Local Coordinate System Research Articles

Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns

A finite element analysis (FEA) model was developed for Euler and Timoshenko curved beam elements by incorporating trigonometric displacement distribution patterns. Local polar coordinate stiffness matrices were derived based on force-displacement relations and static equilibrium conditions. By employing the kinetic energy theorem and triangular displacement functions, an expression for the consistent mass matrix of a curved beam element was obtained. A coordinate transformation matrix for the curved beam element was established by relating the local polar coordinate system to the global polar coordinate system. Calculation programs were implemented in the Fortran language to evaluate the static–dynamic performance and natural frequency characteristics of curved beam bridges. The obtained results were then compared with those obtained using ANSYS solid models and “replace curve with straight” beam element models. The comparison demonstrated a strong agreement between the results of the Euler and Timoshenko curved beam element models and those of the ANSYS solid models. However, discrepancies were observed when comparing with the results of the “replace curve with straight” beam element model, particularly in terms of lateral static displacement. This discrepancy suggests that the characteristic matrix derived in this study accurately represents the stiffness and mass distribution of the curved beam, making it suitable for mechanical performance analysis of curved beam bridges. It should be noted that the “replace curve with straight” method overlooks the initial curvature and the bending–torsion coupling effects of a curved beam, resulting in calculation deviations. On the other hand, the use of curved beam elements in numerical analysis provides a simple and practical approach, which facilitates further research in areas such as vehicle–bridge coupling vibrations and seismic analysis of curved beam bridges.

An efficient analytical model for the swept volume generation of a flat-end mill in 5-axis CNC milling

5-axis CNC (Computer Numerical Control) milling is widely used to create complex part geometries in the industrial area. The cutting tool creates the swept volume as it moves along the defined path. The swept volume is subtracted from the initial stock for the machining simulation. Although a swept volume consists of three parts such as ingress, egress, and swept envelope, the number of faces of the swept volume is higher than three. In this work, parametric equations of the faces of the swept volume were obtained for a flat-end mill in four steps. The model is based on the decomposition of the tool into circles along the tool orientation vector since a flat-end mill can be modeled as a cylinder. The fundamental principle is that each circle is tangent to the swept envelope of the cylinder. Locations of the grazing points with respect to a local coordinate system were determined by applying the Envelope Theory to the parameterized circle of the cylinder. Then, each face of the swept volume was represented based on the equation of the parameterized circle. The model was verified by using an alternative analytical model. As a result, boundaries of the swept volume were represented fully analytically for a flat-end mill in 5-axis CNC milling in an efficient way.

Corotational Finite Element Dynamic Analysis of Space Frames with Geometrically Nonlinear Behavior Based on Tait–Bryan Angles

The aim of this study is to compose a corotational finite element formulation for space frames with geometrically nonlinear behavior under dynamic loads. Using a moving frame through three successive rotations similar to Euler angles is one of the oldest techniques; however, there are still some gaps that require attention, mainly due to singularity. Hence, alternative techniques had been developed, sometimes elusive and computationally expensive. In this paper, we went back to the old technique and filled the gaps. Three-coordinate systems are used, i.e., the fixed global coordinate system, the fixed local coordinate system that is attached individually to every element, and the corotational local frame for each element that moves and rotates with the element. The deformation is always small relative to the corotational frame. The successive rotations between different coordinate systems are expressed using Tait–Bryan angles. Lagrange’s equation is used to derive the equation of motion, and the stiffness and mass matrices are obtained using the Euler–Bernoulli beam model. A MATLAB code is developed based on the Newton–Raphson method and the Newmark direct integration implicit method. In traditional techniques, singularity is attained when any rotation angle in the fixed local frame approaches π / 2 , and if any is greater than π / 2 , the techniques could fail to specify the location of the element. In this paper, each case is treated with a proper procedure, and special handling of trigonometric formulations prevents singularity and correctly specifies the location of elements in all situations. Different examples of beams and frames are analysed. While the method is not intricate, it is timesaving, is highly effective, provides more stable and robust analysis, and gives sufficiently accurate results. Compared to the parametrization of the finite rotations technique, the method has a significant reduction in the convergence rate because it avoids the storage of joint orientation matrices.

VRKeyLogger: Virtual keystroke inference attack via eavesdropping controller usage pattern in WebVR

WebVR is an emerging technology that allows users to experience VR (Virtual Reality) through typical web browsers, providing an integrated environment for various VR applications. One important problem of the VR technology is how to securely interact with users, in particular, implementing secure text input. A promising approach is to use a virtual keyboard rendered as a VR object. The VR user can enter certain text by clicking a sequence of virtual keys through the VR controllers, and the input text is handled in a secure way. However, despite the sensitivity of the input text, we found that there is a critical vulnerability that the VR controllers are not properly protected. The VR controller status can be disclosed to malicious entities, imposing a severe threat that an attacker's website can infer the input text by eavesdropping and analyzing the VR controller's movements. To accurately infer the input, the attacker should address two challenges: 1) determining which clicks correspond to the virtual keyboard and 2) identifying which key is pressed. In this paper, we propose a new keystroke inference attack framework, VRKeyLogger, that addresses such challenges with two key components: key-click classifier and key-click identifier. The key-click classifier effectively distinguishes clicks on the virtual keyboard based on the SVM classifier trained by the major features of the VR controller uses. The key-click identifier then accurately identifies which key is pressed by transforming the clicked position into the local coordinate system of the virtual keyboard. We implemented a proof-of-concept prototype and conducted a user study with nine participants. In the extensive user study with three real-world WebVR applications, our VRKeyLogger results in classification and identification accuracy of 93.98 and 96.8% on average, respectively. This implies that the proposed attack poses a serious threat to WebVR security.

정부간협력에 대한 조정제도의 영향

The study examined how the perception of the effectiveness of the dispute mediation institution and the local financial coordination system affects intergovernmental cooperation. To this end, the study conducted a comprehensive analysis using crosssectional regression analysis and joint OLS based on the “Survey on Intergovernmental Relations(IGR)” data(2011, 2014, 2017, 2020) provided by the Korea Institute of Public Administration.
 Summarizing the results, the perception of the effectiveness of the dispute mediation system and the local financial coordination system had a static effect on the perception of intergovernmental cooperation, and the sense of cooperation among public officials and financial decentralization also had a static effect.
 Based on this, in order to further promote intergovernmental cooperation, policy implications such as changing the perception of not only the local self-government system but also the dispute mediation system and the local financial coordination system were proposed.

A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: Discretization with geometric finite elements

We investigate discretizations of a geometrically nonlinear elastic Cosserat shell with nonplanar reference configuration originally introduced by Bîrsan, Ghiba, Martin, and Neff in 2019. The shell model includes curvature terms up to order 5 in the shell thickness, which are crucial to reliably simulate high-curvature deformations such as near-folds or creases. The original model is generalized to shells that are not homeomorphic to a subset of R2. For this, we replace the originally planar parameter domain by an abstract two-dimensional manifold, and verify that the hyperelastic shell energy and three-dimensional reconstruction are invariant under changes of the local coordinate systems. This general approach allows to determine the elastic response for even non-orientable surfaces like the Möbius strip and the Klein bottle. We discretize the model with a geometric finite element method and, using that geometric finite elements are H1-conforming, prove that the discrete shell model has a solution. Numerical tests then show the general performance and versatility of the model and discretization method.

Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form

We generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give explicit necessary and sufficient conditions for a tensor field of type (0, 2) which is not necessary symmetric or skew-symmetric, and is possibly degenerate, to have constant entries in a local coordinate system.

Optimized GICP registration algorithm based on principal component analysis for point cloud edge extraction

For iterative closest point (ICP) algorithm, the initial position and the number of iterations are needed in registration. At the same time, the ICP algorithm is easy to fall into local convergence and convergence speed is slow. By constructing K-D tree to search neighborhood points and artificially set threshold, plane fitting is carried out, the on-time point cloud to be deployed is separated from the complex background, and statistical analysis is used to calculate the distance between the point cloud and the neighborhood point to quickly remove the invalid point cloud. The surface equation is set to calculate the tangent plane of point cloud normal vector and each normal vector, and the local coordinate system is constructed. The angle between adjacent vectors and the local coordinate system is calculated to determine the feature point set of edge contour. According to the covariance matrix of the feature points set, the principal feature component is obtained, the principal axis direction of the two sets of point clouds is found, and the rotation matrix and the displacement vector are obtained. Finally, GICP precise registration of point cloud is carried out according to initial pose parameters and rigid body transformation matrix obtained by maximum likelihood estimation method. The results show that the optimized algorithm can effectively avoid local convergence. Compared with the traditional ICP algorithm, when the algorithm achieves the same registration accuracy in the public dataset experiment, the registration speed is on average 44.82% faster and the overlap rate is on average 15.26% higher. In the real dataset experiment, the registration speed is on average 59.04% faster, the registration accuracy is on average 30.24% higher and the overlap rate is on average 10.61% higher. This shows that the optimization algorithm is superior to the traditional ICP algorithm in registration accuracy and convergence speed.

Three-component volume coordinate system for constructing high performance elements

In finite element method (FEM), the volume-coordinate system (VCS) plays a very important role. To date, the number of coordinate components of all VCSs equals the number of faces of polyhedral elements (e.g. 4-component tetrahedral VCS or 6-component hexahedral VCS). To break the current situation, a 3-component VCS is established systematically based on hexahedron. The definition of the new 3-component VCS is still suitable for these degenerated solids from hexahedron, including tetrahedron and several 5-surface solids. In the proposed VCS, the number of coordinate components is unrelated to the number of faces of polyhedron. It is the very first shape-independent VCS in the history of FEM. The new 3-component VCS has both the superiorities of the local natural coordinate system and the simplicities of the Cartesian coordinate system. Based on the presented 3-component VCS, we construct a new incompatible eight-node hexahedral element, which is characterized by the high accuracy and the insensitivity to mesh distortion. This adequately demonstrates that the proposed 3-component VCS is a powerful tool for developing high-performance elements.

A fully nonlinear BEM-beam coupled solver for fluid–structure interactions of flexible ships in waves

A fully nonlinear hydroelastic numerical method is proposed for the fluid–structure interactions of elastic ships. The boundary value problem is solved by the three-dimensional boundary element method. To simulate the instantaneous evolution on the free surface, an effective mesh optimization solution consisting of the local coordinate system and an elastic mesh technique has been developed. The mixed Eulerian–Lagrangian method is implemented to update the fully nonlinear free surface conditions in the local coordinate system. The hull structure is simplified as a non-uniform Timoshenko beam, and the modal superposition approach is adopted to analyse the symmetric responses in the head sea. Convergence of the model is evaluated for mesh resolutions and the time step size, and then comprehensive investigations of vertical motions as well as vertical bending moment are carried out for an advancing ship in a range of wave frequencies. The numerical solutions are compared with the experimental data and a satisfactory agreement is demonstrated. The distribution of high-order harmonics and whipping responses are predicted by the amplitude spectrum, in which the water entry and water exit are considered. The high-frequency vertical bending moments are investigated, in which the effects of higher harmonics and whipping responses are addressed.

Localisation of Ultrasonic NDT Data Using Hybrid Tracking of Component and Probe

Knowledge about the location of a defect is essential for damage assessment. In terms of a digitalised maintenance, inspection data is combined with position information. The presented approach regards the manual ultrasonic inspection, where the ultrasonic probe and the inspected component are both hand-held. By using markerless tracking technologies, it is possible to track the component without any markers. The ultrasonic probe is tracked by a more stable marker-based tracking technology. This results in a hybrid tracking system, which allows a referencing of the non-destructive testing (NDT) data directly to the local coordinate system of the 3D model that corresponds to the inspected component. Transferring this approach to other manual inspection technologies allows for a superimposition of recorded NDT data without any postprocessing or transformation. A better damage assessment is thus enabled. The inspection system, the inspection tool calibration and the camera registration process are described and analysed in detail. This work is focused on the analysis of the system accuracy, which is realised by using a reference body.

3D Cartographic Generalization of LiDAR Point Clouds Based on the Principle of Self-Similarity of a Deterministic Fractal Structure

The rendering of virtual three-dimensional (3D) structures represented by Point Cloud (PC) allows the representation of internal and/or external environments to buildings. However, the compilation of 3D geometric models is influenced by the intrinsic characteristics of PCs, which can be mitigated by the application of an PC simplification operator. According to the mathematical norms of fractal geometry, it was assumed that a PC is characterized by self-similarity. Two experimental datasets acquired with an SLT in static mode indoors were used. Four tasks were accomplished: sampling and structuring of a PC to solve the problem of random distribution, from an octree structure; estimation of the curvature of the points and the roughness of a neighbourhood for the extraction of edge points by the analysis of self-similarity and application of the Statistical Outliers Remove (SOR) algorithm, for the elimination of outliers points; uniform voxelization, to simplify the intermediate points; application of the Iterative Closest Point (ICP) algorithm to register the sets generated in the same local coordinate system. The use of voxelization was satisfactory, but once the voxel size is manually defined, the PC can be oversimplified and lose essential characteristics. This can be minimized by the primary analysis of the edge points, generating a set that is uniform, less noisy, and self- similar to the original set. To achieve a minimum density of points to model an environment three-dimensionally, one must analyse the geometric self- similarity characteristics of the PC to produce a simplified set self-similar to the original, considering the premises of fractal geometry. It is recommended to create an automatic simplification process to minimize the subjectivity coming from the analyst.

SITE CALIBRATION WITH PROJ AND WKT2

Abstract. In surveying projects, a site calibration is the solution to the problem of finding a transformation between the coordinate space of a site local coordinate reference system and a well known coordinate reference system given a set of pairs of corresponding coordinates. A site calibration enables the localization of new positions with cm accuracy using a RTK/PPK GNSS receiver and a transformation, which is a much more cost-effective than using a total station and much faster than other more traditional surveying methods. While site calibration is featured by almost every modern professional-grade GNSS receiver, the implementation is closed source and the output stored in proprietary file formats, tying the user to the vendor’s ecosystem. In this paper we propose a complete solution to the site calibration problem that can be fully implemented with open source software (in particular PROJ for coordinate transformations) and whose output can be represented in terms of an open standard (WKT version 2). Two methods and representations of a site calibration are described, a fully 3D one and a split horizontal and vertical one. Our main contribution is the openness and interoperability of the solution. Another important contribution is the analysis of the sensitivity of these solutions to measurement errors.

Loading–shape interaction analysis of membrane structures subjected to deformation dependent hydrostatic loadings

Due to their flexibility, membrane structures loaded and/or supported by gas and/or fluid undergo large deformations when subjected to external loads, for example when a relatively flat membrane deflects under accumulative ponding. The most noteworthy feature during the deformation process is the loading–shape interaction since changes in the form of the structure induce changes in the loading profiles, and vice versa. Description of the hydrostatic loading is complex since the discontinuity of structural domain and fluid domain occurs with the deformation of membrane. In this paper, an interactive model dealing with accurate hydrostatic load description and nonlinear finite element analysis is employed to analysis the structural response. The hydrostatic loading is described in vectors by fluid level and loading direction in current mesh of the membrane. In case to conserve a specific volume, the free surface height is calculated with a Newton algorithm. Equivalent nodal forces evaluation on different elements are deduced especially when they are partially or fully loaded by judging the spatial relation between the element and the fluid domain, and integrating with shape functions and area coordinates in a local coordinate system. In case of multiple fluid domains, the hydrostatic load description procedure is proposed to be conducted for each fluid domain with care in identifying respective loading direction and then sum them up to get the total hydrostatic loading forces. Two numerical examples, (a) single fluid domain case: a flat membrane subjected to accumulative water loading, and (b) multiple fluid domains case: an air-inflated dam partially filled with water and loaded by lateral pressures of water, are presented to demonstrate correctness, performance and effectiveness of the proposed method in large displacement analysis of flexible membrane structures subjected to deformation dependent hydrostatic loading.

Global functional calculus, lower/upper bounds and evolution equations on manifolds with boundary

Given a smooth manifold M (with or without boundary), in this paper we establish a global functional calculus, without the standard assumption that the operators are classical pseudo-differential operators, and the Gårding inequality for global pseudo-differential operators associated with boundary value problems. The analysis that we follow is free of local coordinate systems. Applications of the Gårding inequality to the global solvability for a class of evolution problems are also considered.

Modeling and Simulation of the Hysteretic Behavior of Concrete under Cyclic Tension-Compression Using the Smeared Crack Approach.

Concrete structures under wind and earthquake loads will experience tensile and compressive stress reversals. It is very important to accurately reproduce the hysteretic behavior and energy dissipation of concrete materials under cyclic tension-compression for the safety evaluation of concrete structures. A hysteretic model for concrete under cyclic tension-compression is proposed in the framework of smeared crack theory. Based on the crack surface opening-closing mechanism, the relationship between crack surface stress and cracking strain is constructed in a local coordinate system. Linear loading-unloading paths are used and the partial unloading-reloading condition is considered. The hysteretic curves in the model are controlled by two parameters: the initial closing stress and the complete closing stress, which can be determined by the test results. Comparison with several experimental results shows that the model is capable of simulating the cracking process and hysteretic behavior of concrete. In addition, the model is proven to be able to reproduce the damage evolution, energy dissipation, and stiffness recovery caused by crack closure during the cyclic tension-compression. The proposed model can be applied to the nonlinear analysis of real concrete structures under complex cyclic loads.

Research on Visual Measurement of Aperture and Hole Group Center Distance Based on Geometric Constraint

Hole is the most common symmetrical geometric structure of mechanical parts, and aperture and hole center distance are important measured dimensions in machining. However, existing visual measurement methods often require high equipment installation accuracy and low measurement accuracy. To solve the problem of projection deformation of the measured hole: Firstly, a local coordinate system is created, and the coordinate plane of the coordinate is parallel to the end face of the measured hole. Secondly, a cone is established, the end face of the measured hole is alike to the bottom face of the cone, and the optical center of the camera is the vertex. The space equation of the cone is represented by the coordinates of the center point of the hole. Finally, a cutting plane is established near the imaging plane of the camera, and the intersection line equation between the plane and the cone is obtained, and the diameter of the measured hole and the coordinates of the center of the circle are obtained through the parameters of the intersection line equation. In order to solve the problem of errors in edge points of the hole, geometric constraints based on the center of the circle are used to improve measurement accuracy. This experiment takes the automobile insert mold as the measured part and uses the measurement model of this paper to measure the aperture and hole center distance of the mold. The measurement results show that the measurement accuracy of the aperture is 0.018 mm, the measurement accuracy of the center distance of the hole is 0.05 mm, and the maximum relative error is 2.2%.

3D Solar Irradiance Model for Non-Uniform Shading Environments Using Shading (Aperture) Matrix Enhanced by Local Coordinate System

Building-integrated photovoltaics (BIPVs) and vehicle-integrated photovoltaics (VIPVs) receive solar irradiance through non-uniform shading objects. Standard scalar calculations cannot accurately determine the solar irradiance of BIPV and VIPV systems. This study proposes a matrix model using an aperture matrix to accurately calculate the horizontal and vertical planes affected by non-uniform shading objects. This can be extended to the solar irradiance on a VIPV by applying a local coordinate system. The 3D model is validated by a simultaneous measurement of five orientations (roof and four sides, front, left, tail, and right) of solar irradiance on a car body. An accumulated logistic function can approximate the shading probability. Furthermore, the combined use of the 3D solar irradiance model is effective in assessing the energy performance of solar electric vehicles in various zones, including buildings, residential areas, and open spaces. Unlike standard solar energy systems, the energy yield of a VIPV is affected by the shading environment. This, in turn, is affected mainly by the location of vehicle travel or parking in the city rather than by the climate zones of the city.

A governing equation of Rossby waves and its dynamics evolution by Bilinear neural network method

This paper studies an extended evolution equation of large-scale waves by means of bilinear neural network method, which is obtained from local Cartesian coordinate system of the basic equation set by using scaling analysis method and perturbation expansions method. First, we convert the equation into a Hirota equation by using variable transformation. Then, we give the structure framework and the model of the bilinear neural network. We build the test function in two dimensions: depth and breadth. With choosing appropriate activation functions and neuron coefficients, we get many rational function exact solutions, including rogue waves and interaction phenomenon consisting of rogue wave and soliton wave. At last, the figures of these exact solutions are exhibited by selecting suitable value of parameters. We think that these results are very important in ocean dynamics.

Analysis of Arbitrary EM Field Exposure to a Multilayer Spherical Head Model Using Spherical Vector Wave Functions

A semi-analytical method is presented for the assessment of induced electromagnetic field inside a multilayer head model exposed to radiated field of an arbitrary source antenna. First the source antenna is simulated by a full-wave software in the absence of the head model to evaluate its radiating characteristics. Then, by sampling of the source radiated fields, its spherical vector wave function (SVWF) amplitudes are evaluated. The well-known translation addition theorem for spherical vector wave functions (SVWFs) is implemented to translate radiating field SVWFs to the local coordinates system of head model. Neglecting the reaction of model on source fields, using boundary conditions on the interfaces of adjacent layers, the unknown SVWF amplitudes of the fields inside each layer as well as those of the scattered field outside the head model are evaluated. Some numerical examples are presented for the verification of the proposed method. The acceptable consistency between the results obtained by the proposed method and full-wave simulations of the problem verifies the authenticity of the proposed method. In comparison to a full-wave numerical method, the proposed method provides an efficient repeatable simulation approach due to the independency of the source and head model analyses.