A finite element method (FEM)-based solution of an industry-grade problem with complex geometry, partially-validated material property databases, incomplete knowledge of prior loading histories, and an increasingly user-friendly human-computer interface, is extremely difficult to verify because of at least five major sources of errors or solution uncertainty (SU), namely, (SU-1) numerical algorithm of approximation for solving a system of partial differential equations with initial and boundary conditions; (SU-2) the choice of the element type in the design of a finite element mesh; (SU-3) the choice of a mesh density; (SU-4) the quality measures of a finite element mesh such as the mean aspect ratio.; and (SU-5) the uncertainty in the geometric parameters, the physical and material property parameters, the loading parameters, and the boundary constraints. To address this problem, a super-parametric approach to FEM is developed, where the uncertainties in all of the known factors are estimated using three classical tools, namely, (a) a nonlinear least squares logistic fit algorithm, (b) a relative error convergence plot, and (c) a sensitivity analysis based on a fractional factorial orthogonal design of experiments approach. To illustrate our approach, with emphasis on addressing the mesh quality issue, we present a numerical example on the elastic deformation of a cylindrical pipe with a surface crack and subjected to a uniform load along the axis of the pipe.

This content is only available via PDF.
You do not currently have access to this content.