Closed form buckling and sensitivity analysis of isotropic and orthotropic columns with uncertain material and geometric properties via convex modeling Part II: Application and validation

Abstract

In Part I of this work, closed form analytical formulas were developed including the effect of dimensional and material uncertainties for isotropic and orthotropic columns for a number of cross-sectional shapes widely-used in several engineering applications. In the present Part II of the work on uncertainty modelling of isotropic and orthotropic columns, numerical results are presented with a view towards assessing the effect of material and geometric uncertainties on the buckling load. Results are given for most commonly used cross-sectional shapes and for different levels of uncertainty. Numerical implementation of the sensitivity analysis presented in Part I identifies the degree of sensitivity of the buckling load to different problem parameters. As such, the material and geometric properties affecting the buckling load the most and to what degree are identified. The findings are of importance in the design of columns in the face of manufacturing uncertainties as well as material imperfections. Results are given for a range of problem parameters in the form of contour plots, graphs and tables. The types of cross-sections which perform better under uncertainty are identified for isotropic and orthotropic columns. This enables the engineer to make informed decisions as a priority, particularly in the early stages of the design process. The results identify for the types of cross-sectional shapes which will be more reliable and less sensitive to imperfections taking various design uncertainties into account. Present results, obtained by symbolic computation, are verified using the finite element counterparts and close agreement between the two sets of results are observed.