# On using Ritz Method to solve a Mindlin–Reissner plate

I am trying to replicate the method given in the this paper. I have written a Matlab program which determines the displacement field of Mindlin–Reissner plate theory using Ritz method. The limitation of the program is that the plate should lie on xy-plane.

Now I want to extend it to plates that are NOT aligned with any coordinate plane. One such example is given below:

My questions are:

How can I find the Jacobian matrix in this case? $$x = \sum_{i=1}^{4}x_i \times N_{i}(\xi, \eta)$$ and $$y = \sum_{i=1}^{4}y_i \times N_{i}(\xi, \eta)$$ still valid in this case?

When integrating with respect to $$z$$, what will be the limits of integration? For a plate parallel to $$xy-plane$$, I have used $$z_m - \frac{t}{2}$$ to $$z_m + \frac{t}{2}$$, where $$z_m$$ is the distance of middle surface from $$xy-plane$$ and $$t$$ is the thickness of the plate.

My Matlab program can accessed from this link.

• Can you provide some of the details used in the paper? – nicoguaro Sep 2 '19 at 16:44
• @nicoguaro The paper deals with the topic of structural analysis of equivalent plate model of an aircraft wing. All the structural members (skins, spar caps, spar webs, etc.) are treated as a plate. The plate theory used is the First-order shear deformation theory. To find numerical solution, Ritz method is used with Legendre polynomials. I hope this answers your query. However, if you have any specific question you want to ask, please do let me know. Thanks – Ali Baig Sep 2 '19 at 17:33