On small finite deflections of sheardeformable elastic plates
We are concerned in what follows with a tenth-order system of differential equations which, in a certain sense, may be thought of as a limit of possible generalizations, including the effect of transverse sheardeformability, of von Kármán's equations for isotropic nonsheardeformable plates. We show that, subject to certain restrictions, this system of equations can be written, in direct extension of von Kármán's result and in direct extension of a special case of a recent result of sheardeformable shallow shells [the author and \textit{F. Y. M. Wan}, Z. Angew. Math. Phys. 33, 425-427 (1982; Zbl 0485.73055)], in the form of two simultaneous fourth-order equations supplemented by one equation of second order. We further establish contact with our original formulation of a variational equation for stresses and displacements within the framework of small finite deflection plate theory [the author, J. Math. Phys. 32, 129-135 (1953; Zbl 0051.163)], and we transform the present generalized version of this earlier result in a manner which is related to a very recent consideration of a mixed variational equation for displacements and transverse stresses in three-dimensional elastic layers [the author, Int. J. Numer. Methods Eng. 23, 193-198 (1986; Zbl 0579.73018)]. With this we then formulate a mixed variational equation with the property that it's Euler equations come out to be just that system of equations which we here consider the limit of possible generalizations of von Kármán's equations.
uniform, homogeneous, constitutively linear
tenth-order system of differential equations
generalizations of von Kármán's equations
scientific article; zbMATH DE number 3958839