Abstract
This short note considers thin circular plates, functionally graded in both axial and transverse directions and loaded in compression on the middle plane by a uniform axisymmetric load. The functional grading is based on recent literature on the subject and we deal with a direct problem for buckling, i.e., given the geometry of the plate and its constitutive properties, the critical load multiplier and the buckling mode are determined by a usual non-triviality condition. Original expressions are found in a nearly closed form and show that suitable functional grading, actually achievable in practice, may lead to gentle solutions. Numerical examples, physical interpretations and comments are provided.
Highlights
Graded materials (FGM) have attracted interest in the scientific community in the last decades due to their promising possible applications in several branches of engineering and applied sciences
One benchmark study in structural mechanics is on the possible buckling of an element, since the pioneering works by Euler on the bifurcated solutions of a compressed elastic column
This is out of our scope, since in this short note we wish to deal with a simple problem and look for possible closed-form solutions
Summary
Graded materials (FGM) have attracted interest in the scientific community in the last decades due to their promising possible applications in several branches of engineering and applied sciences. There is a vast literature on this subject, considering various beam models (purely flexible, fully deformable, sheardeformable at higher orders with respect to the standard theories), various plate models (according to Kirchhoff and Love, Reissner and Mindlin, Von Karman), plus interactions with elastic foundations, porosity and other physical aspects. This is out of our scope, since in this short note we wish to deal with a simple problem and look for possible closed-form solutions. We are satisfied to show that by recent technological suggestions we are able to find closedform solutions for buckling loads; we will not investigate here about possible imperfections, postbuckling behaviour, sensitivity to initial imperfections, limit loads for actual equilibria
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