Thin Plates with Rapidly Varying Thickness, and Their Relation to Structural Optimization.

Mathematical models are described for plates with rapidly varying thickness we place special emphasis on their relation to problems in optimal design. Our plate models extinguish between variations on a scale larger than the mean thickness, on a scale comparable to the mean thickness and on a scale smaller than the mean thickness. We review a number of theoretical results that compare the relative strengths of these three design options. The paper also contains exact numerical values for the rigidities of certain interesting plate profiles. These values were computed by a finite element method.