Solving Euler Bernoulli 4th order partial derivative equation

Dear fellow coders,

I want to numerically solve a 4th order Euler Bernoulli partial differential equation in Matlab. The equation is as follows:

 E*I*(d^4w/dz^4) + rho*A*g*z*(dw/dz) = q

Where,

      E = the elastic modulus
      I = the second moment of area
      w(z) = the displacement of the beam along the length of the beam in z-direction
      rho = density of the beam
      A = the area of the beam
      g = gravitational acceleration
      q = a constant uniform load
      z = distance over beam
      L = total length of beam

And the boundary conditions are:

 w(0) = 0
 dw/dz(0) = 0
 d^2w(L)/dz^2 = 0
 d^3w(L)/dz^3 = 0

I'd like to approximate the solution for w(z) numerically, but for the life of me I don't know how to implement this in matlab.

[Torsten]

Write it as a system of first order ODEs and use bvp4c to solve:

y1'=y2
y2'=y3
y3'=y4
y4'=(-rho*A*g*z*y2+q)/(E*I)

Best wishes

Torsten.

Answer 1

[Van-Duong NGUYEN]

Hi everyone, Can everyone help me, Finite Element Code for SimplySupported Beam, give it to me please.

Thank you very much.

My email: [e-mail]