Abstract
In this paper, load step reduction techniques are investigated for adjoint sensitivity analysis of path-dependent nonlinear finite element systems. In particular, the focus is on finite strain elastoplasticity with typical hardening models. The aim is to reduce the computational cost in the adjoint sensitivity implementation. The adjoint sensitivity formulation is derived with the multiplicative decomposition of deformation gradient, which is applicable to finite strain elastoplasticity. Two properties of adjoint variables are investigated and theoretically proved under certain prerequisites. Based on these properties, load step reduction rules in the sensitivity analysis are discussed. The efficiency of the load step reduction and the applicability to isotropic hardening and kinematic hardening models are numerically demonstrated. Examples include a small-scale cantilever beam structure and a large-scale conrod structure under huge plastic deformations.
Highlights
Shape optimization plays an important role in industrial structure design
A unified framework has been presented on how to formulate sensitivity with adjoint variable method for a wide range of path-dependent system behaviors (Michaleris et al 1994; Alberdi et al 2018). It shows that the adjoint variable method should follow a backward solution
According to Eqs. (44) to (46), the major computational effort in the adjoint sensitivity analysis is the backwards solution of adjoint variables
Summary
Shape optimization plays an important role in industrial structure design. Non-parametric shape optimization, which dates back to the work by Zienkiewicz and Campbell (1973), employs nodal coordinates in a finite element system as design variables. A unified framework has been presented on how to formulate sensitivity with adjoint variable method for a wide range of path-dependent system behaviors (Michaleris et al 1994; Alberdi et al 2018). Techniques to reduce the computational cost in the sensitivity analysis are highly demanded For this purpose, sensitivity reanalysis in the frame of independent coefficients strategy has been suggested, which employs local modification of a large-scale structure to avoid repeated solutions of full finite element analysis (Liu and Wang 2008). Sensitivity reanalysis in the frame of independent coefficients strategy has been suggested, which employs local modification of a large-scale structure to avoid repeated solutions of full finite element analysis (Liu and Wang 2008) This has been demonstrated to be effective only for linear structural systems.
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