Nonplanar Sections Research Articles

Non-planar parallel sections: A new approach in digital image analysis of CT volume datasets to improve the assessment of pottery-forming methods

The paper presents a newly developed technique for displaying sections of CT reconstructions of pottery fragments. Currently, planar tangential sections are the primary way to show a view perpendicular to the surface of the pottery fragment. This section is essential as it displays structural phenomena critical to interpreting pottery-forming methods. However, the planar tangential sections in curved vessel walls show only a limited area of the wall and, even in this area, the sections cannot display structural phenomena at a constant depth of the wall. Consequently, we designed the construction of a non-planar section that follows the vessel’s shape and can be embedded at a defined depth from the surface so that it maps structural phenomena in defined subsurface layers coaxial with the vessel surface. The newly designed imaging technique was applied to the selection of archaeological pottery from the Czech Republic dated to the La Tène period. We demonstrate the usefulness of the non-planar sections for visual inspection of the diagnostic features related to pottery forming as well as for more accurate calculation of the orientation of the components of the ceramic body.

A general theory for the bending of multilayer van der Waals materials

Multilayer van der Waals (vdW) materials exhibit nontrivial out-of-plane responses and deformability due to their inherent atomic scale thickness coupled with weak interlayer vdW interactions, which call for a general mechanical framework to quantify such extraordinary characteristics given the structure and material properties. Here, we demonstrate that by considering the competing mechanisms between intralayer stretching, interlayer shearing, and monolayer bending, a general centerline-based theory for multilayered structures is developed to portray the bending landscape of multilayer vdW materials. Combined with large-scale molecular dynamics simulations of three-point bending, we find that when the slenderness ratio or the interlayer shear rigidity is smaller or the intralayer elasticity is higher, the multilayered structures exhibit pronounced nonplanar section deformation due to the interlayer shear capacity. To elucidate quantitative correlations between deformation distribution and structural dimensions and material properties, a critical criterion is proposed to depict the transformation from planar to nonplanar section deformation through a dimensionless characteristic parameter. The effective bending stiffness is then systematically explored in the space of characteristic geometries and material properties to reveal the underlying mechanism of the anomalous size effect. We identify that the effective bending stiffness follows a unified scaling law regarding the dimensionless characteristic parameter. More importantly, a series of deformation-mode phase diagrams are constructed using two universal characteristic lengths, intuitively illustrating the transition of dominated deformation modes and the synergism of geometries and inherent material properties on the bending responses. Validated by several typical vdW materials and novel semiconducting two-dimensional materials, the proposed diagrams not only deepen the understanding of bending in multilayer vdW materials but also provide guidelines for the design and optimization of vdW material-based devices.

Application of the method of nonplanar sections to determine stresses in the zones of concentration caused by weld reinforcement in butt-welded joints

A procedure for determining stresses in butt-welded joints, which is based on the hypothesis of nonplanar sections, has been justified. The analytical expressions describing the variation of normal stresses in the concentration zone both over the contour and the depth of the joint have been obtained. At the point, where the concentration reaches its maximum value, the expression for calculating the stress concentration factor has been derived. The results from the calculation of the stress concentration factor are compared with those in references. The expressions for determining both the stress gradient at any point in the section, which is beyond the stress concentration zone, and the relative stress gradient at the point where the stress attains its maximum value have been obtained.

Polygon Morphing and Its Application in Orebody Modeling

Three different polygon morphing methods are examined. The first one is based on the utilization of the trimmed skeleton of the symmetric difference of the source and target polygons as an intermediate polygon. The second one reduces the problem to the problem of morphing compatible planar triangulations and utilizes the representation of planar triangulations as a matrix constructed using barycentric coordinates of the planar triangulation′s vertices relative to their neighbors. The third and last one describes the polygon by the parametric curve representation based on estimated Fourier parameters and thus transfers the morphing process to Fourier parametric space. The different features and comparative results of these methods are shown by the tests with different examples. These methods are used for generating a set of polygonal sections from two nonplanar polygonal sections which are nearly planar in 3D before constructing a three‐dimensional object from these nonplanar sections.

Extraction of sheet resistance from four-terminal sheet resistors replicated in monocrystalline films with nonplanar geometries

This paper describes limitations of conventional methods of extracting sheet resistance from four-terminal sheet resistors incorporated into electrical linewidth test structures that are patterned in [110] monocrystalline silicon-on-insulator (SOI) films. Nonplanar sections of these structures render the extraction of sheet resistance by conventional techniques subject to systematic errors. The errors are addressed here by algorithms incorporating the results of finite-element current flow analysis. The intended end application is to facilitate the use of the uniquely high repeatability and low cost of electrical critical dimension (CD) metrology as a secondary reference in a traceability path for CD-reference artifacts.

Design of orthotropic parts of complex shape by the method of nonplanar sections

Procedures based on the hypothesis of nonplanar sections are used to derive equations for determining the normal stresses at an arbitrary point of a body of complex shape in tension and bending. The anisotropy of the material properties is taken into account by introducing a variable modulus of elasticity. The theoretical results have been checked experimentally.

Determination of the stresses in an orthotropic plate with fillets bent by forces normal to the plane of the plate

Methods based on Verkhovskii's hypothesis of nonplanar sections are used to derive equations for the stresses in an orthotropic plate with fillets bent by forces or moments whose plane of action is normal to the plane of the plate. In deriving these equations the depth of the fillets is taken into account.