This article addresses one of the major constraints imposed by additive manufacturing processes on shape optimization problems -that of overhangs, i.e. large regions hanging over void without sufficient support from the lower structure. After revisiting the 'classical' geometric criteria used in the literature, based on the angle between the structural boundary and the build direction, we propose a new mechanical constraint functional, which mimics the layer by layer construction process featured by additive manufacturing technologies, and thereby appeals to the physical origin of the difficulties caused by overhangs. This constraint, as well as some variants, are precisely defined; their shape derivatives are computed in the sense of Hadamard's method and numerical strategies are extensively discussed, in two and three space dimensions, to efficiently deal with the appearance of overhang features in the course of shape optimization processes.

To cite this version:Charles Dapogny, Alexis Faure, Georgios Michailidis, Grégoire Allaire, Agnes Couvelas, et al.. Geometric constraints for shape and topology optimization in architectural design.Abstract. This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.

Ballistic helmets made of composite materials could be optimized to avoid extensive transient deformation and thus reduce the impact and blunt trauma to the head. However, this deformation cannot be completely removed, which is why the gap between the helmet and the head must be maintained at more than 12 mm.

Ramsden CE, McDaniel MC, Harmon RL, Renney KM, Faure A: Pudendal nerve entrapment as source of intractable perineal pain. Am J Phys Med Rehabil 2003;82:479 -484.Perineal pain caused by pudendal nerve entrapment is a rarely reported entity, with only a handful of cases in the modern literature. A 25-yr-old male medical student had refractory unilateral orchialgia for 32 mo and concomitant proctalgia for 14 mo. Pain was positional in nature, exacerbated by sitting and partially relieved when standing or recumbent. Pudendal nerve entrapment was diagnosed clinically, with computed tomography-guided nerve blocks providing temporary relief. A prolonged left pudendal nerve distal motor latency on electrodiagnostic testing later confirmed the diagnosis. At surgery, the left pudendal nerve was found flattened in the pudendal canal of Alcock and in contact with the sharp inferior border of the sacrospinous ligament. After surgical decompression and rehabilitation, the patient experienced significant relief of pain and returned to medical school. This case suggests pudendal nerve entrapment should be considered in the differential diagnosis of chronic urogenital or anorectal pain, particularly if the pain is aggravated by sitting or if there is a history of bicycle riding.

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This article considers the modelling of the effective properties of the constituent material of structures fabricated by additive manufacturing technologies; the influence of these properties on the design optimization process is analyzed, and the opportunities that they offer in this context are investigated. On the one hand, emphasizing on the case where the particular material extrusion techniques are used for the construction, we propose a model for the anisotropic material properties of shapes depending on the (user-defined) trajectory followed by the machine tool during the assembly of their 2d layers. On the other hand, we take advantage of the potential of additive manufacturing technologies for constructing very small features: we consider the optimization of the infill region of a shape with given external contour with the goal to improve at the same time its lightness and its robustness. The optimized and constraint functionals of the domain involved in the shape optimization problems in both contexts are rigorously analyzed, notably by relying on the notion of signed distance function. Eventually, several numerical experiments are conducted in two dimensions to illustrate the main points of the study.

A study was made of 100 homogeneous CT scans of the petrous part of the temporal bone to determine whether or not the arcuate eminence (AE) is a good landmark for the superior semicircular canal (SSCC) in the suprapetrous approach to the internal acoustic meatus which is used in the extirpation of acoustic neuromas. Direct measurements were made on consecutive coronal sections, 1 mm thick. The AE was absent from the petrous surface in 15% of cases. It corresponded to the relief of the SSCC in 37% of cases; laterally, however, it was separated from the petrous cortex by bone whose thickness varied from 0.5 to 5 mm. Finally, in 48% of cases, the AE was not a good landmark for the canal although nonetheless it participated in the development of this bulge in 46% of cases, always lying towards the medial border of the pneumatized eminence. In addition, study of the coronal sections with MRI allowed us to confirm that the AE does not routinely correspond to the imprint of a temporal sulcus. The AE, whose presence on the petrous surface is due to the combined effects of the SSCC, the air cells of the petrous part of the temporal bone and the temporal sulci, is only a good guide to the SSCC in 37% of cases and should not be considered as a reliable surgical landmark.

A simple occipitocervical osteosynthesis technique using cervical CCD (compact Cotrel-Dubousset) material is described in a clinical case. The originality of this technique consists in the occipital fastening used, involving the simultaneous insertion of two hooks into a single burr-hole. This greatly facilitated the positioning of the osteosynthesis rods, reduced surgical time, and provided immediate stability. These criteria are of considerable importance since this difficult surgical procedure is often performed in patients in a frail condition.