Journal of Structures
234085 (13 pp.)
A systematic approach is presented in this paper to derive the analytical deflection function of a stepped beam using singularity functions. The discontinuities considered in this development are associated with the jumps in the flexural rigidity and the applied loads. This approach is applied to static and vibration analyses of stepped beams. The same approach is later extended to perform sensitivity analysis of stepped beams. This is done by directly differentiating the analytical deflection function with respect to any beam-related design variable. The particular design variable considered here is the location of discontinuity in flexural rigidity. Example problems are presented in this paper to demonstrate and verify the derivation process.
Original Publication Citation
Cheng, P., Davila, C., & Hou, G. (2014). Static, vibration analysis and sensitivity analysis of stepped beams using singularity functions. Journal of Structures, 2014, 234085. doi:10.1155/2014/234085
Cheng, Peng; Davila, Carla; and Hou, Gene, "Static, Vibration Analysis and Sensitivity Analysis of Stepped Beams Using Singularity Functions" (2014). Mechanical & Aerospace Engineering Faculty Publications. 46.