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

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.

[1]  E. Schnack,et al.  A fatigue model for shape optimization , 1997 .

[2]  D. Goldfarb.  A family of variable-metric methods derived by variational means , 1970 .

[3]  Simon Barter,et al.  Aspects of fatigue affecting the design and maintenance of modern military aircraft , 1993 .

[4]  Eckart Schnack,et al.  An optimization procedure for stress concentrations by the finite element technique , 1979 .

[5]  S. Vigdergauz,et al.  A hole in a plate, optimal for its biaxial extension - compression , 1986 .

[6]  Susan Pitt,et al.  Weight functions, CTOD, and related solutions for cracks at notches , 2004 .

[7]  C. Mattheck,et al.  Effect of loading on the optimized shape of a kinked bar , 1991 .

[8]  S. Mall,et al.  Dugdale plastic zone size and CTOD equations for the compact specimen , 1984 .

[9]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations , 1970 .

[10]  Satish Chandra,et al.  Damage tolerance based shape design of a stringer cutout using evolutionary structural optimisation , 2007 .

[11]  D. Shanno.  Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .

[12]  M. Mcdonald,et al.  F-111 AIRFRAME LIFE EXTENSION THROUGH REWORK SHAPE OPTIMISATION OF CRITICAL STIFFENER RUNOUT FEATURES IN THE WING PIVOT FITTING , 2002 .

[13]  Satya N. Atluri,et al.  Analytical solution for embedded elliptical cracks, and finite element alternating method for elliptical surface cracks, subjected to arbitrary loadings , 1983 .

[14]  Yi Min Xie,et al.  Design of structures for optimal static strength using ESO , 2005 .

[15]  Erik Steen Kristensen,et al.  On the optimum shape of fillets in plates subjected to multiple in‐plane loading cases , 1976 .

[16]  M Heller,et al.  Investigation of shape optimization for the design of life extension options for an F/A-18 airframe FS 470 bulkhead , 2000 .

[17]  C. Mattheck,et al.  Three-dimensional shape optimization of a bar with a rectangular hole , 1992 .

[18]  J. C. Townsend,et al.  Very Large Scale Optimization , 2000 .

[19]  W. Elber.  The Significance of Fatigue Crack Closure , 1971 .

[20]  M. Mcdonald,et al.  SHAPE OPTIMISATION OF FATIGUE PRONE HOLES IN THE WING PIVOT FITTING OF THE RAAFS F-111 AIRCRAFT , 2002 .

[21]  S. Atluri,et al.  Structural integrity of aging airplanes , 1991 .

[22]  Daren Peng,et al.  3232 - OPTIMAL SHAPE DESIGN WITH FATIGUE LIFE AS DESIGN CONSTRAINT USING A 3D BIOLOGICAL METHOD , 2005 .

[23]  Kevin C. Watters.  Strain Surveys of Fuel Flow Vent Hole Number 13 and Stiffener Runout Number 2 in the F111 Wing Pivot Fitting for a Range of Rework Shapes. , 1997 .

[24]  Garret N. Vanderplaats,et al.  Numerical Optimization Techniques for Engineering Design: With Applications , 1984 .

[25]  M. Heller,et al.  Through-thickness shape optimisation of bonded repairs and lap-joints , 2002 .

[26]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[27]  Yury Grabovsky,et al.  The cavity of the optimal shape under the shear stresses , 1998 .

[28]  M. Mcdonald,et al.  Shape optimization of critical stiffener runouts for F-111 airframe life extension , 2002 .

[29]  J. Newman.  A crack opening stress equation for fatigue crack growth , 1984 .

[30]  Rajarshi Das,et al.  Optimisation of damage tolerant structures using a 3D biological algorithm , 2006 .

[31]  M. Heller,et al.  Through-thickness shape optimisation of typical double lap-joints including effects of differential thermal contraction during curing , 2005 .

[32]  C. Mattheck,et al.  Shape Optimization of Engineering Components by Adaptive Biological Growth , 1991 .

[33]  E. Schnack,et al.  Shape optimization of dynamically loaded machine parts , 1994 .

[34]  Paull Pedersen,et al.  Design for Minimum Stress Concentration by Finite Elements and Linear Programming , 1982 .

[35]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..