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3 votes
Accepted

Deflection of thin plate with 1 free edge and deflection > thickness

You are correct that this problem falls within the category of 'large-deflection' problems since the deflection is larger then about $\frac{t}{2}$. To correctly analyse a plate under large-deflections ...
atom44's user avatar
  • 2,641
3 votes

How to derive deformation gradient or displacement gradient?

From a theoretical standpoint, the displacement gradient is equivalent to strain (assuming a structural problem). Numerically, you can obtain the derivate of a quantity through multiplication with ...
Robbie van Leeuwen's user avatar
3 votes

Negative Eigenvalues in Ritz Solution of First-Order Shear Deformation Theory

The only way you can get negative eigenvalues is by including stress stiffness effects (sometimes called "geometric stiffness"), if there are compressive stresses which would cause the plate to buckle....
alephzero's user avatar
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2 votes
Accepted

FEA: Newton-Raphson algorithm for Dirichlet BC non-linear static analysis

The discretized problem that you are trying to solve is $$ \text{find}\,\, \mathbf{u}^{n+1} \,\, \text{such that} \,\, \mathbf{r}(\mathbf{u}^{n+1}) = \mathbf{0} \,\, \text{subject to the constraints} ...
Biswajit Banerjee's user avatar
2 votes

Does Finite Element Method use direct stiffness method?

FE solvers are not dependent on the direct stiffness method. You can introduce conceptually the FE methodology to students using the direct stiffness method. FEM Solvers use different formulations/...
NMech's user avatar
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2 votes
Accepted

How to use the Ritz method with the weak form to approximate solution of differential equation

Everything in your OP looks correct. I think you have just got into a muddle with the notation, and what is known and what is unknown. $\phi_1$ and $\phi_2$ are known functions, i.e. you choose two ...
alephzero's user avatar
  • 12.5k
2 votes

Why does it take lesser iterations for a stiffer model in my FEA than a less stiffer model to converge?

depending on the type of non linear analysis you used, then conceptually the analysis takes the following steps (again depending on the type on analysis you use): An iterative process starts: A small ...
NMech's user avatar
  • 24.4k
1 vote

Why is FEA used for structural analysis?

"Finite Element Analysis" is used for the analysis of simple linear (or linearizable) systems where volume is not conserved. "Finite Volume Analysis" is used in computational fluid ...
david's user avatar
  • 821
1 vote

In FEM, can each instance of a Transient Analysis be thought of as a Static Analysis of its own?

I am not aware there is such an analysis method called "transient analysis" for civil/structural engineering, I think you mean the analysis of structure with the "transient loads. By ...
r13's user avatar
  • 8,227
1 vote

Why is the amount of force/moment transfer occurring between bodies in FEA is independent of mesh size?

Forces do not disappear without resistance. For a statically balanced system, globally, the sum of the applied Forces must equal to the sum of the resistance forces, so the number, and size of the ...
r13's user avatar
  • 8,227
1 vote

Extracting Uncertainty from Numerical Solution

I'll try to address the question in bold. The expression for the angle function can be expressed as $f(\delta, M; \theta)$. You can compute partial derivatives of this function as $$ \frac{\...
Biswajit Banerjee's user avatar
1 vote

How to code this iterative scheme for solving 2-group diffusion equation?

You haven't given enough information to answer this exactly, but I am assuming from your equations that you are solving mesh-centered equations and the assumption is that the flux is linear in each ...
NuclearFission's user avatar
1 vote

Implicit and Explicit finite difference discretization of steady state heat conduction equation

A non-iterative solution for steady-state heat flow must be implicit. You are solving for the temperatures "everywhere" in the structure in a single "step", so every boundary condition must affect the ...
alephzero's user avatar
  • 12.5k
1 vote

Calculate surface area and outward normal of each face(non-planar) for a irregular hexahedron.

If the surface is nonplanar then the surface normal is a (hopefully continuous and differentiable) function of location. You will have to integrate the surface function S(x,y,z) over any two of the ...
Carl Witthoft's user avatar
1 vote

Temperature not changing in my code for 1-D heat equation: Explicit Scheme

This stackexchange doesn't really seek to solve these homework-like problems directly. However, I can offer some hints on how to proceed. Are you sure the scale of ...
do-the-thing-please's user avatar
1 vote

Example of real-life problem solved with numerical methods?

You could develop some saturated steam equations by running a regression on steam table data. Even if it was a giant equation, sure would be nice to not have to do a a table lookup in an otherwise ...
ericnutsch's user avatar
  • 8,181
1 vote

Mechanical Engineering- Modeling contact in Abaqus

There can be thousands of causes for your error. You need to give many more informations to be able to make a guess. Like: discretization, solving methods for the DEQs, grid topology, boundary ...
JE_Muc's user avatar
  • 223
1 vote

J2 orbit propagation problem in MATLAB (solver instability)

https://www.mathworks.com/matlabcentral/fileexchange/55167-high-precision-orbit-propagator?s_tid=srchtitle https://www.researchgate.net/publication/340793133_High_Precision_Orbit_Propagator_C_code The ...
Meysam Mahooti's user avatar
1 vote
Accepted

J2 orbit propagation problem in MATLAB (solver instability)

Solved it, thanks to a colleague. The problem is, I used "J2 Propagator" in STK, which in fact uses secular rates of orbital precession. Comparing that result with the real integration that MATLAB ...
AliRD's user avatar
  • 31
1 vote

J2 orbit propagation problem in MATLAB (solver instability)

As far as I can see, you are trying to integrate a nonlinear ODE of a conservative system. It is very likely that your system exhibits chaotic behavior. RK4 is a fourth order numerical scheme. These ...
MrYouMath's user avatar
  • 1,036
1 vote

Deflection of thin plate with 1 free edge and deflection > thickness

The small deflection approximation is not based on deflection vs thickness, it is based on deflection over span. So for your maximum case of 10mm deflection on a 1250mm span, you are only looking at a ...
OSUZorba's user avatar
  • 111
1 vote

Normalization and Non-Dimensionalization of a mass balance equation

Sorry with not being familiar with all of your variables. If it is a mass balance as you say, then you can't get a Reynolds or P├ęclet number. A Reynolds number appears in the dimensional analysis of ...
Robin's user avatar
  • 679
1 vote

External diffusion: calculation of surface concentration

The way you have solved your problem you have treated the concentration at the surface of the sphere as known ($y_{B,\text{surf}}$). Notice that in your final answer, if you plug in $r=r_\text{sphere}$...
Salomon Turgman's user avatar

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