Circular thin plates in bending: notes
This form uses a polynomial expansion for y as indicated in form's formulae (hit the 'Formulas' button, equations enforcing boundary conditions not shown).
The coefficients of the expansion are calculated by means of strain energy minimization. The expression used for strain energy is shown in the 'Formulas' as V.
For concentrated center loads no stress value is calculated for r<t/4, as stresses become infinite in the solution. With r=t/4 the maximum stress at the center will be close to the maximum tensile stress as quoted by Timoshenko Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed.,page 70. When present, the button 'Data' will download the vectors of the coefficients (without dimensions) ai,Ai, as defined in sheet's formulae.
Note that it is up to the user to link the downloaded vectors to the input data: when you download it, the vectors match the data in the sheet as you view it.
The coefficients of the expansion are calculated by means of strain energy minimization. The expression used for strain energy is shown in the 'Formulas' as V.
For concentrated center loads no stress value is calculated for r<t/4, as stresses become infinite in the solution. With r=t/4 the maximum stress at the center will be close to the maximum tensile stress as quoted by Timoshenko Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed.,page 70. When present, the button 'Data' will download the vectors of the coefficients (without dimensions) ai,Ai, as defined in sheet's formulae.
Note that it is up to the user to link the downloaded vectors to the input data: when you download it, the vectors match the data in the sheet as you view it.