A variational formulation for motion design of adaptive compliant structures

Sachse, Renate; Bischoff, Manfred

doi:10.1002/nme.6570

Cited by 13 publications

(34 citation statements)

References 64 publications

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“…As objective function it represents the property that is to be assigned to the motion. The procedure is described in detail in Sachse and Bischoff 31 and only the most important basics are repeated herein. Geometrically nonlinear, quasi‐static structural behavior is assumed.…”

Section: Motion Design Of Structuresmentioning

confidence: 99%

“…Geometrically nonlinear, quasi‐static structural behavior is assumed. Following Reference 31, the internal energy, integrated along the motion path s is considered. With the Green–Lagrange strain E and a linear elastic St. Venant–Kirchhoff material law this leads to

\begin{align} J = \int_{s} {normalΠ}_{normalint} d s = \int_{s} \int_{normalΩ} \frac{1}{2} {boldE}^{normalT} boldC boldE d normalΩ d s = \min . \end{align}

…”

Section: Motion Design Of Structuresmentioning

confidence: 99%

“…To guarantee uniqueness of the solution, the evolution of at least one displacement degree of freedom has to be controlled throughout the entire deformation process. The entire derivation and further explanations are given in Reference 31.…”

Section: Motion Design Of Structuresmentioning

confidence: 99%

“…The motion design method from Reference 31 relies on the hypothesis that discrete actuation forces can potentially be applied to every degree of freedom. This is illustrated in the simple truss system in Figure 2(A).…”

Section: Constraints For Prescribed Sets Of Actuation Forcesmentioning

confidence: 99%

“…In order to verify the applicability of the presented method, numerical experiments are presented in the next section. Among others, problems from Reference 31 are reused to demonstrate the correlation between unconstrained and constrained motion design with restrictions concerning the actuation forces.…”

Section: Constraints For Prescribed Sets Of Actuation Forcesmentioning

confidence: 99%

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Constrained motion design with distinct actuators and motion stabilization

Sachse

Geiger

Bischoff

2021

Numerical Meth Engineering

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The design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape changes. In the latter case, also the mechanics and properties of the deformation process play a role for the structure's energy efficiency. The method of variational motion design, previously developed in the group of the authors, allows to identify deformation paths between two given geometrical configurations that are optimal with respect to a defined quality function. In a preliminary, academic setting this method assumes that every single degree of freedom is accessible to arbitrary external actuation forces that realize the optimized motion. These (nodal) forces can be recovered a posteriori. The present contribution deals with an extension of the method of motion design by the constraint that the motion is to be realized by a predefined set of actuation forces. These can be either external forces or prescribed length chances of discrete, internal actuator elements. As an additional constraint, static stability of each intermediate configuration during the motion is taken into account. It can be accomplished by enforcing a positive determinant of the stiffness matrix.

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Section: Motion Design Of Structuresmentioning

confidence: 99%