Abstract

Master Degree Students in Civil and Mechanical Engineering were given specific geometries to model in a finite element analysis course to validate the theoretical stress concentration factor for a common stress riser. Their results that met all proper analysis guidelines were considered typical in industrial applications even though each student obtained a different K_t. The authors take the uniaxial, isothermal results and expand the study to element types in ANSYS. For more challenging finite element analyses, one must consider composite materials definition, biaxiality of stress, thermal gradients, pre-stress modeling, nonlinear property modeling, etc. Those effects on prediction can be added stochastically to variation due real world loads, wall thickness variation, actual thermal values, real world stress strain relationships, etc. One can postulate level of difficulty in a finite element analysis increases with level of complexity and variation in the system being modeled. The analyses detailed include the K_t of a hole where the theoretical K_t approaches 2.5 in a finite width plate. This represents the simplest of analyses in that it is effectively two-dimensional, isothermal, uniaxial, and isotropic. The authors expand results for gradually improved mesh densities. The accuracy of the results would be suspect in most applications and so the authors attempt a patch test study. Verification and validation have been critical to the aerospace industry. The authors have also noted variation in the simplest of analyses. This computational variation can be added to physical variation in the same set of analyses and may inherently be present. The authors considered the following computational influences 1) Linear isotropic material properties 2) Element shape biasing 3) Element skewness 4) Element aspect ratio 5) Convergence criteria for load and displacement 6) Solver chosen 7) Thick walled shell theory vs thin walled Finite Element analysis results can vary for the same problem due to changes in the finite element code, the operation system, the user, the mesh bias, the element skewness, element mesh density, exactness of boundary conditions, and unknown sources. We postulate the more variables in an analyses, the greater the deviation can be from the exactly solution and that a design system has to consider these factors. We further postulate a critical review of certain elements may be necessary.