Keywords: composite structure, surrogate modelling, system reliability, multiple failures, robust design.

Composite plate and shell structures develop interactions in their physical response between ply, laminate and structure levels inducing failure events at different scales and competing failure paths [1]. As a result of the associated complexity of the analysis and design the structural response becomes highly unpredictable because of uncertainties in the geometry, loading, or material properties can completely change the failure path. The introduction of reliability assessment methods in the safety analysis of composite structures increased the complexity and the efficiency of the failure evaluation methodologies proposed in the literature. In this paper, an approach based on surrogate modelling of first ply failure to obtain the reliability of whole composite structure is proposed and analysed. This approach overcomes the expensive costs associated with exhaustive local reliability evaluation. However, the problem of coupling the finite element method applied to composite laminates with the most probable failure point search is difficult to solve.

In this paper the errors introduced by approximations used in the structural reliability calculation of composite laminate structures are studied within the context of robust design optimisation. So, the analysis is performed considering the maximum loading capability of the composite structure for a prescribe reliability level [2]. The identification of multiple failure modes and its importance in reliability analysis are outlined and discussed. From the performed analysis some appointments should be referred as follows:

1. There are different length scales. For a limit state function:
   • The interval of variation of the Tsai number is narrow,
   • The interval of variation of the reliability index is large.
2. The reliability index:
   • The relationship with the applied loading is a quadratic function and depends on the anisotropy,
   • The relationship with the Tsai number is a quadratic function and depends on the anisotropy,
   • Maximum load is very sensitive to ply angle variation (for fixed reliability index),
   • Reliability index is very sensitive to load increasing (fixed ply angle).
3. The Tsai number versus the reliability index:
   • It is necessary to establish a relationship between both parameters,
   • For service conditions corresponding to the Tsai number in the neighbourhood of the failure surface (Tsai number equals 1), the reliability index of the composite structure can be safely associated to critical Tsai number and the proposed surrogate modelling is valid. Furthermore, new investigations are needed to overcome the high computational costs in the reliability assessment of composite structures.

1

M. Rais-Rohani, M.N. Singh, "Comparison of global and local response surface techniques in reliability-based optimization of composite structures", Structural and Multidisciplinary Optimization, 26, 333-345, 2004. doi:10.1007/s00158-003-0353-0

2

C. Conceição António, L.N. Hoffbauer, "An approach for reliability-based robust design optimisation of angle-ply composites", Composite Structures, 90, 53-59, 2009. doi:10.1016/j.compstruct.2009.01.008

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