# Finite element analysis Definition and 18 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).

View More On Wikipedia.org
1. ### 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...
2. ### 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...
3. ### 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...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### "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...
10. ### 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...
11. ### 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...
12. ### 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 ?
13. ### 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...
14. ### 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...
15. ### 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...
16. ### 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...
17. ### (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...
18. ### 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...