This paper presents new and transferable design data defining precise optimal free-form shapes for holes in large and finite width plates under biaxial and uniaxial loading conditions respectively. An iterative two-dimensional finite element gradientless shape optimization procedure was used to obtain the optimal shapes, which offer the lowest possible stress concentration, subject to geometric constraints. Precise non-dimensional coordinates are given for a range of hole aspect ratios and are presented in tabular form that allows them to be easily used by designers. The optimal shapes were determined both with and without minimum radius of curvature constraints. Optimal shapes in large plates were found to provide up to a 28 per cent reduction in peak local stress over elliptical shapes of the same aspect ratio. For finite width plates the reduction in peak local stress was as high as 44 per cent. The results obtained are applicable to both the initial design of components with cut-outs and the shape rew...

Optimal free-form shapes for holes in flat plates under uniaxial and biaxial loading:

An approach based on biological algorithm for three-dimensional shape optimisation with fracture strength constrains

This paper presents design data defining 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 ite...

Optimal notch shapes for loaded plates

Flat ends of boilers with stress relief grooves have been used for many years. The existing standards set the value for the endplate thickness and admissible range of values for radius of the groove and the minimum thickness of the endplate under the relief groove. However, the codes do not specify the optimal parameters values for the endplate with stress relief groove. In this paper, the authors study the optimal choice of parameters for circular groove, and then propose its shape modification to elliptical, which considerably decreases stress concentration appearing in the zone of the groove. In the next step, the elliptical shape is replaced by the groove modelled by two spline functions, which results in further reduction of stress concentration. Finally, the groove with shape including several spline functions is proposed as an optimal one. In the performed study, the finite element modelling and the simple search method in optimisation procedures are used.

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

This paper investigates the design optimisation of a fuel flow vent hole (FFVH) located in the wing pivot fitting (WPF) of an F-111 aircraft assuming a damage tolerance design philosophy. The design of the vent hole shape is undertaken considering the basic durability based design objectives of stress, residual (fracture) strength, and fatigue life. Initially, a stress based optimised shape is determined. Damage tolerance based design optimisation is then undertaken to determine the shape of the cutout so as to maximise its residual strength and fatigue life. For stress optimisation, the problem is analysed using the gradient-less biological algorithm and the gradient-based nonlinear programming methods. The optimum designs predicted by the two fundamentally different optimisation algorithms agree well. The optimum shapes of the vent hole are subsequently determined considering residual strength and fatigue life as the distinct design objectives in the presence of numerous 3D cracks located along the vent hole boundary. A number of crack cases are considered to investigate how the crack size affects the optimal shapes. A semi-analytical method is employed for computation of the stress intensity factors (SIF), and an analytical crack closure model is subsequently used to evaluate the fatigue life. The 3D biological algorithm is used for designing the cutout profiles that optimise residual strength and fatigue life of the component. An improved residual strength/fatigue life (depending on the optimisation objective) is achieved for the optimal designs. The variability in SIF/fatigue life around the cutout boundary is reduced, thereby making the shape more evenly fracture/fatigue critical. The vent hole shapes optimised for stress, residual strength, and fatigue life are different from each other for a given nature and size of the flaws. This emphasises the need to consider residual strength and/or fatigue life as the explicit design objective. The durability based optimal vent hole shapes depend on the initial and final crack sizes. It is also shown that a damage tolerance optimisation additionally produces a reduced weight WPF component, which is highly desirable for aerospace industries. The design space near the ‘optimal’ region is found to be flat. This allows us to achieve a considerable enhancement in fatigue performance without precisely identifying the local/global optimum solution, and also enables us to select a reduced weight ‘near optimal’ design rather than the precise optimal shape.

Damage tolerance based design optimisation of a fuel flow vent hole in an aircraft structure

Optimal rework shapes for the most critical stiffener runout fatigue locations in the F-111 wing pivot fitting have been determined using a recently developed finite-element-based gradient-less shape optimization procedure. The resulting precise free-form shapes render the local notch stress distributions near uniform and typically provide a 30-40% reduction in peak elastic stresses as compared to the current rework shapes that exist for aircraft in service with the Royal Australian Air Force. The present numerical results are also consistent with recent preliminary experimental results, and a significant program of further validation testing is envisaged. Hence it is expected that the stress reductions predicted in the present work will lie sufficient to provide a basis for extending inspection intervals by at least a factor of two; from 500 to 1000 h. Implementation of such an extension to the F-111 fleet in service with the Royal Australian Air Force would provide a very significant maintenance cost saving. The anticipated reduction in local crack growth rates would also allow achievement of the planned withdrawal date for the aircraft.

Shape optimization of critical stiffener runouts for F-111 airframe life extension

F-111 airframe life extension through rework shape optimisation of critical stiffener runout features in the wing pivot fitting

Airframe Life Extension By Optimised Shape Reworking — Overview Of Dsto Developments

Shape optimisation of fatigue prone holes in the wing pivot fitting of the raafs f-111 aircraft

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Shape optimization of critical stiffener runouts for F-111 airframe life extension

F-111 airframe life extension through rework shape optimisation of critical stiffener runout features in the wing pivot fitting

Airframe Life Extension By Optimised Shape Reworking — Overview Of Dsto Developments

Shape optimisation of fatigue prone holes in the wing pivot fitting of the raafs f-111 aircraft