Kirchhoff-Love Plate Theory Research Articles

BENDING OF A THIN ELASTIC PLATE OF VARIABLE THICKNESS

The classical Kirchhoff-Love theory of thin plates when applied to plates of variable thickness results in a fourth-order partial differential equation with variable coefficients which is difficult to solve. So far, only three cases are known with numerical certainty, namely, the symmetrical bending of circular plates, the unsymmetrical bending of a circular plate with quadratically varying stiffness, and a rectangular plate with linear stiffness in one direction and simply supported on two opposite edges. These solutions are analytic, generally involving special functions such as the exponential integrals and the confluent hypergeometric functions. The only difficulties involved are apparently in the nature of disagreeable computation.The problem of a clamped edge circular plate under uniform load with thickness represented by the expression .