Finite Element Method
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Fem lecture
The document provides an introduction to finite element analysis. It discusses the need for computational methods to solve problems involving complex geometries and boundary conditions that cannot be solved through closed-form analytical methods. The finite element method is introduced as a numerical technique that involves discretizing a continuous domain into discrete subdomains called elements, and approximating variations in dependent variables within each element. This allows setting up algebraic equations that can be solved to approximate the continuous solution. Advantages of the finite element method include its ability to model complex shapes and behaviors, and refine solutions through mesh refinement. Basic concepts such as element types, discretization, and derivation of element equations are described.
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The document discusses various numerical methods for analyzing mechanical components under applied loads, including the finite element method. It describes weighted residual methods like the Galerkin method and collocation method which approximate solutions by minimizing residuals. The variational or Rayleigh-Ritz method selects displacement fields to minimize total potential energy. The finite element method divides a structure into small elements and applies these methods to obtain approximate solutions for displacements and stresses at discrete points.
Multiple Degree of Freedom (MDOF) Systems
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
Finite element method vs classical method 1
The document provides an introduction to the finite element method. It compares the finite element method to classical methods and the finite difference method. Some key differences highlighted include:
- Classical methods obtain exact solutions for simple cases while finite element methods obtain approximate solutions for all problems.
- Finite element methods can handle problems with complex geometry, multi-materials, and non-linearities, while classical methods have difficulties with these.
- Finite difference methods make point-wise approximations while finite element methods make piece-wise approximations, allowing for continuity along element boundaries.
- Finite element methods can evaluate values between nodes through interpolation, while finite difference methods only provide values at nodes.
Finite Element Analysis - UNIT-1
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.
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it tells u what is finite element method and it's use in solving typical 1D, 2D rods along with some soved problems .
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This document provides an overview of a course on engineering design and rapid prototyping. It discusses the finite element method (FEM) which will be covered in class. FEM involves cutting a structure into small elements and connecting them at nodes to form algebraic equations that can be solved numerically. This allows for approximate solutions to complex problems. The document outlines the typical FEM procedure of preprocessing, analysis, and postprocessing using software. It also discusses sources of errors in the FEM approach and mistakes users may make.
Recommended
Fem lecture
The document provides an introduction to finite element analysis. It discusses the need for computational methods to solve problems involving complex geometries and boundary conditions that cannot be solved through closed-form analytical methods. The finite element method is introduced as a numerical technique that involves discretizing a continuous domain into discrete subdomains called elements, and approximating variations in dependent variables within each element. This allows setting up algebraic equations that can be solved to approximate the continuous solution. Advantages of the finite element method include its ability to model complex shapes and behaviors, and refine solutions through mesh refinement. Basic concepts such as element types, discretization, and derivation of element equations are described.
Finite Element Methods
The document discusses various numerical methods for analyzing mechanical components under applied loads, including the finite element method. It describes weighted residual methods like the Galerkin method and collocation method which approximate solutions by minimizing residuals. The variational or Rayleigh-Ritz method selects displacement fields to minimize total potential energy. The finite element method divides a structure into small elements and applies these methods to obtain approximate solutions for displacements and stresses at discrete points.
Multiple Degree of Freedom (MDOF) Systems
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
Finite element method vs classical method 1
The document provides an introduction to the finite element method. It compares the finite element method to classical methods and the finite difference method. Some key differences highlighted include:
- Classical methods obtain exact solutions for simple cases while finite element methods obtain approximate solutions for all problems.
- Finite element methods can handle problems with complex geometry, multi-materials, and non-linearities, while classical methods have difficulties with these.
- Finite difference methods make point-wise approximations while finite element methods make piece-wise approximations, allowing for continuity along element boundaries.
- Finite element methods can evaluate values between nodes through interpolation, while finite difference methods only provide values at nodes.
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https://wikicourses.wikispaces.com/TopicX+Bars+and+Trusses
Introduction to finite element method(fem)
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This document provides an overview of a course on engineering design and rapid prototyping. It discusses the finite element method (FEM) which will be covered in class. FEM involves cutting a structure into small elements and connecting them at nodes to form algebraic equations that can be solved numerically. This allows for approximate solutions to complex problems. The document outlines the typical FEM procedure of preprocessing, analysis, and postprocessing using software. It also discusses sources of errors in the FEM approach and mistakes users may make.
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The document provides an overview of the finite element method (FEM). It explains that FEM is a numerical technique used to approximate solutions to partial differential equations that describe physical phenomena. It works by dividing a complex geometry into small pieces called finite elements that can then be solved using a computer. The method was developed in the 1950s and has since become widely used in engineering fields to simulate systems like heat transfer, stress analysis, and fluid flow. The document outlines the basic approach of FEM and traces the history and development of its early software programs.
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- 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.
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Frequency Response to harmonic excitation,
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base excitation, magnification factor,
Force and Motion transmissibility,
Quality Factor.
Half power bandwidth method,
Critical speed of shaft having single rotor of undamped systems.
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The document introduces the finite element method (FEM). It defines FEM as a numerical method used to solve mechanical engineering problems. It discusses the key steps and types of elements in FEM. The pre-processing step involves discretization or meshing. The solution process involves determining the local and global stiffness matrices. The post-processing step analyzes the results. It also describes the different types of forces (body, surface, point) and elements (1D, 2D, 3D) used in FEM.
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- 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.
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The document discusses the finite element method (FEM) for analyzing beam structures. FEM involves subdividing a structure into finite elements of simple shape and solving for the whole structure. Elements can be one-, two-, or three-dimensional, with accuracy increasing with more elements. Nodes are points where elements connect, and nodal displacements describe element deformation. FEM allows analyzing complex shapes like plates by treating them as assemblies of beams. A simple bar analysis example demonstrates deriving and solving the stiffness matrix to determine displacements and forces from applied loads.
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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.
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Half power bandwidth method,
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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.
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01. steps involved, merits, demerits & limitations of fem
The Finite Element Method (FEM) is a numerical technique for solving problems of engineering and mathematical physics. It subdivides a large problem into smaller, simpler parts that are called finite elements. FEM allows for complex geometries and loading conditions to be modeled. The process involves discretizing the domain into elements, deriving the governing equations for each element, assembling the element equations into a global system of equations, and solving the system to obtain the unknown variable values. FEM can handle a wide range of problems including nonlinear problems and transient problems.
Introduction to finite element method
The document introduces the finite element method (FEM). It defines FEM as a numerical method used to solve mechanical engineering problems. It discusses the key steps and types of elements in FEM. The pre-processing step involves discretization or meshing. The solution process involves determining the local and global stiffness matrices. The post-processing step analyzes the results. It also describes the different types of forces (body, surface, point) and elements (1D, 2D, 3D) used in FEM.
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01. steps involved, merits, demerits & limitations of fem
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In many applications one observes rapid change of the solution in the boundary region. Accurate and numerically efficient resolution of the solution close to the moving boundaries is considered to be and important problem. We develop an approach to grid optimization for finite-difference scheme for elliptic problem. Using this approach we are able to achieve exponential convergence of the boundary Neumann-to-Dirichlet map when applied to the bounded domains. It increases the convergence order without increasing the stencil size of the finite-difference scheme and without losing stability.
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The document discusses finite element methods and their applications in microelectromechanical systems (MEMS). It covers the basic formulation of finite element methods, including discretization, selection of displacement functions, derivation of element stiffness matrices, and assembly of global equations. It also discusses specific applications of finite element analysis to problems in MEMS like heat transfer analysis, thermal stress analysis, and static/modal analysis. The finite element method is well-suited for complex geometries and materials and can model irregular shapes, general loads/boundary conditions, and nonlinear behavior.
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This document discusses finite element analysis and nonlinear finite element analysis. It introduces the finite element method and how it approximates solutions by dividing them into discrete elements. It explains that higher order polynomials and more nodes/elements increase accuracy. The document distinguishes between linear and nonlinear problems, with nonlinear problems not obeying Hooke's law. It lists common finite element methods for nonlinear mechanics like updated Lagrangian formulations. Finally, it discusses solution algorithms for nonlinear problems like Newton's method and line searches.
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This document provides an overview of a course on the finite element method for analyzing linear systems taught at the Swiss Federal Institute of Technology. The first lecture covers the motivation and organization of the course, introduces the use of finite elements by relating physical problems to mathematical modeling and finite element solutions, and discusses basic mathematical tools used in finite element analysis like vectors, matrices, and tensors.
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#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
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- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
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Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
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留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
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8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
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本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问微bwp0011
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◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
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Finite Element Method
- 1. JK Lakshmipat University Institute of Engineering and technology Finite Element Method Submitted to: Prof R.K. Agrawal Submitted by: Bharat Sharma 2012BTechME008
- 2. Contents • Analytical methods v/s Numerical method • FEM • FVM • A Case study
- 3. Analytical Methods V/S Numerical Methods Find the root of f(x)=x−5 Analytical solution: f(x)=x−5=0 add +5 to both sides to get the answer x=5 Numerical solution: Let's guess x=1: f(1)=1−5=−4. A negative number. Let's guess x=6: f(6)=6−5= 1. A positive number. And you get a range in which solution exists.
- 4. Why use Numerical method • Can Solve Complex Problems with ease • Example:- Higher Order Differential equations
- 5. Why use Analytical Method • To validate results from Numerical Methods • Analytical solutions can be obtained exactly with pencil and paper
- 6. What is FEM ? • Finite Element Method • A type of Numerical Method • Used for solving a differential or integral equation. • It has been applied to a number of physical problems, where the governing differential equations are available.
- 8. Area of geometry = A1 + A2 + A3 – A4 1 2 3 4 Finite Element method It is not of course used to calculate areas, but things like displacements, temperatures, velocities, stresses and so on Meshing
- 9. Is FVM related to FEM • Finite volumetric method • 3D version of FEM • Most of the commercial analysis software work on the principle of FVM
- 10. A Case Study
- 11. Stress Analysis of LP Rotor Problem:- • To determine stresses in the existing rotor • To modify the defective Rotor geometry and limit the stress to the existing value Client : N.T.P.C. New Delhi Done by : IIT Madras
- 12. You can see that there is a small hole there. The problem is that this small hole or defect which has been created due to improper manufacturing, it so happens that it is at a place where the stresses are also high
- 13. Can’t you just manufacture another ? • Rotor is very expensive, it is about 10 crores • Lead time to manufacture this rotor is nearly 6 months • A particular thermal power project worth about 3000 crores is going to stand still.
- 14. And Rotor is very big
- 15. NTPC wanted to • Check whether this manufactured rotor is tolerable • If not then can we modify this
- 16. What IIT Did • Compared stresses in good LP rotor and modified rotor
- 17. After some modifications and 4 iterations they were able to make the stresses equal in a matter of about 5 days and they used FEM.