A numerical integration method for evaluating the structural failure probability is proposed. A hypersphere of a specified radius in polar coordiantes is considered and then the surface of that is divided into several finite element meshes at constant step angles of the respective arguments. A failure probability element related to a certain mesh is formulated as the mesh area multiplied by the probability dneisty at the same radial distance and an index, one or zeor, indicating whether or not the mesh is located in the failure domain. The sum of all the failure probability elements gives the failure probability contribution of the hypersphere. The structural failure probability elements gives the failure probability contribution of the hypersphere. The structural failure probability is evaluated approximately by the sum of the failure probability contribution of several concentric hyperspheres, each radius of which is changed at a constant width within an effective distance range. Numerical examples are presented to show the validity of the proposed method.
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