# Strange spectral (finite) element results of a solid plate

I tried to implement the spectral element method1 as proposed in [1]. I simulated an aluminum plate and a vertical concentrated force was applied at the middle of the top left quarter of the plate2. I should get a wave with circular crest, coming from the point where I exerted the force. But apparently the wavefront got inverted as illustrated in the following picture.

(This is the z displacement at a particular instant.)

There must be something wrong in my code . What could have happened? Something wrong during assembling of the stiffness and mass matrix? This link contains my python source code in pdf format and the video that illustrates the propagation of the wave. I will try rewrite my code with ordinary plate element first.

1Here, SEM is just finite element method with higher order polynomial shape functions. Some other works use sinusoidal shape functions.
2I didn't abuse symmetry since I will add something to the plate later.

Update: I tried using ordinary plate element instead, but the results are the same given that the mesh is fine enough.

Edit 2: I think my code is actually correct, given that the Abaqus simulation also show such circular pattern on the top, bottom, left and right of the main crest (they are more obscure though). But I am still puzzled about why those circular pattern appear. I guess it has to do with the concentrated load and the effect of such spurious pattern would be weakened only if I refine the mesh (h-refinement). But from my observation, p-refinement does not help.

• It seems like you are solving a plane strain problem and not a plate problem, writing down the equations doesn't hurt. Also, it works be easier if you add a minimum working example to the question instead of a PDF version the code. – nicoguaro May 24 at 12:12
• FYI, that was a 400mmx600mm plate with 1.5mm and the figures above are the $u_3$-displacement field from the top view. – Li Chun Min May 25 at 4:14
• Do you mean the circular arcs that appear to have centers to the left, right, above and below the wave? Those looks exactly like aliasing artifacts. It's not surprising that h-refinement helps; apparently your mesh resolution (or at least, the resolution at which you are visualising the solution) is not fine enough to support the waves. – Rahul May 26 at 5:51
• Many thanks. Apparently, this problem does not happen if I apply horizontal force (that excites $S_0$ waves) instead of a vertical one (that excites $A_0$ waves). For structural health monitoring purpose, I have to do a lot of these simulations and I can't afford much extra DOF. So currently I just generate my data using horizontal excitation, but I would look into why aliasing happen and how to alleviate it later. – Li Chun Min May 26 at 9:00
• Your problem should have symmetry with respect to 90° rotations. I would doubt that you are doing things correctly. – nicoguaro May 26 at 22:27