In 1918 Pólya formulated the following problem: “How thick must the trunks of the trees in a regularly spaced circular orchard grow if they are to block completely the view from the center?”(Pólya and Szegő [2]). We study a more general orchard model, namely any domain that is compact and convex, and find an expression for the minimal radius of the trees. As examples, solutions for rhombus-shap...

The calculation of the load carrying capacity of variable thickness circular plates subjected to arbitrary rotational symmetric loading is presented. The analysis considers plate materials that obey either the square or the Tresca yield criterion. By using upper and lower bound theorems of limit analysis, corresponding estimations for the load carrying capacity of the plate are obtained. It is ...

In this paper, the thermal buckling analysis of a circular plate made of FGM materials with actuator/actuator piezoelectric layers based on neutral plane, classical plate theory and first order shear deformation plate theory is investigated. Reddy's model is assumed for material properties of FGM plate. Plate under the thermal loading, nonlinear temperature rise through the thickness and clampe...