In a plate bending problem using classical plate theory (CPT), the moment under the applied point load is singular. Series-based solutions such as Navier and Levy result in a rapid increase in the bending moment under the load by increasing the number of terms in the series and the solution does not converge. Other methods involve the fundamental solution capture the singularity under the point load and result in an infinite bending moment under the point load. Mathematically, the methods of fundamental solutions are stronger in capturing the singularity under the load but leading to an unacceptable result physically (infinite bending moment is not accepted for designers). One of possible treatments is to look at the load as a patched load and using the area under which the load is applied (even if it is very small). It is also noted that the bending moment increases dramatically near the patched load as the patched area gets smaller.
If we reduce classical plate theory (CPT) governing equations to the governing equation for a beam problem by cancelling the terms related to the other direction, the singularity disappears, and the variation of the bending moment becomes smoothly till the point of the applied load. Why?
The behavoir of CPT under point loads is not the only issue with CPT.
So, what is the source of the singularity problem and why the same does not happen in beams under almost same formulations.
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