Optimal notch shapes for loaded plates

Abstract

This paper presents design data de®ning optimal freeform notch shapes for use in tensile loading conditions for a range of geometries, notably the notch aspect ratio and plate widths. Here, an iterative two-dimensional ®nite element gradientless shape optimization procedure was used to obtain the optimal shapes, which o er the lowest possible stress concentration, subject to the geometric constraints. Precise non-dimensional coordinates are given, for a range of notch aspect ratios and plate widths, and are presented in a tabular form that allows them to be easily used by designers. All cases have been solved with a minimum radius of curvature constraint, which results in a`robust' optimal shape that has no sharp corners. The optimal shapes were found to provide up to a 26 per cent reduction in local peak stress over circular shapes of the same aspect ratio. Optimal geometries are also given for limiting notches that provide a net section stress equal to unity, at a ®nite notch aspect ratio. The results obtained are applicable to both the initial design of notched components and the shape reworking of existing components to remove damage.

Parametric optimisation of stress relief groove shape in flat ends of boilers

“…The procedure of introducing several spline functions to modify the groove shape follows to a certain extent optimisation proposals. 8–11,13 The optimisation methods proposed and studied there rely on addition of material in the zones where stress is above the limit and withdrawal of material in zones with lower stresses.…”

“…Then, many others dealt with similar problems. To name only a few of them: Francavilla et al 6 considered Tvergaard’s problem and solved it with use of FEM, and also searched for optimal shape of a connecting rod; Pedersen and Pedersen 7 considered optimisation of grooves in shafts and notches in flat bars; Burchill and Heller 8 investigated notch problem in plates, Heller et al 9,10 analysed problem of cavities in plates; Waldman et al 11 studied fillets in flat plates subjected to tension and bending. The state of the art in this matter is discussed and summarised in Pedersen.…”

Design of notches and grooves by means of elliptic shapes

“…A number of recent papers on optimal design for minimum stress concentration are available (see reference [8] for further information). The results are mainly for plane problems and based on heuristic optimization to obtain a constant maximum stress at the boundary.…”

Optimization of Flat Ends in Pressure Vessels

“…The preliminary numerical calculations performed for certain values for both proposals shown in Figure 10 were encouraging; it appeared that a full elimination of plastic deformations was possible for certain combinations of reinforcing ring dimensions and The application of the biological growth approach proposed by Mattheck [27] may be useful in this case; this approach respectively adds or removes some material portions in the most and the least strenuous zones of structure. The engineering application of this approach has been presented in papers by Burchill, Heller, Waldman, and others [28,29]. Additionally, the proposed modification of the considered design should be low cost, as simple as possible, and should add or remove some parts of the material in a relatively easy way.…”