Design Sensitivity Analysis and Optimization of Nonlinear Structural Systems With Critical Loads

[+] Author and Article Information
Jong Sang Park, Kyung K. Choi

Department of Mechanical Engineering and Center for Simulation and Design Optimization of Mechanical Systems, College of Engineering, The University of Iowa, Iowa City, IA 52242

J. Mech. Des 114(2), 305-312 (Jun 01, 1992) (8 pages) doi:10.1115/1.2916947 History: Received March 01, 1990; Online June 02, 2008


A continuum formulation for design sensitivity analysis of critical loads is developed for nonlinear structural systems that are subjected to conservative loading. Both geometric and material nonlinear effects are considered. Sizing design variables such as cross-sectional areas of beam or truss design components and thicknesses of plate or membrane design components, together with their shape design variables, are treated. A continuum approach is used to obtain design sensitivity expressions in integral form. For shape design sensitivity analysis, the material derivative concept and domain method are used to find variations of the critical load due to variations in shape of the physical domain. The total Lagrangian formulation for incremental equilibrium equation and one-point linearized eigenvalue problems are utilized. A numerical method is presented to evaluate continuum design sensitivity expressions using analysis results of established finite element codes. It is found that no adjoint system is necessary for design sensitivity analysis of the critical load. Numerical results show the proposed method for design sensitivity of critical loads is accurate for both sizing and shape design variables. A numerical procedure for optimal design of nonlinear structural systems is presented, using the proposed continuum design sensitivity analysis method. An optimal design problem with a stability constraint is solved.

Copyright © 1992 by The American Society of Mechanical Engineers
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