What is Finite element analysis: Definition and 49 Discussions

The finite element method (FEM) is a widely used method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points.
The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.
The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).

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  1. M

    Engineering Current density calculation in anisotropic ferromagnetic film

    Hi everyone! First time posting here, so I apologize in advance for any bad formatting. I am working on a mathematical model of an anisotropic magnetoresistive sensor. The central part of such a device is a Wheatstone bridge that consists of four current-carrying ferromagnetic (FM) films, the...
  2. Vanilla Gorilla

    B Solving PDEs via FEM: A Gut Check of the Procedure

    Hi, I am a newcomer to FEA/FEM. I am aware that for any practical purpose, software is used to solve problems. However, before I utilize software, I want to understand the process the computer goes about doing. This document is simply an attempt to summarize the solving procedure in a concise...
  3. Vanilla Gorilla

    B Incorporating boundary conditions in the Finite Element Method (FEM)

    I have been watching Mike Foster's video series of the Finite Element Method for Differential Equations (FEM). In this episode, he solves a DE relating to temperature. As the final step, he gives the following equation: $$[K] [T] = [F]$$ In this equation, I understand that ##[K]## is the...
  4. A

    Modal mass and kinetic energy in FEM modal analysis

    So, I use Ansys (well known FEM software) and get the next output for a modal analysis toy problem (If you happen to know Ansys that's a pre, but I promise it shouldn't matter). The problem is a simple beam, clamped at one end. I used 160 20-node brick elements to solve it (so no Timoshenko...
  5. JH_1870

    A A question about current density in finite element analysis

    I know that if there is only one conductor providing the current density, then the current density can be used. But if you apply Maxwell's equation when there are multiple current sources, I don't know which value to use. This is not an analysis using a tool, but a problem when I develop the...
  6. A

    I Formula for integration of natural coordinates over an element

    In a textbook I own a formula is given for the integration of natural coordinates over an element. In this case it is a 1 dimensional element (i.e. a line segment) with coordinates ##x_i## and ##x_j##. The coordinate ##x## over the element is written as: $$ x = L_1(x) x_i + L_2(x) x_j $$ with...
  7. L

    Engineering Hand tool boundary conditions - Forces determination

    Hello, I' m trying to make a linear static analysis (Finite Element Analysis) on the following hand tool. I want to determine the boundary conditions. In order to do that I have decided to use a force couple to represent the forces that a bolt exerts on the jaws of this spanner. Despite using...
  8. FEAnalyst

    Corrugated tube (bellow) under axial load

    Hi, I'm trying to verify the results of a finite element analysis of a corrugated tube (bellow) subjected to axial load. Here are my analytical calculations based on Roark's Formulas for Stress and Strain (originally the formulas are from the article "On the Theory of Thin Elastic Toroidal...
  9. D

    I Usage of First Order Elastic Constants in Soft Body Equations

    Hi, I have some soft body equations that require first order elasticity constants. Just trying to figure out the proper indexing. From Finite Elements of Nonlinear Continua by J.T. Oden, the elastic constants I am trying to obtain are the first order, circled below: My particular constitutive...
  10. M

    Treatment of source term on the boundary: FEA and Comsol

    I would like to solve a coupled system of two PDEs using Comsol for the following geometry: Equation 1 (valid for 0⩽Z⩽bm): The initial and boundary conditions are: Tm(r,t→0)=20 Tm(r→rw,t)=70 Tm(r→∞,t)=20 However, for bm⩽Z⩽bm+b2, the equation to solve is: With the following initial and...
  11. B

    Hi I'm Jayvhie, Mechanical Engineer from PH

    ◎ As Structural Design Engineer, Highly-motivated individual with a demonstrated history in Finite Element Analysis to solve complex structural engineering problems, applying numerical methods approach and view solution results (Post- Processing) to optimize the design of a Ship to Shore (STS)...
  12. B

    Poisson Ratio -- Finding a corresponding analytical solution for the strain

    Hi, I ran into problems using the poisson ratio. For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge. Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir. The material parameters are E = 100, and v...
  13. P

    Engineering Finite Element Analysis / Structural Analysis

    Hello engineer's community ! I got a problem. If i got a truss frame with 2 bars and an initial nodal displacement for the common node , then how can i calculate the velocity of the oscillation as function of time ? (the 2 bars have different length , same elasticity modulus , same density and...
  14. A

    "Assembly" of elements of different dimensionalities (1-D, 2-D)

    I am currently working on a problem which involves both 1D and 2D elements. I know that these elements have different degrees of freedom at a node and, therefore, the procedure of assembly of elements will different from a purely 1D or a purely 2D mesh. I don't know the rest of the details. Any...
  15. Shackleford

    PhD in Applied Mathematics - Finite Element Analysis

    My background is BS Math with Physics minor (3.5) and MA Math (3.7) from the University of Houston. My current plan is to explore the necessary background for doing research in finite element analysis. Over the next few semesters, I plan to take Numerical Methods for PDEs, Statistical Computing...
  16. H

    Which strain tensor is used by Abaqus?

    Hi all, I have some doubts regarding the strain tensors Abaqus uses for the case of Geometrical non linear analysis. In the case of geometrically linear analysis, all the strain tensors will be equal to engineering strain, So it doesn't matter which strain tensor Abaqus uses. But for...
  17. T

    Abaqus FEA Problem - Displacing an Entire Part at Once

    Hi all, I have a personal project I am working on in Abaqus CAE/Explicit 2017. I have a tube, that I am trying to advance into a larger tube with a bend in it. The idea is that the small tube enters and then deforms around the bend as it comes into contact with the radius of curvature of the...
  18. mertcan

    Finite element analysis node displacement

    Hi, I would like to ask why center of element displacement is always estimated with polynomial equation involving nodes displacement (like in attachment/picture)? Also I know that if nodes' number increase for an element then displacement of center of element is estimated with higher order...
  19. mertcan

    Studying Finite element analysis for Electromagnetism

    HI, initially I would like to put into words that there are sufficient resources, books or lecture videos on YouTube related to finite element analysis especially for structural dynamics (for instance JURGEN BATHE in MIT). But I would like to make you sure that there NO lecture videos or other...
  20. maistral

    Discussions about Finite Element Analysis (PDFs)

    Hi. Can someone point me to a good (and really basic) PDF file or text regarding Finite Element analysis? I would prefer it having an example where it would solve the 1D heat equation or the Laplace equation so I can extend what I know from finite difference methods to it. Sorry if this seems...
  21. M

    FEA Results Interpretation for a Pin Support

    Greetings to all, I am doing FEA analysis of a jib crane. I am using Autodesk Inventor. The results show that the max Von Mises stress in the support pin is 773 MPa. This value exceeds the yield strength of the Carbon Steel. Does this mean that the Pin will fail under load ?
  22. M

    Different FEA results of the same element

    Hello. Consider the model shown below. The problem is to be solved by FEA. The plane element is constrained from moving at the red line. A concentrated load P is applied at the red point and pointing downward. We solve the problem using the following meshes. Same elements are being used and...
  23. C

    Can You Help With Finite Element Analysis in Cylindrical Coordinates?

    I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...
  24. F

    Finite Element Analysis: PE of an element

    Homework Statement The potential energy of an element in terms of local displacements q1 and q2 is given by the expression: Π = 3(q1^2) - 6q1q2 + 9(q2^2) + 9q1 Write down the expressions for element stiffness matrix k and element force f. I am at a complete loss as to what...
  25. N

    Unwanted Node Movement in Abaqus

    Hi, I am brand new to these forums and fairly new to abaqus as well. I am doing a simple radial expansion on an axi-symmetric semicircle with a smaller semicircular hole in it. In order to do so, I created a datum CSYS that is cylindrical in nature but aligned with the global CSYS. In other...
  26. R

    Ansys 15 - create moving loads

    Hi, I am trying to simulate a moving load in ansys 15. Could anybody guide me on how I could do it? A typical example: Calculating stress across a steel Rope ( assume solid circular c/s) between point A to B while a pulley load moves over it between the 2 points with a certain velocity. I will...
  27. I

    (Composite) In plane principal stress or normal stress?

    Hey everybody, I went through a discussion with a colleague today about Finite element modeling of composite structures and how to interpret the stress analysis. I understand that for isotropic materials, principal stresses could be used against the allowable stresses to see if failure will...
  28. marellasunny

    Superposition of loadcases in FEA software (with SPC+inrel)

    I am curious as to how finite element analysis software(like Hypermesh) go about superposition of loadcases(applied on the same model). I constrain my vehicle body for 1.loadcase (say bending) with the standard SPC's and constrain my 2.loadcase(say torsion) with Inertia relief constraints...
  29. S

    What is the best book to start learning Finite Element Analysis?

    Hi guys, :smile: I am a mechanical engineer, and want to learn finite element analysis. I want to know what is the best book to start with. Assume I have no prior knowledge of the subject. :redface: Thanks, Sety.
  30. F

    Finite Element analysis: Free body diagram help

    Homework Statement Hey guys, my problem is not really the end solution, but the preliminary step that I'm not too sure about. Given the following diagram: The image on the left is the given model, and the right image is my nodal element FBD, but somehow i don't believe that's correct. Can...
  31. A

    Free Finite Element Analysis Software

    Anyone know of some good, free finite element analysis software? I used NASTRAN in college, but from what I can tell that costs at least several thousand.
  32. F

    Interpretation of finite element analysis results

    Hi, Recently started with FEA - loving it, at least the modelling / load application part. Interpreting the results is tricky - particularly around where loads are applied. Got a project (no pics sorry) which has a drilled hole in a plate, and have applied the load as a a pressure...
  33. B

    Introduction to Finite Element Analysis

    Folks, I have the book An Introduction to the Finite Element Method by J.N Reddy. The following website provides http://highered.mcgraw-hill.com/sites/0072466855/student_view0/executables.html access to the Fortran Executable but I am not sure how to work them. I am just beginning to...
  34. B

    Finite Element Analysis - Author J.N Reddy Book

    Folks, Is there anyone out there familiar with 'An introduction to the Finite Element Method' by J.N. Reddy? I am struggling to decipher what is happening on page 129 as shown in the attachment. If some-one is willing to help I will reply with a more specific query on that page. Thanks
  35. O

    How finite element analysis differs from mathematic derivation in beam bending?

    So I just started learning to use the finite element package abaqus for modelling beam tip deflection under different loading conditions. I think I understand the theory behind it but was wondering if some one could answer a few questions about it to further my understanding. Firstly, how do...
  36. G

    Finite element analysis results interpretation

    Hello, I have been following this forum for some time now, but this is the first time I participate. I would appreciate if you could give me a hand in understanding the results of a finite element analysis of an automotive component we have designed. The analysis results indicate that the...
  37. M

    Estimation of residual stress by finite element analysis

    I am trying to do a finite element analysis ofcold extrusion process of a tube wherein the steel tube is reduced from a larger outer diamter to a smaller one by extrusion process.The tube is held stationary and the die is pushed into the tube for a particular length and then retrieved.I am...
  38. D

    Finite element analysis software

    i am a 3rd year civil engineering student, currently taking a course in which i need to use finite element software for assignments. the course is 100% theory, and i need to learn how to use the software on my own, i am looking for FREE software with FE capabilities, and preferably one that...
  39. A

    Finite Element Analysis of Collision Impact in MD Patran/Nastran

    I am trying to run a finite element analysis for a collision impact. The program I am using is MD Patran/Nastran. My model consists of moving object colliding with a stationary object. I have created the mesh, applied the appropriate material, applied the boundary conditions (fixed for the...
  40. D

    Finite Element Analysis Program

    I am on a research project where I am finding the heat capacitance and thermal conductance of a material and would like to simulate it on a larger scale as material for heated flooring. Is there a program where I can do a looping heating pipe at a set temperature and show the conductance of the...
  41. G

    Is my landing gear design suitable for the cyclone airplane?

    Hello I have an assignemt to analysis a landing gear for the cyclone earoplane, an initial design being supplied, I have being askedto check for the suitability of the part, the conditions are: Aircraft mass with fuel: 43000 lbs Landing speed: 65 Knots Maximum deceleration: 3g Each part...
  42. R

    Transient conduction with finite element analysis

    Homework Statement Hi, I've got a civ engineering problem relating to conductive heat flow using finite element analysis. I'm investigating the dissipation of heat from square and circular pile foundations. I'm applying a thermal load to the centre of the concrete pile which induces heat...
  43. B

    Mathematics for Finite Element Analysis

    Can anyone tell me what book is best to learn MATHEMATICS that used in Finite Element Analysis (FEA) algebraically and analytically?
  44. A

    MATLAB Finite Element Analysis in Matlab

    Hello folks :) I need to model a finite element model of a beam in bending in matlab i need directions and help thanks
  45. I

    Can Finite Element Analysis Programs Analyze Inflatable Vacuum Chambers?

    This summer i have an internship that expects me to write a program to analyze this inflatable vacuum chamber. The advisor wants to be able to put in a geometry and see if it will be stable. Would finite element analysis programs be able to do this? If so which one should I look into getting?
  46. Astronuc

    Finite Element Analysis (FEA) Products and Developers

    These are the one with which I am most familiar. There are others, but these are the biggies. We use ABAQUS as well as our own proprietary methods, particularly for dynamic, large strain and nonlinear FEA. ABAQUS (HKS) - for nonlinear Finite Element Analysis (FEA) www.hks.com...
  47. C

    Nonlinear Finite Element Analysis: When & How

    what is a non linear finite element finite element analysis. When does a structure behave non linearly and how do we calculate non linearity of an element by the nodal displacements.
  48. brewnog

    Finite element analysis problem

    Hello all, I've been trying to model a plate under uniform tension using FEA techniques (in ANSYS). The plate has a circular hole in the centre, and has two axes of symmetry so I've created a mesh based upon the 'top right' quarter of the plate. I'm pretty sure I've done everything right...
  49. C

    Finite element analysis alternative?

    finite element analysis alternative?? hi do you happen to know any alternative for using Finite Element Analysis(FEA)? i need to know it badly.. hope someone could help. thanks!