DESIGN SENSITIVITY ANALYSIS OF CRITICAL LOAD-FACTOR FOR NONLINEAR STRUCTURAL SYSTEMS

A continuum formulation of sizing design sensitivity analysis of the critical load factor is developed for nonlinear structural systems that are subject to conservative static loadings. Both geometric and material nonlinear effects are considered. Sizing design variables, such as thickness and cross-sectional areas of structural components, are treated. The total Lagrangian formulation for an incremental equilibrium equation and one- and two-point linearized eigenvalue problems are utilized to estimate the critical load factor. A distributed parameter approach and the adjoint variable method are used to obtain design sensitivity expressions in continuum mechanics formulation. A numerical method is presented to evaluate design sensitivity expressions using established finite element codes. The proposed method is tested using several examples. The numerical results show that the proposed method for design sensitivity of the critical load factor is accurate. It is found that, as the applied load approaches the critical load, the design sensitivity of the critical load factor does not converge to the design sensitivity of the actual critical load, even though the estimated critical load converges to the actual critical load and the design sensitivity of the critical load factor is correct. © 1990.