Shape identification of plates through an integro-differential condition

Abstract

Abstract A shape identification problem for a thin hollow plate with a uniform transverse loading is treated in the present analysis. The identification condition is an integro-differential condition, constraining the total amount of rotation of the inner edge surface to a prescribed value. Reformulating the problem into a shape optimization problem, a shape sensitivity analysis is performed yielding the material derivative (i.e., total variation) of the objective function of optimization. Primary and adjoint problems are defined and decoupled in the case of simply supported boundary conditions. Boundary integral equations with no domain integrals are derived for the equations, and linear boundary elements are used for the numerical solutions. Employing the so-called ray functions as the decision parameters for the shape optimization problem, numerical results are obtained by nonlinear minimization techniques.