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A B S T R A C T This paper aims at proposing a new fatigue life estimation model that is preferably adapted to welded joints subjected to multiaxial loading. First, a mesh-size insensitive structural stress is defined that enables to characterize the stress concentration effect appropriately. Second, the multiaxial stress state and loading path influence are taken into account in the lifetime prediction model by adopting a suitable critical plane method, originally proposed by Carpinteri and co-authors. Experimental verification is conducted for a given welded joint geometry under different loading conditions, including uniaxial, torsional and multiaxial loads. The reliability and effectiveness of the new method are validated through substantive fatigue testing data.Keywords critical plane method; fatigue; multiaxial load; structural stress; welded joint. N O M E N C L A T U R Ef x′ , f y′ = nodal forces h = thickness of plate or tube k = negative inverse slope of the S-N curve k σ , k τ = stress concentration factors k 0 = negative inverse slope of the standard torsional fatigue curve k 1 = negative inverse slope of the standard uniaxial fatigue curve K τ = negative inverse slope of the modified Wöhler curve l k , m k , n k = principal stress direction cosines m x′ , m y′ = nodal moments M b = bending moment M t = torsion moment N Ref = reference number of cycles to failure N f,es = estimated number of cycles to failure N f,ex = experimental number of cycles to failure W(t i ) = weight function at time instant t i W S = summation of the weights W(t i ) ϕ, θ, ψ = principal Euler angleŝ ϕ,θ,ψ = weighted mean principal Euler angles λ = distance from the reference plane to the weld toe ρ w = multiaxiality factor σ hs = normal stress at the hot spot σ m = membrane stress σ b = bending stress σ a = normal stress amplitude σ mean = mean normal stress σ npl = nonlinear stress peak σ x = normal stress along the x direction σ n = nominal stress σ s = structural stress

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Traditional reliability-based design optimization (RBDO) generally describes uncertain variables using random distributions, while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information. Then, an important probability-interval hybrid reliability problem emerged. For uncertain problems in which interval variables are included in probability distribution functions of the random parameters, this paper establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm, which aims to provide an effective computational tool for reliability design of many complex structures. The reliability of an inner constraint is an interval since the interval distribution parameters are involved; this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure. An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis. By using an incremental shifting vector (ISV) technique, the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis. Three numerical examples are presented to verify the proposed method, which include one simple problem with explicit expression and two complex practical applications.

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