Variational method for design sensitivity analysis in nonlinear structural mechanics

AIAA Journal ◽  
1988 ◽  
Vol 26 (5) ◽  
pp. 595-603 ◽  
Author(s):  
J. B. Cardoso ◽  
J. S. Arora
Keyword(s):  
Sensitivity Analysis ◽  
Variational Method ◽  
Structural Mechanics ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Nonlinear Structural ◽  
Nonlinear Structural Mechanics

Design Sensitivity Analysis in Structural Mechanics. I. Static Response Variations

1980 ◽  
Vol 8 (1) ◽  
pp. 17-41 ◽  
Author(s):  
Edward J. Haug ◽  
Bernard Rousselet
Keyword(s):  
Sensitivity Analysis ◽  
Structural Mechanics ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Static Response

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

1990 ◽  
Author(s):  
Jong Sang Park ◽  
Kyung K. Choi
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Critical Load ◽  
Critical Loads ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Shape Design ◽  
Structural Systems ◽  
Nonlinear Structural ◽  
Design Variables

Abstract 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.

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