...Introduction to Finite Element Analysis (FEA) or Finite Element Method (FEM) Finite Element Analysis (FEA) or Finite Element Method (FEM) The Finite Element Analysis (FEA) is a numerical method for solving problems of engineering and mathematical physics. Useful for problems with complicated geometries, loadings, and material properties where analytical solutions can not be obtained. The Purpose of FEA Analytical Solution • • Stress analysis for trusses, beams, and other simple structures are carried out based on dramatic simplification and idealization: – mass concentrated at the center of gravity – beam simplified as a line segment (same cross-section) Design is based on the calculation results of the idealized structure & a large safety factor (1.5-3) given by experience. FEA • Design geometry is a lot more complex; and the accuracy requirement is a lot higher. We need – To understand the physical behaviors of a complex object (strength, heat transfer capability, fluid flow, etc.) – To predict the performance and behavior of the design; to calculate the safety margin; and to identify the weakness of the design accurately; and – To identify the optimal design with confidence Brief History Grew out of aerospace industry Post-WW II jets, missiles, space flight Need for light weight structures Required accurate stress analysis Paralleled growth of computers Common FEA Applications Mechanical/Aerospace/Civil/Automotive ...
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...Circuit Analysis using the Node and Mesh Methods We have seen that using Kirchhoff’s laws and Ohm’s law we can analyze any circuit to determine the operating conditions (the currents and voltages). The challenge of formal circuit analysis is to derive the smallest set of simultaneous equations that completely define the operating characteristics of a circuit. In this lecture we will develop two very powerful methods for analyzing any circuit: The node method and the mesh method. These methods are based on the systematic application of Kirchhoff’s laws. We will explain the steps required to obtain the solution by considering the circuit example shown on Figure 1. R1 + Vs R3 R2 R4 _ Figure 1. A typical resistive circuit. The Node Method. A voltage is always defined as the potential difference between two points. When we talk about the voltage at a certain point of a circuit we imply that the measurement is performed between that point and some other point in the circuit. In most cases that other point is referred to as ground. The node method or the node voltage method, is a very powerful approach for circuit analysis and it is based on the application of KCL, KVL and Ohm’s law. The procedure for analyzing a circuit with the node method is based on the following steps. 1. Clearly label all circuit parameters and distinguish the unknown parameters from the known. 2. Identify all nodes of the circuit. 3. Select a node as the reference node also called the ground and...
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...Concurrent Courses: None Course Outline Revision Date: Fall 2010 Course Description: This is a calculus-based course in electric circuit theory and analysis for Engineering AS degree program students interested in pursuing computer or electrical engineering. It includes DC and AC principles with an emphasis on Kirchhoff's Laws, network theorems for resistive, capacitive, and inductive networks, mesh and nodal analysis, and sinusoidal steady-state analysis. Also, power, resonance, and ideal transformers are studied. The theory is reinforced with instructor-run demos. Assignments include the use of circuit analysis computer software. Course Goals: Upon successful completion of this course, students should be able to do the following: 1. analyze passive electric circuits to predict their behavior; 2. identify, analyze, and solve technical problems in linear systems; and 3. use state-of-the-art technology to solve problems in linear systems. Measurable Course Performance Objectives (MPOs): Upon successful completion of this course, students should specifically be able to do the following: 1. Analyze passive electric circuits to predict their behavior: 1. use mesh analysis to calculate the voltages and currents in a circuit with two or more voltage sources; 2. use nodal analysis to calculate the voltages and currents in a circuit with two or more current sources; 3. calculate and graph the transient response (to a...
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...DESIGN AND ANALYSIS OF A CHASSIS FOR A 60 TON PAY LOAD Abstract: As the chassis frame forms the backbone of a heavy vehicle, its principal function is to safely carry the maximum load for all designed operating conditions. To achieve a satisfactory performance, the construction of a chassis is the result of careful design and rigorous testing. Various manufacturers have individual design concepts and different methods of achieving the desired performance standards for the complete chassis, not all chassis components are interchangeable between various makes and models of vehicles. So, there is no standard design for chassis frame. Even though start with the chassis frame design start with selection of the section for side rails and cross members. In this paper we have designed a chassis for storage cum resting fixture. Storage cum resting fixture is a structure of length 11000mm & width 2300mm, used to store cylindrical specimens of various sizes and weights in horizontal configuration. The storage cum resting fixture is used to carry the propellant stored in the cylindrical specimens. The trolley fixture should be designed for a maximum pay load of 60 tons. The Objective of my project is to design a chassis for a pay load of 60 Tons. The design process involves manual design calculations, 3d modeling using UNIGRAPHICS software and analysis to validate the design. Ansys package has been implemented to perform the structural analysis. ...
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...Chapter 3, Problem 1. Determine Ix in the circuit shown in Fig. 3.50 using nodal analysis. 1 kΩ Ix 9V + _ 2 kΩ + _ 6V 4 kΩ Figure 3.50 For Prob. 3.1. Chapter 3, Solution 1 Let Vx be the voltage at the node between 1-kΩ and 4-kΩ resistors. 9 − Vx 6 − Vx Vk + = 1k 4k 2k Vx Ix = = 3 mA 2k ⎯⎯ Vx = 6 → PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 3, Problem 2. For the circuit in Fig. 3.51, obtain v1 and v2. Figure 3.51 Chapter 3, Solution 2 At node 1, − v1 v1 v − v2 − = 6+ 1 10 5 2 At node 2, 60 = - 8v1 + 5v2 (1) v2 v − v2 = 3+ 6+ 1 4 2 Solving (1) and (2), v1 = 0 V, v2 = 12 V 36 = - 2v1 + 3v2 (2) PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter...
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...Electrical Circuit Analysis – Part A Name: Student Num. Due Date: Table of Contents Introduction 3 1.0 Mesh Analysis 4 1.1 Determining mesh currents 4 1.2 Determining Nodal Voltage 5 1.2.1 Node A 5 1.2.2 Node B 6 2.0 Thevenin’s Theorem 6 2.1 Application of Thevenin’s Theorem 6 3.0 Comparing and Analysis of Results 9 3.1 Results 9 3.2 Analysis 9 Introduction The purpose of this assignment is to analyse a DC circuit provided and ascertain certain properties within the circuit. To do this will require the application of Mesh Analysis, Thevenin’s Theorem and simple DC Theory... 1.0 Mesh Analysis Applying mesh analysis to the circuit will determine the currents that flow through each of the three meshes provided. From these current values, simple DC theorem will be applied using Ohm’s law in order to calculate the voltage of node A and node B with respect to the ground node. 1.1 Determining mesh currents The following steps will outline what will be required to calculate mesh 1, 2 and 3 currents. 1. Observing the circuit, use Kirchhoff’s voltage rule to determine each mesh into a formula resulting in three separate formulas. Mesh 1 20(i1-2) + 20(i1-i3) + 50(i1-i2) = 0 90i1 - 50i2 - 20i3 = 40 Mesh 2 50(i2-i1) + 25i2 + 26 = 0 -50i1 + 75i2 = -26 Mesh 3 30i3 – 25 + 20(i3-i1) = 0 -20i1 + 50i3 = 25 2. Once completed simplify each formula by dividing by 10 in order to make calculations much simpler. Mesh 1 9i1 - 5i2 – 2i3...
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... Abucejo, Jervic B. Antinopo, James Arbil E. Digamon, Rosie Gay S. ABSTRACT This study aimed to design a low cost “Laboratory Modules for Circuit Courses in St. Paul University Surigao” to help engineering students developed their skills and knowledge regarding built-in laboratory experiments. This study is entitled Laboratory Modules for Circuit Courses in St. Paul University Surigao, was aimed to developed a better understanding of electronic circuit analysis and implement a simulation of actual...
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...civil, and mechanical engineering. In spite of the presence of local stiffeners in different structures, the analysis of stiffened frames is scarce in the literature. The effect of local stiffeners on the stability of frame structures is investigated in this paper using detailed modelling of columns. A stiffener reduces the flexibility of a stiffened column. It is a common practice to model a stiffened column by a system of springs in series. This system is not suitable for simulating stiffness in finite element models. Consequently, this has been replaced by an equivalent parallel spring system. The parallel system is used in studying the effects of stiffener on the stability of a structural frame. The exact formulation for simple system is mapped onto the real structure and the exact finite element formulation is derived. The effect of stiffeners on the stability analysis of structural frames is considered and the governing equations are derived. For simple members, a closed form solution and, for stiffened structural frames, the finite element formulation have been proposed. The formulation is implemented in a computer programme. The accuracy, efficiency, and robustness of the presented formulation work are verified using case studies. Keywords: stiffener; stiffener factor; finite element; step function; Dirac delta; stability; buckling. Introduction Buckling analysis is a technique used to determine buckling loads-critical loads at which a structure becomes unstable-and...
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...transfer in Cartesian coordinate [pic] + [pic] = 0 The above equation can be put in the finite difference form. We divide the medium of interest into a number of small regions and apply the heat equation to these regions. Each sub-region is assigned a reference point called a node or a nodal point. The average temperature of a nodal point is then calculated by solving the resulting equations from the energy balance. Accurate solutions can be obtained by choosing a fine mesh with a large number of nodes. We will discuss an example from Incropera’s1 text to illustrate the method. Example 2.1-1 A long column with thermal conductivity k = 1 W/m(oK is maintained at 500oK on three surfaces while the remaining surface is exposed to a convective environment with h = 10 W/m2(oK and fluid temperature T(. The cross sectional area of the column is 1 m by 1 m. Using a grid spacing (x = (y = 0.25 m, determine the steady-state temperature distribution in the column and the heat flow to the fluid per unit length of the column. Solution The cross sectional area of the column is divided into many sub-areas called a grid or nodal network with 25 nodes as shown in Figure 2.1-1. There are 12 nodal points with unknown temperature, however only 8 unknowns need to be solved due to symmetry so that the nodes to the left of the centerline are the same as those to the right. [pic] Figure 2.1-1 The grid for the column cross sectional area. The energy balance is now applied to...
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...EXPERIMENT # 1 OBJECTIVE: The Basic DC Circuit and the use of an Instrument for the Measurement of Voltage, Current and Resistance. Equipment Required: • Circuit #1 of D3000 - 1.1 DC Circuits-1 Module • Shorting links and connecting leads. • Multimeter. CIRCUIT DIAGRAM: [pic] [pic] THEORY: Measurement of Voltage: [pic] Voltage is measured using a multimeter set to a voltage range, or using a dedicated instrument called a voltmeter. The meter is connected across (in parallel with) the circuit component under test as shown in Fig 1.2. With analog meters, the meter leads must be connected with the correct polarity, as indicated in Fig 1.2. If the lead polarity is incorrect, the pointer will try to move in the wrong direction and the meter could be permanently damaged. With digital multimeters however, should the meter be connected with incorrect polarity, damage will not occur, and a - symbol is shown on the display. Measurement of Current: [pic] Current is measured using a multimeter set to a current range, or using a dedicated instrument called an ammeter. The meter is connected in series with the circuit so that the circuit current flows through the meter as shown in Fig 1.3. Measurement of Resistance: Resistance is measured using a multimeter set to a resistance range, or a dedicated instrument called an ohmmeter. The meter is connected across the resistor being measured as shown in Fig 1.4. [pic] ...
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...ANALYSIS OF CIRCUIT (EE001-3-1) Instructions: • This assignment is to be carried out individually Learning Outcomes ON COMPLETION OF THE MODULE YOU SHOULD BE ABLE TO DEMONSTRATE THE FOLLOWING LEARNING OUTCOMES: | | |ABLE TO UNDERSTAND, AND BE ABLE TO APPLY BOTH ANALYSIS AND DESIGN THE OVERALL PROCESS OF DESIGN, INCLUDING MODELING AND COMPONENT | |DESCRIPTION. | | | |ABLE TO UNDERSTAND PASSIVE AND ACTIVE COMPONENTS. | | | |ABLE TO UNDERSTAND AND APPLY KIRCHHOFF’S LAWS, NODAL AND MESH ANALYSIS. | | | |ABLE TO UNDERSTAND THE OPERATION AND APPLICATIONS OF OPERATIONAL AMPLIFIER. | | ...
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...Introduction to Finite Element Method Mathematic Model Finite Element Method Historical Background Analytical Process of FEM Applications of FEM Computer Programs for FEM 1. Mathematical Model (1) Modeling Physical Problems Mathematica l Model Solution Identify control variables Assumptions (empirical law) (2) Types of solution Sol. Eq. Exact Sol. Approx. Sol. Exact Eq. Approx. Eq. ◎ ◎ ◎ ◎ (3) Methods of Solution (3) Method of Solution A. Classical methods They offer a high degree of insight, but the problems are difficult or impossible to solve for anything but simple geometries and loadings. B. Numerical methods (I) Energy: Minimize an expression for the potential energy of the structure over the whole domain. (II) Boundary element: Approximates functions satisfying the governing differential equations not the boundary conditions. (III) Finite difference: Replaces governing differential equations and boundary conditions with algebraic finite difference equations. (IV) Finite element: Approximates the behavior of an irregular, continuous structure under general loadings and constraints with an assembly of discrete elements. 2. Finite Element Method (1) Definition FEM is a numerical method for solving a system of governing equations over the domain of a continuous physical system, which is discretized into simple geometric shapes called finite element. Continuous system Time-independent PDE Time-dependent...
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...Chapter 2 Introduction to Rotor Dynamics Rotor dynamics is the branch of engineering that studies the lateral and torsional vibrations of rotating shafts, with the objective of predicting the rotor vibrations and containing the vibration level under an acceptable limit. The principal components of a rotor-dynamic system are the shaft or rotor with disk, the bearings, and the seals. The shaft or rotor is the rotating component of the system. Many industrial applications have flexible rotors, where the shaft is designed in a relatively long and thin geometry to maximize the space available for components such as impellers and seals. Additionally, machines are operated at high rotor speeds in order to maximize the power output. The first recorded supercritical machine (operating above first critical speed or resonance mode) was a steam turbine manufactured by Gustav Delaval in 1883. Modern high performance machines normally operates above the first critical speed, generally considered to be the most important mode in the system, although they still avoid continuous operating at or near the critical speeds. Maintaining a critical speed margin of 15 % between the operating speed and the nearest critical speed is a common practice in industrial applications. The other two of the main components of rotor-dynamic systems are the bearings and the seals. The bearings support the rotating components of the system and provide the additional damping needed to stabilize the system and contain...
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...ANALYSIS OF CONTACT STRESS OF SPUR GEAR BY FEM 1 Dr. JITENDRA KUMAR PANDEY, 2 CHANDRA PRAKASH 1 Associate Professor 2 M. Tech Student, Mechanical Engineering Department NRIIST BHOPAL (M.P) India Email: 1jitendra.me@gmail.com, 2chandraprakash210@gmail.com Abstract: Gears which are most widely used for transmission of power from one shaft to the shaft are considered in this paper for analysis and hence predict the stresses in them using the most versatile numerical techniques in practice, the Finite Element Method (FEM). In all spur gears are the most preferred type of gear because of simplicity of use & manufacturing with high degree of transmission efficiency. They develop high stress concentration at the root and the point of contact...
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...Tsukerman*a, F. Čajkoa, A.P. Sokolovb Department of Electrical & Computer Engineering, The University of Akron, OH 44325-3904, USA b Department of Polymer Science, The University of Akron, OH 44325-3909, USA ABSTRACT Several classes of computational methods are available for computer simulation of electromagnetic wave propagation and scattering at optical frequencies: Discrete Dipole Approximation, the T-matrix − Extended Boundary Condition methods, the Multiple Multipole Method, Finite Difference (FD) and Finite Element (FE) methods in the time and frequency domain, and others. The paper briefly reviews the relative advantages and disadvantages of these simulation tools and contributes to the development of FD methods. One powerful tool – FE analysis − is applied to optimization of plasmon-enhanced AFM tips in apertureless near-field optical microscopy. Another tool is a new FD calculus of “Flexible Local Approximation MEthods” (FLAME). In this calculus, any desirable local approximations (e.g. scalar and vector spherical harmonics, Bessel functions, plane waves, etc.) are seamlessly incorporated into FD schemes. The notorious ‘staircase’ effect for slanted and curved boundaries on a Cartesian grid is in many cases eliminated – not because the boundary is approximated geometrically on a fine grid but because the solution is approximated algebraically by suitable basis functions. Illustrative examples include problems with plasmon nanoparticles and a photonic crystal with a waveguide...
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