Method for the calculation of displacements and internal forces for a plate of arbitrary shape
A method for the calculation of displacements and internal forces for a plate of arbitrary shape and under arbitrary support conditions, being under static loading, is presented. This problem has been solved on the basis of the classical linear theory of ideally elastic thin plates. A set of Fredholm's integral equations, which expressed the support conditions, was used to solve this problem.
The particular integral W* = r2 ln r2/16πD of the differential equationDΔΔW(r) =δ(0)/r, or a combination of the corresponding differentials was assumed to be the kernels of the integral equations. This particular integral expressing the deflection of an infinite plate under a simple force loading will be termed later as the fundamental solution.
The formulation of integral equations is independent of the static scheme of the plate being solved. Some examples of calculations using a computer program developed by the author are also presented.
References
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