Abstract
We present a design sensitivity analysis and isogeometric shape optimization with path-dependent loads belonging to non-conservative loads under the assumption of elastic bodies. Path-dependent loads are sometimes expressed as the follower forces, and these loads have characteristics that depend not only on the design area of the structure but also on the deformation. When such a deformation-dependent load is considered, an asymmetric load stiffness matrix (tangential operator) in the response region appears. In this paper, the load stiffness matrix is derived by linearizing the non-linear non-conservative load, and the geometrical non-linear structure is optimally designed in the total Lagrangian formulation using the isogeometric framework. In particular, since the deformation-dependent load changes according to the change and displacement of the design area, the isogeometric analysis has a significant influence on the accuracy of the sensitivity analysis and optimization results. Through several numerical examples, the applicability and superiority of the isogeometric analysis method were verified in optimizing the shape of the problem subject to deformation-dependent loads.
Highlights
Special attention is required in the structural analysis of the pressure loading, as its loading direction could change with the deformation of the structure
The obtained isogeometric sensitivity means a gradient of the objective function, which is utilized as important information in the gradient-based optimization algorithm, the modified method of feasible direction (MMFD) in this study
Design sensitivity analysis and shape optimization were performed on nonlinear structures subjected to loads that depend on design change and structural deformation
Summary
Special attention is required in the structural analysis of the pressure loading, as its loading direction could change with the deformation of the structure. Engineering problems with deformation-dependent loading are frequently encountered, for example, in the design of dams, tires, airbags, and pressurized vessels. When such a deformationdependent load is considered, an asymmetric tangential operator expressed as a load stiffness matrix appears in the governing equation. Hibbit [1] first mentioned the concept of load stiffness, and in the case of a surface traction load, the load stiffness is symmetric if it is applied to the fully enclosed volume If it is not the case, the equation has an asymmetric term which is to be solved using the approximation method, assuming it is symmetric while refining the mesh. The convergence rate dependent on tangent stiffness was discussed in numerical examples for an axisymmetric case
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
