State Transition Approach to Reliability Based Design of Composite Structures

*† The paper presents a new approach to the optimal design of composite structural systems in the presence of uncertainties. A progressive damage propagation model for composites, based on transformation field analysis (TFA), is used to develop a design for reliability that includes multiple failure modes typical in laminated composite structural systems. This analysis involves multiscale computations, with complex interactions between response parameters at different length scales. Not all failure modes are equally catastrophic and may only result in degraded structural performance. A design problem formulation based on a state transition approach is introduced, and allows for the handling of multiple failure modes in a rational manner. This methodology termed as a system effectiveness approach, models designer preference as to acceptability of degraded performance, and is used to develop optimal designs. A comparison of these designs against those obtained from a more widely used competing risk methodology provides insight into the advantages of the new approach.

[1]  John W. Hutchinson,et al.  Models of fiber debonding and pullout in brittle composites with friction , 1990 .

[2]  R. Pyrz,et al.  IUTAM Symposium on Microstructure-Property Interactions in Composite Materials : proceedings of the IUTAM symposium held in Aalborg, Denmark, 22-25 August 1994 , 1995 .

[3]  Achintya Haldar,et al.  Probability, Reliability and Statistical Methods in Engineering Design (Haldar, Mahadevan) , 1999 .

[4]  Toshio Mura,et al.  Sliding Inclusions and Inhomogeneities With Frictional Interfaces , 1992 .

[5]  John Erjavec,et al.  Modern Statistics for Engineering and Quality Improvement , 2000 .

[6]  Henrik O. Madsen,et al.  Structural Reliability Methods , 1996 .

[7]  Sankaran Mahadevan,et al.  Adaptive simulation for system reliability analysis of large structures , 2000 .

[8]  Galib H. Abumeri,et al.  Probabilistic dynamic buckling of composite shell structures , 2005 .

[9]  M. Toya,et al.  A crack along the interface of a circular inclusion embedded in an infinite solid , 1974 .

[10]  George J. Dvorak,et al.  Transformation Analysis of Inelastic Laminates , 1995 .

[11]  William W. Feng,et al.  A Failure Criterion for Composite Materials , 1991 .

[12]  Bhushan Lal Karihaloo,et al.  Elastic Field of an Elliptic Inhomogeneity With Debonding Over an Arc (Antiplane Strain) , 1985 .

[13]  Toshio Mura,et al.  The Elastic Inclusion With a Sliding Interface , 1984 .

[14]  Z. Hashin.  Failure Criteria for Unidirectional Fiber Composites , 1980 .

[15]  Paul S. Steif,et al.  Longitudinal Shearing of a Weakly Bonded Fiber Composite , 1988 .

[16]  A. Wronski,et al.  Kinking and compressive failure in uniaxially aligned carbon fibre composite tested under superposed hydrostatic pressure , 1982 .

[17]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[18]  Jian Deng,et al.  Structural reliability analysis for implicit performance function using radial basis function network , 2006 .

[19]  Richard M. Christensen,et al.  A critical evaluation for a class of micro-mechanics models , 1990 .

[20]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[21]  Sankaran Mahadevan,et al.  Probabilistic fatigue life prediction of multidirectional composite laminates , 2005 .

[22]  Jian Zhang,et al.  Transformation field analysis of damage evolution in composite materials , 2001 .

[23]  P. D. Soden,et al.  Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: failure exercise benchmark data , 2002 .

[24]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[25]  Ritesh Khire,et al.  Handling Uncertainty Propagation in Laminated Composites Through Multiscale Modeling of Progressive Failure , 2007 .

[26]  L. J. Hart-Smith.  Should fibrous composite failure modes be interacted or superimposed , 1993 .

[27]  Mark W. Hilburger,et al.  Toward a Probabilistic Preliminary Design Criterion for Buckling Critical Composite Shells , 2003 .

[28]  Rakesh K. Kapania,et al.  Probability of Failure of Composite Cylinders Subjected to Axisymmetric Loading , 2004 .

[29]  Toshio Mura,et al.  The stress field of a sliding inclusion , 1985 .

[30]  Sanghyun Choi,et al.  Efficient method for calculation of system reliability of a complex structure , 2004 .

[31]  Glynn J. Sundararaj,et al.  Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers , 2000 .

[32]  R. Christensen.  Stress based yield/failure criteria for fiber composites , 1997 .

[33]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[34]  Irem Y. Tumer,et al.  A NEW APPROACH TO PROBABILISTIC RISK ANALYSIS IN CONCURRENT AND DISTRIBUTED DESIGN OF AEROSPACE SYSTEMS , 2005, DAC 2005.

[35]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[36]  Toula Onoufriou,et al.  Reliability-based importance assessment of structural members with applications to complex structures , 2002 .

[37]  Richard M. Christensen,et al.  Tensor Transformations and Failure Criteria for the Analysis of Fiber Composite Materials , 1988 .

[38]  Christos C. Chamis,et al.  Non-Deterministic Optimization of Composite Structures Reliability , 2004 .