Adjoint optimization of pressurized membrane structures using automatic differentiation tools

Niewiarowski, Alexander; Adriaenssens, Sigrid; Pauletti, Ruy Marcelo de Oliveira

doi:10.1016/j.cma.2020.113393

Cited by 5 publications

(1 citation statement)

References 44 publications

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“…Following the work of Reference 58, we apply Taylor test to verify the accuracy of the gradients computed by the adjoint method. Given a perturbation

δ α

, the convergence rate of the residual is 1 using a zeroth‐order expansion:

\begin{align} r_{zeroth} = (||, \overset{J}{true} false(bold-italicα + h δ bold-italicα false) prefix- \overset{J}{true} false(bold-italicα false)) \to 0 at 𝒪 false(h false), \end{align}

and the convergence rate is 2 by a first‐order expansion:

\begin{align} r_{first} = (||, \overset{J}{true} false(bold-italicα + h δ bold-italicα false) prefix- \overset{J}{true} false(bold-italicα false) prefix- h \frac{normald \overset{J}{true}}{normald bold-italicα} \cdot δ bold-italicα) \to 0 at 𝒪 false(h^{2} false) . \end{align}

The results above are direct consequences of the Taylor's theorem 55 .…”

Section: Mapped Shape Optimization Methodsmentioning

confidence: 99%

Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation

Xue

Sheng

2022

Numerical Meth Engineering

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Soft cellular mechanical metamaterials (CMMs) have gained increasing attention due to their unique mechanical properties, especially when under large deformation. However, the strong nonlinearities and complex instabilities brought by the large deformation field is a critical challenge for the rational design of soft CMMs. In this work, we propose a mapped shape optimization method as a computational framework for inverse designs of soft CMMs.The core of this method is to introduce a fixed referential configuration. The geometric changes of the cellular structures are reflected by altering a differentiable shape map; and the deformation of the corresponding structures are determined by mapping the finite element computations to the referential configuration. Such formulation avoids the need to alter the background mesh and more importantly, provides an efficient way to compute the gradient of the objective functions with respect to the design variables via the adjoint method. The proposed method is of general purpose, and three distinct yet representative numerical examples are used to demonstrate the effectiveness of the method: optimizing unique overall mechanical properties, precise control of the onset of instability, and optimizing phononic band gaps. These examples cover a broad range of important engineering applications of soft CMMs.

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“…Following the work of Reference 58, we apply Taylor test to verify the accuracy of the gradients computed by the adjoint method. Given a perturbation