Kaza Vijayakumar - Poisson Theory of Elastic Plates

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In a recent article, On the Kirchhoff-Love hypothesis (revised and vindicated), Ozenda and Virga rather hold, in the context of analysis of elastomeric materials, that it is just deceptively simple to presume that the theory of elasticity is a dead subject in a postmodern view. This monograph deals, exclusively, with the analysis of elastic plates and one finds, surprisingly, with new theories presented here for analysis of homogeneous and laminated plates with anisotropic plies conforms their view.

Their statement that It makes one believe that everything is understood and only routine computations need to be done, for which it suffices to devise the most appropriate algorithm (the distinguished job of computational mechanics) appears to be true even in the analysis of elastic plates within small deformation theory of elasticity. It is factual, perhaps, due to extensive use (even today) of Kirchhoff theory of plates in bending along with highly cited Reddys third-order shear deformation theory and systematic presentation of various orders of approximation of bending of elastic plates by Kienzler and his colleagues, apart from vast literature on extension and associated torsion problems.

Science and Mechanics are full of examples where a scholar with repute and authority has made some prediction which did not live long up to its expectations. Poisson-Kirchhoff Paradox is perhaps one among such predictions. This paradox (to use Reissners expression) will only be fully comprehended a little less than a century later (Reissner 1985, Reflections on the Theory Elastic Plates. Applied Mechanics Reviews 38, pp. 14531464).

Scientific literature has many instances where swimming against the currents of contemporary thought, people have produced seminal works. Even the music of Thyagaraja and Mozart fall into the same paradigm and we would have missed out their music, had they listened to the critics too much. This monograph is a seminal work and unique addition to the existing literature on plate theories.

Lacuna in the widely used Kirchhoff theory is due to in-plane displacements expressed as gradients of lateral displacement, resulting in fourth-order theory with two-edge conditions instead of a sixth-order theory with three-edge conditions as demanded by Poisson. This is what is known as Poisson-Kirchhoff boundary condition paradox.