Optimization of Support Locations of Beam and Plate Structures Under Self-Weight by Using a Sprung Structure Model

To find support locations minimizing uneven deformation is an important design issue in a large plate under self-weight. During the imprinting process of LCD panels, for instance, a large variation in the deflection of an LCD panel due to its self-weight deteriorates the quality of nanoscale imprinted lines. Motivated by this need, this research aims to develop an efficient gradient-based optimization method of finding optimal support locations of beam or plate structures under self-weight. To use a gradient-based algorithm, the support locating problem is formulated with continuous design variables. In this work, a beam or plate structure is assumed to be supported by a set of distributed springs, which are attached to all nodes of the discretized model of a given structure. The spring stiffness is made to vary continuously as a function of the design variable in which unsupported and supported states of a structure are represented with springs having limit stiffness values. Because elastically supported structures exhibit considerably different structural behaviors from structures without elastic supports, it is difficult to select an objective function fulfilling the design goal and ensuring convergence to distinct supported-unsupported states without ambiguous intermediate states. To address this issue, an extensive study is conducted and an appropriate objective function is then suggested. An optimization formulation using the objective function is presented and several numerical problems are considered to check the validity and usefulness of the developed formulation.