A methodology for structural optimisation with damage tolerance constraints

Abstract This paper presents recent developments in the optimal design of structural components with fracture constraints. To minimise the computational effort it is suggested that an initial “near optimum” shape be used. One approach could be to begin with the optimal shape for the non-cracked geometry. This initial near optimum shape would then be used in conjunction with the alternating finite element method, for multiple cracks, which builds on existing CAD based finite element models and the resultant formulation then linked to available optimisation codes. This approach is illustrated by considering the problem of an optimum cut-out geometry for a square plate subjected to a 4:1 and a 2:1 biaxial stress field. When considering the problem of shape optimisation with static fracture constraints it was found that an initial “near optimal” shape, based on the optimal shape for the uncracked geometry, was in fact an excellent approximation to the optimal solution for the cracked problem. It was also found that, in each case, for a given crack length the stress intensity factors, for cracks emanating at any arbitrary point around the hole, were essentially constant along most of the circumference. This behaviour is intuitively expected for an optimised geometry, where it would be hoped that all locations around the hole would be equally critical. A similar behaviour was found when considering shape optimisation with durability, i.e. crack growth, constraints. In this case it was hypothesised that the optimum shape would be such that all locations around the cut-out would be equally fatigue critical. However, in this case it is believed that the final optimal shape will depend on: the initial flaw size, the critical crack length, the load spectrum and the overall geometry of the structure. The analysis also reveals that, as the geometry of the cut-out or hole changes, the location of the crack which determines the minimum fatigue life can also change. This makes it necessary to consider flaws at a range of locations around the hole.

[1]  Satya N. Atluri,et al.  An alternating method for analysis of surface-flawed aircraft structural components , 1983 .

[2]  J Visick.  Damage Tolerance/Maintenance of Airworthiness - an Operators Viewpoint , 1991 .

[3]  U. Berkes.  Efficient optimization of aircraft structures with a large number ofdesign variables , 1990 .

[4]  J. F. Williams,et al.  A numerical study of MSD in aluminium alloys , 1995 .

[5]  Philip E. Gill,et al.  Practical optimization , 1981 .

[6]  A. J. Durelli,et al.  OPTIMUM HOLE SHAPES IN FINITE PLATES UNDER UNIAXIAL LOAD , 1979 .

[7]  R. Haftka,et al.  Structural shape optimization — a survey , 1986 .

[8]  Farrokh Mistree,et al.  Compromise: An effective approach for the design of damage tolerant structural systems , 1987 .

[9]  Susan Pitt,et al.  MULTIPLE-SITE AND WIDESPREAD FATIGUE DAMAGE IN AGING AIRCRAFT , 1997 .

[10]  Yeh-Liang Hsu,et al.  A review of structural shape optimization , 1994 .

[11]  Martin P. Bendsøe,et al.  Topology design of structures , 1993 .

[12]  Satya N. Atluri,et al.  An Embedded Elliptical Crack, in an Infinite Solid, Subject to Arbitrary Crack-Face Tractions , 1981 .

[13]  Robert A. Canfield,et al.  ASTROS - A multidisciplinary automated structural design tool , 1987 .

[14]  Michael A. Saunders,et al.  User''s guide for NPSOL (Ver-sion 4.0): A FORTRAN package for nonlinear programming , 1984 .

[15]  Eckart Schnack.  A Method of Feasible Direction with FEM for Shape Optimization , 1988 .

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

[17]  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 .

[18]  J Samuelson,et al.  Optimization of hydraulic cylinder housing , 1990 .

[19]  Prabhat Hajela,et al.  Genetic Algorithms in Structural Topology Optimization , 1993 .

[20]  C. Mattheck,et al.  AN INTELLIGENT CAD‐METHOD BASED ON BIOLOGICAL GROWTH , 1990 .

[21]  Z. Fu,et al.  An integrated approach to structural shape optimization , 1996 .

[22]  Pauli Pedersen.  Design for Minimum Stress Concentration — Some Practical Aspects , 1988 .

[23]  P. Gage,et al.  Variable-complexity genetic algorithm for topological design , 1995 .

[24]  Ren-Jye Yang,et al.  Component shape optimization using bem , 1990 .

[25]  C. Mattheck,et al.  DESIGN AND GROWTH RULES FOR BIOLOGICAL STRUCTURES AND THEIR APPLICATION TO ENGINEERING , 1990 .

[26]  Prabhat Hajela,et al.  COMPUTATIONAL EFFICIENCY ASPECTS IN BOUNDARY ELEMENT BASED STRUCTURAL SHAPE OPTIMIZATION , 1991 .

[27]  R. Kaye,et al.  Structural Shape Optimisation by Iterative Finite Element Solution , 1997 .

[28]  A. J. Durelli,et al.  Optimization of hole shapes in circular cylindrical shells under axial tension , 1981 .

[29]  H. L. Groth,et al.  Shape optimization of bonded joints , 1991 .

[30]  M. Touratier,et al.  Optimal design for minimum weight in a cracked pressure vessel of a turboshaft , 1996 .

[31]  Hojjat Adeli,et al.  Distributed Genetic Algorithm for Structural Optimization , 1995 .

[32]  C. Mattheck,et al.  A new method of structural shape optimization based on biological growth , 1990 .

[33]  Satya N. Atluri,et al.  Developments in the analysis of interacting cracks , 1995 .

[34]  Satya N. Atluri,et al.  Analysis of Surface Flaw in Pressure Vessels by a New 3-Dimensional Alternating Method , 1982 .

[35]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[36]  Eisuke Kita,et al.  Boundary element method for quasi-harmonic differential equation with application to stress analysis and shape optimization of helical spring , 1990 .

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

[38]  Klaus Bethge,et al.  Fatigue testing of a shape-optimized circular hole in a plate under tensile and bending loads , 1990 .

[39]  Gengdong Cheng,et al.  SHAPE OPTIMIZATION OF CONTINUUM WITH CRACK , 1988 .

[40]  Satya N. Atluri,et al.  Computational Schemes for Integrity Analyses of Fuselage Panels in Aging Airplanes , 1991 .

[41]  D. J. Neill,et al.  ASTROS - A multidisciplinary automated structural design tool , 1987 .

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

[43]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary aerospace design optimization - Survey of recent developments , 1996 .

[44]  M. Kitano,et al.  An efficient shape optimization technique of a two-dimensional body based on the boundary element method , 1993 .