Linked Questions

2 votes
0 answers
532 views

Solving a 4th order PDE (Plate bending) [duplicate]

I'm trying to solve the following PDE but I'm getting this error. The PDE represents the bending of a thin plate. ...
Mr. Pi's user avatar
  • 391
0 votes
0 answers
238 views

Analytical solve for biharmonic equation [duplicate]

I want to analytical Solve or numerical solve by Mathematica a biharmonic equation with homogeneous boundary conditions homogeneous? I considered its solution using Fourier analysis, which is not ...
Mohammad Bagher Bagheri's user avatar
103 votes
17 answers
6k views

Future enhancements for the finite element method

How should the finite element method (FEM) framework in the language be extended to be more useful? With the release of version 12.0 all fundamental FEM solvers (linear, nonlinear, stationary, ...
user21's user avatar
  • 40k
54 votes
4 answers
8k views

Dynamic Euler–Bernoulli beam equation

I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is $\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$ For the boundary conditions I ...
Hugh's user avatar
  • 16.5k
8 votes
2 answers
511 views

Solving a biharmonic eigenvalue Problem

I am interested in solving the following biharmonic eigenvalue problem. $$\begin{array}{cccc} & \Delta ^2 \Psi (x,y) = \lambda \Psi (x,y), & - \frac{\pi}{2} \le x \le \frac{\pi}{2} & -\...
Hosein Rahnama's user avatar
4 votes
1 answer
1k views

Euler-Bernoulli beam equation

I'm trying to solve Euler-Bernoulli beam equation with simply supported edges.$\frac{\partial^2} {\partial x^2} [ E I \frac{\partial^2 w} {\partial x^2}] + \rho S \frac{\partial^2 w} {\partial t^2} = ...
Rafik Zh.'s user avatar
3 votes
1 answer
678 views

Solving a BC Differential equation, (Buckling) any way possible

I am trying to verify my manual solution for this problem by any way, so I tried NDSolve, and DSolve, with no success. Can some one help, or even give me the final numbers :D I need the first 3 ...
Aladdin's user avatar
  • 93
2 votes
1 answer
603 views

2D inhomogeneous biharmonic equation with wedged edge

I'm solving bending of rectangular plate while, boundary conditions are I have found similar problem solved: datavoreconsulting.com/programming-tips/numerically-solving-pdes-mathematica-finite-...
Katarina's user avatar
  • 151
2 votes
0 answers
248 views

Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \begin{equation} \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
sferics's user avatar
  • 330
2 votes
0 answers
70 views

Introduce second derivative region boundary condition for 4th order PDE

I am trying to play around with the Foppl von Karman plate equations and solve for $w[x,y]$. I want to consider a plate with a free edge, i.e. no forces or moments at the edge. As such I want to ...
Barnacle's user avatar