Indentation mapping of stretched adhesive membranes

Unilateral adhesive contact between a rigid indenter and a uniformly stretched membrane of arbitrary shape is considered. The generalized Johnson–Kendall–Roberts (JKR)-type and Derjaguin– Muller–Toporov (DMT)-type models of non-axisymmetric adhesive contact are presented for short- and long-range adhesion, respectively, and the JKR–DMT transition is established in the framework of the generalized Maugis–Dugdale model. A refined method of matched asymptotic expansions is applied to construct the leading-order asymptotic model for indentation mapping of freestanding two-dimensional materials with an axisymmetric probe, using the approximate analytical solution obtained in explicit form for an infinite membrane in the limit of short-range adhesive contact with an indenter in the form of an elliptic paraboloid. The cases of a spherical indenter and a rectangular membrane are studied in detail.

Root-Soil Plate Characteristics of Silver Birch on Wet and Dry Mineral Soils in Latvia

Climate change manifests itself as a change in the probability of extreme weather events, and it is projected that windstorms will become more frequent and intense in Northern Europe. Additionally, the frequency and length of warm periods with wet, unfrozen soil in winter will rise in this region. These factors will lead to an increased risk of storm damages in forests. Factors affecting trees’ resistance to wind uprooting have been well quantified for some species but not for a common and economically important tree, the silver birch (Betula pendula Roth.). Therefore, this study aimed to assess the root-soil plate characteristics of silver birch on wet and dry mineral soils in hemiboreal forests. The root-soil plate and aboveground parameters were measured for 56 canopy trees uprooted in destructive, static-pulling experiments. The shape of the root-soil plate corresponds to the elliptic paraboloid. A decreasing yet slightly different trend was observed in root depth distribution with increasing distance from the stem in both soils. The main factors determining root-soil plate volume were width, which was notably larger on wet mineral soils, and tree diameter at breast height. Consequently, the root-soil plate volume was significantly larger for trees growing on wet mineral soils than for trees growing on dry soils, indicating a wind adaptation.

Differentiable mapping generated by elliptic parabo­loid complexes

In three-dimensional equiaffine space, we consider a differentiable map generated by complexes with three-parameter families of elliptic paraboloids according to the method proposed by the author in the mate­rials of the international scientific conference on geometry and applica­tions in Bulgaria in 1986, as well as in works published earlier in the sci­entific collection of Differ. Geom. Mnogoobr. Figur. The study is carried out in the canonical frame, the vertex of which coincides with the top of the generating element of the manifold, the first two coordinate vectors are conjugate and lie in the tangent plane of the elliptic paraboloid at its vertex, the third coordinate vector is directed along the main diameter of the generating element so that the ends are, respectively, the sums of the first and third, and also the sums of the second and third coordinate vec­tors lay on a paraboloid, while the indicatrixes of all three coordinate vec­tors describe lines with tangents, parallel to the first coordinate vector. The existence theorem of the mapping under study is proved, according to which it exists and is determined with the arbitrariness of one function of one argument. The systems of equations of the indicatrix and the main directions of the mapping under consideration are obtained. The indicatrix and the cone of the main directions of the indicated mapping are geomet­rically characterized.

Buckling mechanism of cable-stiffened lattice shells with bolted connections

The cable-stiffened lattice shell is a new structural system for its translucence and lighting. This article discusses the effect of the connections’ behavior and geometric imperfection on the structural stability and reveals the buckling mechanism of the cable-stiffened lattice shell. The spring stiffness for bolted connections of cable-stiffened lattice shells is deduced from the spring in series model. The buckling mechanism of cable-stiffened lattice shells with three types of joints have been studied based on the prototypical static experiments of bolted connections. The decrease of bolted connections’ stiffness would lead to the change in the displacement distribution for the lattice shell under its ultimate load. The buckling loads and initial structural stiffness of cable-stiffened lattice shells with shim-strengthened bolted joints are approximately 80% of those for cable-stiffened lattice shells with rigid joints. The result indicates that the buckling loads of cable-stiffened lattice shells with bolted connections decrease much more slowly than the decrease of bolted connections’ stiffness. The cable-stiffened lattice shell with SBP connections is more sensitive to the initial geometric imperfection. Finally, a formula has been proposed for estimating buckling loads of elliptic paraboloid cable-stiffened lattice shells with bolted connections.

L1-NORM FITTING OF ELLIPTIC PARABOLOIDS WITH PRIOR INFORMATION FOR ENHANCED CONIFEROUS TREE LOCALIZATION IN ALS POINT CLOUDS

<p><strong>Abstract.</strong> Airborne laser scanning (ALS) is an established tool for deriving various tree characteristics in forests. In some applications, an accurate pointwise estimate of the tree position is required. For dense data acquired by TLS or UAV-mounted scanners, this can be achieved by locating the stem, whose center coordinates are then used for deriving the planimetric tree position. However, in case of standard ALS data this is often not an option due to the low probability of obtaining stem hits in operational scenarios of forest mapping campaigns. This paper presents an alternative, indirect approach where the tree position is approximated as the center of a quadric surface which best represents the tree crown shape. The study targets coniferous trees due to their distinct crown shape which may be approximated by an elliptic paraboloid. It is assumed that individual tree point clusters are given and the task is to find the tree center for each cluster. We first consider the general problem of fitting an elliptic paraboloid with a known axis and an L1 residual norm error criterion, which is more robust to outliers compared to least-squares fitting. We formulate this problem as a quadratically constrained quadratic program (QCQP), and show how prior knowledge on the crown shape and center position can be incorporated. Next, a computationally simpler problem is considered where the paraboloid semiaxis lengths are constrained to be equal, and a corresponding linear program is constructed. Experiments on ALS datasets of forest plots from Bavaria, Germany and Oregon, USA reveal that a reduction in median tree position error of up to 20% can be attained compared to both least-squares fitting and other baseline techniques, resulting in an absolute error of ca. 22&amp;thinsp;cm on both datasets.</p>