Optimization of elastic columns using axial grading concept

This paper presents an exact method for obtaining column’s designs with the maximum possible critical buckling load while maintaining the total structural mass at prescribed value equal to that of a known baseline design. The developed optimization model dealt with slender elastic columns that are axially graded in either material or wall thickness. The first type of columns with material grading is constructed from uniform segments that are fabricated from two different materials, making the physical and mechanical properties change piecewisely in the axial direction. Design variables include the volume fraction of the constituent materials as well as the length of each segment composing the column. The other type considers piecewise axial grading of the cross-section wall thickness of columns constructed from uniform homogeneous isotropic segments. The associated design variables include the wall thickness and length of each segment composing the column. The buckling load analysis in either case is performed via an exact method, which ensures the attainment of the global maximum critical load under the imposed equality mass constraint for any number of segments, type of boundary conditions, type of cross section and type of material of construction. Numerical examples and detailed results, which are based on dimensionless analysis, are given and useful design charts have been developed for the cases of simply supported and cantilevered columns. Actually, the given approach can be beneficial to guide structural engineers for choosing the significant design variables in a proper and efficient way without violating economic feasibility requirements.