008]
1.123) Compute the value of central deflection in the figure below by assuming
𝑦 =
𝑎𝑠𝑖𝑛𝜋𝑥
𝐿
The beam is uniform throughout and carries a central point load P.
[AU, Nov / Dec – 2007, April / May – 2009]
83. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 13
1.124) A concentrated load P = 50 kN is applied at the centre of a fixed beam of length 3
m, depth 200 mm and width 120 mm. Calculate the deflection and slope at the
midpoint. Assume E = 2 x 105
N/mm2
[AU, May / June – 2016]
1.125) A beam AB of span '1' simply supported at ends and carrying a concentrated load W
at the centre C as shown in fig. Determine the deflection at midspan by using
Rayleigh-Ritz method and compare with exact solution
[AU, May / June – 2016, Nov / Dec – 2016]
1.126) If a displacement field is described by
𝑢 = (−𝑥2
+ 2𝑦2
+ 6𝑥𝑦)10−4
𝑣 = (3𝑥 + 6𝑦 − 𝑦2)10−4
Determine the direct strains in x and y directions as well the shear strain at the point
x = 1, y =0. [AU, April / May – 2011]
1.127) In a solid body, the six components of the stress at a point are given by x= 40
MPa, y = 20 MPa, z = 30 MPa, yz = -30 MPa, xz = 15 MPa and xy = 10 MPa.
Determine the normal stress at the point, on a plane for which the normal is (nx, ny,
nz) = ( ½, ½, 2
1 )
1.128) In a plane strain problem, we have
x = 20,000 psi y = - 10,000 psi E = 30 x 10 6
psi, = 0.3.
84. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 14
Determine the value of the stress z.
1.129) For the spring system shown in figure, calculate the global stiffness matrix,
displacements of nodes 2 and 3, the reaction forces at node 1 and 4. Also calculate
the forces in the spring 2. Assume, k1 = k3 = 100 N/m, k2 = 200 N/m, u1 = u4= 0 and
P=500 N. [AU, April / May – 2010]
1.130) Use the Rayleigh – Ritz method to find the displacement of the midpoint of the rod
shown in figure. [AU, April / May – 2011]
1.131) Consider the differential equation
𝑑2 𝑦
𝑑𝑥2 + 400𝑥2
= 0 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 1 subject
to boundary conditions 𝑦(0) = 0; 𝑦(1) = 0 The functional corresponding to this
problem, to be extremized is given by 𝐼 = ∫ {−0.5 (
𝑑𝑦
𝑑𝑥
)
2
+ 400𝑥2
𝑦
1
0
1.132) Find the solution of the problem using Rayleigh-Ritz method by considering a two-
term solution as 𝑦( 𝑥) = 𝑐1 𝑥 (1 − 𝑥) + 𝐶2 𝑥2
(1 − 𝑥) [AU, Nov / Dec – 2009]
1.133) A bar of uniform cross section is clamped at one end and left free at the other end. It
is subjected to a uniform load axial load P as shown in figure. Calculate the
85. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 15
displacement and stress in the bar using three terms polynomial following Ritz
method. Compare the results with exact solutions. [AU, May / June – 2011]
1.134) A simply Supported beam subjected to uniformly distributed load over entire span
and it is subjected to a point load at the centre of the span. Calculate the deflection
using Rayleigh-Ritz method and compare with exact solutions.
[AU, May / June – 2013]
1.135) A simply Supported beam subjected to uniformly distributed load over entire span
as shown in figure. Calculate the bending moment and deflection at midspan using
Rayleigh-Ritz method. [AU, Nov / Dec – 2015, 2016]
1.136) A simply supported beam (span L and flexural rigidity EI) carries two equal
concentrated loads at each of the quarter span points. Using Raleigh – Ritz method
determine the deflections under the two loads and the two end slopes.
[AU, April / May – 2009]
1.137) Analyze a simply supported beam subjected to a uniformly distributed load
throughout using Rayleigh Ritz method. Adopt one parameter trigonometric
function. Evaluate the maximum deflection and bending moment and compare with
exact solution. [AU, Nov / Dec – 2010]
86. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 16
1.138) Solve for the displacement field for a simply supported beam, subjected to a
uniformly distributed load using Rayleigh – Ritz method. [AU, Nov / Dec – 2013]
1.139) Derive the governing equation for a tapered rod fixed at one end and subjected to its
own self weight and a force P at the other end as shown in fig. Let the length of the
bar be l and let the cross section vary linearly from A1 at the top fixed end to A2 at
the free end. E and γ represents the Young’s modulus and specific weight of the
material of the bar. Convert this equation into weak form and hence determine the
matrices for solving using Ritz technique. [AU, April / May – 2015]
1.140) Use the Rayleigh – Ritz method to find the displacement field u(x) of the rod as
shown below. Element 1 is made of aluminum and element 2 is made of steel. The
properties are
Eal = 70 GPa A1 = 900 mm2
L1 = 200 mm
Est = 200 GPa A2 = 1200 mm2
L2 = 300 mm
Load = P = 10,000 N. Assume a piecewise linear displacement.
87. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 17
Field u = a1 + a2x for 0 x 200 mm, and u = a3 + a4 x for 200 x 500 mm.
1.141) A fixed beam length of 2L m carries a uniformly distributed load of a w(in N / m)
which run over a length of ‘L’ m from the fixed end, as shown in Figure. Calculate
the rotation at point B using FEA. [AU, Nov / Dec – 2011]
1.142) A rod fixed at its ends is subjected to a varying body force as shown in Figure. Use
the Rayleigh-Ritz method with an assumed displacement field 𝑢( 𝑥) = 𝑎0 +
𝑎1 𝑥 + 𝑎2 𝑥2
to find the displacement u(x) and stress σ(x). Plot the variation of the
stress in the rod. [AU, Nov / Dec – 2012]
1.143) A uniform rod subjected to a uniform axial load is illustrated in Figure. The
deformation of the bar is governed by the differential equation given below.
Determine the displacement using weighted residual method.
[AU, April / May – 2011]
88. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 18
1.144) A steel rod is attached to rigid walls at each end and is subjected to a distributed
load T(x) as shown below.
a) Write the expression for potential energy.
b) Determine the displacement u(x) using the Rayleigh – Ritz method.
Assume a displacement field u(x) = a0 + a1 x + a2 x2
.
1.145) Derive the stress – strain relation and strain – displacement relation for an element
in space.
1.146) Derive the equation of equilibrium in case of a three dimensional stress system.
[AU, Nov / Dec – 2008]
1.147) What is constitutive relationship? Express the constitutive relations for a linear
elastic isotropic material including initial stress and strain. [AU, Nov / Dec – 2009]
1.148) Give a detailed note on the following:
(a) Rayleigh Ritz method (b) Galerkin method
(c) Least square method and (d) Collocation method
1.149) Determine using any Weighted Residual technique the temperature distribution
along the circular fin of length 6cm and 1cm. the fin is attached to a boiler whose
wall temperature is 140ºC and the free end is insulated. Assume the convection
coefficient h = 10 W/cm2
ºC. Conduction coefficient K = 70 W/ cm ºC and T∞ =
40ºC. The governing equation for the heat transfer through the fin is given by
−
𝑑
𝑑𝑥
[𝐾𝐴(𝑥)
𝑑𝑇
𝑑𝑥
] + ℎ𝑝(𝑥)(𝑇 − 𝑇∞) = 0 Assume appropriate boundary conditions
and calculate the temperatures at every 1cm from the left end.
[AU, April / May – 2015]
89. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 19
1.150) Give a one – parameter Galerkin solution of the following equation, for the two
domain’s shown below. .1
2
2
2
2
y
u
x
u
1.151) Find the Eigen values and Eigen vectors of the matrix.
[
𝟑 −𝟏 𝟎
−𝟏 𝟐 −𝟏
𝟎 −𝟏 𝟑
]
1.152) Find the Eigen values and Eigen vectors of the matrix.
[
𝟑 𝟏𝟎 𝟓
−𝟐 −𝟑 −𝟒
𝟑 𝟓 𝟕
]
1.153) Find the Eigen value and the corresponding Eigen vector of 𝐴 = [
1 6 1
1 2 0
0 0 3
]
[AU, May / June – 2016]
1.154) Describe the Gaussian elimination method of solving equations.
[AU, April / May – 2011]
1.155) Explain the Gaussian elimination method for the solving of simultaneous linear
algebraic equations with an example. [AU, April / May – 2008]
1.156) Solve the following system of equations using Gauss elimination method.
[AU, Nov / Dec – 2010]
x1 – x2 + x3 = 1
90. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ ME6603 / VI / MECH / JAN – MAY 2017
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 20
-3x1 + 2x2 – 3x3 = -6
2x1 – 5x2 + 4x3 = 5
1.157) Solve the following system of equations by Gauss Elimination method.
2x1 – 2x2 – x4 = 1
2x2 + x3 + 2x4 = 2
x1 – 2x2 + 3x3 – 2x4 = 3 [AU, May / June – 2012]
x2 + 2x3 + 2x4 = 4
1.158) Solve the following equations by Gauss elimination method.
28r1 + 6r2 = 1
6r1 + 24r2 + 6r3 = 0
6r2 + 28r3 + 8r4 = -1
8r3 + 16r4 = 10 [AU, Nov / Dec – 2010, 2012]
1.159) Use the Gaussian elimination method to solve the following simultaneous
equations:
4x1 + 2x2 – 2x3 – 8x4 = 4
x1 + 2x2 + x3 = 2
0.5x1 – x2 + 4x3 + 4x4 = 10
–4x1 – 2x2 – x4 = 0 [AU, April / May – 2009]
1.160) Solve the following system of equations using Gauss elimination method.
x1 + 3x2 + 2x3 = 13
– 2x1 + x2 – x3 = –3
- 5x1 + x2 + 3x3 = 6 [AU, Nov / Dec – 2009]