scholarly journals Adjoint design sensitivity analysis and optimization of nonlinear structures using geometrical mapping approach

2017 ◽  
Vol 183 ◽  
pp. 1-13 ◽  
Author(s):  
Yintao Wei ◽  
Chonglei Zhao ◽  
Zhenhan Yao ◽  
Patrice Hauret ◽  
Xuebing Li ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Nonlinear Structures ◽  
Mapping Approach ◽  
Adjoint Design Sensitivity Analysis

Explicit and Implicit Methods for Design Sensitivity Analysis of Nonlinear Structures Under Dynamic Loads

1997 ◽  
Vol 50 (11S) ◽  
pp. S11-S19 ◽  
Author(s):  
Jasbir S. Arora ◽  
Abhijit Dutta
Keyword(s):  
Sensitivity Analysis ◽  
Stiffness Matrix ◽  
Design Sensitivity ◽  
Implicit Method ◽  
Design Sensitivity Analysis ◽  
Dynamic Loads ◽  
Nonlinear Structures ◽  
Explicit Method ◽  
Implicit Methods ◽  
Analysis Phase

Explicit and implicit methods for design sensitivity analysis of nonlinear structures subjected to transient dynamic loads are described. The direct differentiation method is used to calculate the sensitivities. Elastic and elasto-plastic problems undergoing large deformation are treated in the formulation. The explicit method is quite straightforward to implement for analysis as well as design sensitivity analysis: knowing all the quantities at time t, one updates the quantities for the next time point without solution of any linear system of equations, or any iterations. For the implicit method, the effective stiffness matrix for the sensitivity equation is different from that for the analysis phase due to inclusion of large deformation in the formulation. A numerical procedure to integrate the equation is proposed which uses the symmetric effective stiffness matrix from the analysis phase. Although the sensitivity analysis problem is linear, the procedure requires iterations for sensitivity calculations at each time step, as for the analysis phase. The implicit method is implemented using the pre-conditioned conjugate gradient iterative solution scheme. Numerical results for sensitivities indicate the implicit method to be more accurate than the explicit method for transient elastoplastic problems. However, the explicit method is substantially more efficient than the implicit method.

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