Variability Response Functions of Stochastic Plane Stress/Strain Problems

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Abstract
The concept of variability response function based on the weighted‐integral method is extended to two‐dimensional plane stress/plane strain stochastic problems in order to calculate their response variability (in terms of second moments of response quantities) and reliability (in terms of the safety index) with great accuracy even when using relatively coarse finite‐element meshes. The concept of variability response function is used to establish spectral‐distribution‐free upper bounds of the response variability. In addition, the variability response function based on the local‐averaging method is introduced to reduce the computational effort associated with the weighted‐integral method. The two methods are compared to estimate the relative accuracy of the more approximate local‐averaging method. The response variability is calculated using a first‐order Taylor expansion approximation of the response quantities. The safety index is calculated using the advanced first‐order second‐moment approach. One of the most important findings is that the coefficient of variation of certain response quantities can be much larger than the coefficient of variation of the elastic modulus (the input quantity).

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