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Optimization of the Stress Intensity in Controlled Evolution of a Continuously Inhomogeneous Solid ?

机译：优化在连续不均匀固体的控制演化中的应力强度

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Control and optimization of manufacturing processes play essential role in LbL (layer-by-layer) technologies. Optimal control allows one, in particular, to reduce the residual stresses in produced details. The present paper provides an example of such optimization. The LbL-structure under study is represented as a hyperelastic hollow cylinder with finite thickness. This item is produced by a successive joining of infinitesimally thin layers (laminae) to a cylindrical substrate. Deformations assume to be finite in the course of production. The assembled structure has residual stresses due to layerwise shrinkage. It means that the LbL-structure does not have stress-free shape in Euclidean space. In this regard, a non-Euclidean approach is used: the body is embedded into a space with non-Euclidean connection. This space is considered as a stress free shape for the body. The optimization problem is solved to reduce residual stresses. The control is the hydrostatic loading applied to the internal surface of the cylinder, while the cost function is the maximum of stress intensity.
机译：制造过程的控制和优化在LBL（层）技术中起重要作用。最佳控制允许一个，特别是减少生产细节中的残余应力。本文提供了这种优化的示例。研究下的LBL-结构被表示为具有有限厚度的超坯空心圆柱体。该项目是通过连续连接到圆柱形基板的无限薄层（Laminae）。变形假设在生产过程中是有限的。由于层状收缩，组装结构具有残余应力。这意味着LBL-结构在欧几里德空间中没有压力的形状。在这方面，使用非欧几里德方法：身体嵌入具有非欧几里德连接的空间中。该空间被认为是身体的应力自由形状。解决了优化问题以减少残余应力。控制是施加到气缸内表面的静液压加载，而成本函数是应力强度的最大值。

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