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.

中文翻译：

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具有独特的执行器和运动稳定性的受限运动设计

自适应结构的设计是提高建筑物可持续性的一种方法。自适应结构能够适应不同的负载和环境条件，或者通过大小变化来适应不断变化的要求。在后一种情况下，变形过程的力学和特性也对结构的能效起着重要作用。以前在作者小组中开发的变分运动设计方法允许识别两个给定几何形状之间的变形路径，这些变形路径相对于定义的质量函数而言是最佳的。在初步的学术研究中，此方法假定实现最佳运动的任意外部驱动力都可以访问每个自由度。这些（节点）力可以在后验中恢复。本发明通过约束运动来实现运动设计方法的扩展，该约束是通过预定义的一组致动力来实现运动。这些可以是外力或离散的内部执行器元件的规定长度机会。作为附加约束，考虑了运动期间每个中间构造的静态稳定性。可以通过强制执行刚度矩阵的正行列式来实现。考虑到运动过程中每个中间配置的静态稳定性。可以通过强制执行刚度矩阵的正行列式来实现。考虑到运动过程中每个中间配置的静态稳定性。可以通过强制执行刚度矩阵的正行列式来实现。