International Journal of Solids and Structures
A topology optimization method is proposed for the design of trusses with random geometric imperfections due to fabrication errors. This method is a generalization of a previously developed perturbation approach to topology optimization under geometric uncertainties. The main novelty in the present paper is that the objective function includes the nonlinear effects of potential buckling due to misaligned structural members. Solutions are therefore dependent on the magnitude of applied loads and the direction of resulting internal member forces (whether they are compression or tension). Direct differentiation is used in the sensitivity analysis, and analytical expressions for the associated derivatives are derived in a form that is computationally efficient. A series of examples illustrate how the effects of geometric imperfections and buckling may have substantial influence on truss design. Monte Carlo simulation together with second-order elastic analysis is used to verify that solutions offer improved performance in the presence of geometric uncertainties.
Jalalpour M., Igusa T., and Guest J.K. “Optimal design of trusses with geometric imperfections: Accounting for global instability”, International Journal of Solids and Structures 48(21): 3011-3019, 2011
NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 48, 21, (October 15, 2011) DOI:10.1016/j.ijsolstr.2011.06.020
This work was supported by the National Science Foundation under Grant No. CMMI-0928613 with Dr. Christina Bloebaum serving as program officer. This support is gratefully acknowledged.