Topology optimization of finite strain elastoplastic materials using continuous adjoint method: formulation, implementation, and applications. (English) Zbl 07897591
Summary: This study presents a unified formulation of topology optimization for finite strain elastoplastic materials. As the primal problem to describe the elastoplastic behavior, we consider the standard \(J_2\)-plasticity model incorporated into Neo-Hookean elasticity within the finite strain framework. For the optimization problem, the objective function is set to accommodate both single and multiple objectives, the latter of which is realized by weighting each sub-function. The continuous adjoint method is employed to derive the sensitivity, which is a general form that accepts any kind of discretization method. Then, the governing equations of the adjoint problem are derived as a format that holds at any moment and at any location in the continuum body or on its boundary. Accordingly, the proposed formulation is independent of any requirements in numerical implementation. In addition, the reaction-diffusion equation is used to update the design variable in an optimizing process, for which the continuous distribution of the design variable as well as material properties are maintained. Two specific optimization problems, stiffness maximization and plastic hardening maximization, for two and three-dimensional structures are presented to demonstrate the ability of the proposed formulation.
Keywords:
topology optimization; finite strain; elastoplasticity; sensitivity analysis; adjoint methodReferences:
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