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

• Published in: Computers & structures Vol. 183; pp. 1 - 13
• Main Authors: Wei, Yintao, Zhao, Chonglei, Yao, Zhenhan, Hauret, Patrice, Li, Xuebing, Kaliske, Michael
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 15.04.2017; Elsevier BV
• Subjects: Adjoint variable method; Design optimization; Differentiation; Finite difference method; Finite element analysis; Geometrical mapping approach; Mapping; Mathematical analysis; Nonlinear equations; Nonlinear structures with contact forces; Sensitivity analysis; Shape optimization; Shear strain; Studies; Adjoint variable method; Sensitivity analysis; Geometrical mapping approach; Nonlinear structures with contact forces; Shape optimization
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2017.01.004

•A new adjoint shape design sensitivity for contact nonlinear structures is formulated.•The new method utilizes geometrical mapping approach to derive shape variation velocity field.•An 80% reduction in computational cost with respect to direct differentiation method is obtained.•Using parameterized tire shape arcs, boundary design velocities can be explicitly calculated.•A useful framework for sensitivity analysis of contact nonlinear structures is established. A new adjoint shape design sensitivity formulation for nonlinear structures subject to contact forces is developed. The method is based on a geometrical mapping approach where shape variation is regarded as a mapping characterized by the shape variation velocity field. An adjoint variable method is developed for performing sensitivity analysis of the average shear strain in the tire belt area, which profile is properly parameterized in function of arcs, allowing explicit design velocities calculated. It can be seen that the present method is much faster than the direct differentiation method and more accurate than the classical finite difference scheme.