Solving this equation manually for arbitrary boundary conditions (simply supported, clamped, free, or partially fixed) is mathematically intensive. This is where become indispensable.
If you describe you need (e.g., “continuous two-way slab with cantilever edges” or “trapezoidal diaphragm under in-plane shear”), I can reproduce the elastic coefficients here in a clean table format for you to copy into a PDF or spreadsheet. specifically their seminal book
For (in-plane loading), the tables provide: Tables for the Analysis of Plates
When engineers search for PDFs on this topic, they are most frequently looking for the work of , specifically their seminal book, Tables for the Analysis of Plates, Slabs, and Diaphragms Based on the Elastic Theory . specifically their seminal book