Spring-Value in Kirchhoff-Love Plate: Displacement, Buckling, Pure-Shear, Vibration

Abstract

The stiffness model of the finite element is applied to the Kirchhoff-love closed-form plate buckling; buckling is always in focus in plate assemblages. The useful Eigen-value solutions are unable to separate a square plate from a much weaker long one in the most commonly-used all-simply supported plate (SSSS), among others. Spring-values of the Kirchhoff-Love plate are sought; once found, displacement-factors can be determined. Comparative displacements allow an easier and better evaluation of buckling-factors, pure-shear, vibration and so are termed “buckling-displacement-factors”. In testing, many plates in mixed boundary conditions are evaluated for displacement assisted buckling-solutions, first. The displacement-factors made from fundamental Eigen-vectors, in a single-pass, are found to be within about one-percent of known elastic values. It is found that the Kirchhoff-Love plate spring and the finite-element spring, demonstrated, here, in the assemblage of beam-elements, are equivalent from the results. In either case, stiffness is first assembled, ready for any loading—transverse, buckling, shear, vibration. The simply-supported plate draws the only exact vibration solution, and so, in an additional new effort, all other results are calibrated from it; direct vibration solutions are made for comparison but such results are, hardly, better. In the process, interactive Kirchhoff-Love plate-field-sheets are presented, for design. It is now additionally demanded that the solution Eigen-vector be developable into a recognizable deflection-factor. A weaker plate cannot possess greater buckling strength, this is a check; to find stiffness the deflection-factor must be exact or nearly so. Several examples justify the characteristic buckling displacement-factor as a new tool.