Arbitrary Geometrical Shape Research Articles

A one-time training machine learning method for general structural topology optimization

Machine learning (ML) methods have found some applications in structural topology optimization. In the existing methods, however, the ML models need to be retrained when the design domains and supporting conditions have been changed, posing a limitation to their wide applications. In this paper, we propose a one-time training ML (OTML) method for general topology optimization, where the self-attention convolutional long short-term memory (SaConvLSTM) model is introduced to update the design variables. An extension–division approach is used to enrich the training sets. By developing a splicing strategy, the training results of a small design space (i.e., a basic cell of either two- or three-dimensions) can be extended to tackling the optimization problem of a large design domain with arbitrary geometric shapes. Using the OTML method, the ML model needs to be trained for only one time, and the trained model can be used directly to solve various optimization problems with arbitrary shapes of design domains, loads, and boundary conditions. In the SaConvLSTM model, the material volume of the post-processed thresholded designs can be precisely controlled, though the control precision of the gray-scale designs might be slightly sacrificed. The effects of model parameters on the computational cost and the result quality are examined. Four examples are provided to demonstrate the high performance of this structural design method. For large-scale optimization problems, the present method can accelerate the structural form-finding process. This study holds a promise in the high-resolution structural form-finding and transdisciplinary computational morphogenesis.

An Efficient Algorithm for Gravity Forward Modeling (GFM) with Masses of Arbitrary Shapes and Density Distributions

Summary Currently, gravimetric forward modelling of mass density structures with arbitrary geometries and density distributions typically involves subdividing the mass body into individual geometric elements (such as rectangular prisms), calculating their gravitational contributions that are then summed up to obtain the gravitational attraction of the whole body. To achieve a more accurate approximation of the true geometric shape and density distribution, this rectangular prism model requires fine dividing, which significantly increases computational load and reduces numerical efficiency. To address this issue, we propose the algorithm for gravimetric forward modeling of arbitrary geometric shapes and density distributions in spectral domain that significantly improves numerical efficiency while preserves computational accuracy. The novelty of our proposed algorithm lies in dividing the masses into multiple layers of equal thickness in the vertical direction, providing constant upper and lower bounds. This allows to extended Parker's formulas and apply the Fast Fourier Transform (FFT) to increase numerical efficiency. The algorithm is tested using synthetic models and then used to compute gravitational effects of topography and sediments using real data from Tibet. Results show high accuracy and numerical efficiency than rectangular prism approach.

Deep learning based time-domain inversion for high-contrast scatterers

ABSTRACT In this paper, a deep learning based time-domain inversion method is proposed to reconstruct high-contrast scatterers from the measured electromagnetic fields. The scatterers investigated in this study include four kinds of geometry shapes, which cover the arbitrary geometrical shapes, handwritings and lossy medium. After being well trained, the performance of the proposed method is evaluated from the perspective of accuracy, noise interference, and computational acceleration. It can be proven that the proposed framework can realize high-precision inversion in several milliseconds. Compared with typical reconstruction methods, it avoids the iterative calculation by utilizing the parallel computing ability of GPU and thus significantly reduce the computing time. Besides, the proposed method has shown the potential to be applied in practical scenarios with experimental results. Herein, it is confident that the proposed method has the potential to serve as a new path for real-time quantitative microwave imaging for various practical scenarios. In the end, the limitation of the method is also discussed.

Two-Dimensional Damage Localization Using a Piezoelectric Smart Aggregate Approach-Implementation on Arbitrary Shaped Concrete Plates.

This paper presents the application of a hybrid approach for damage localization in concrete plates of arbitrary geometric shapes and a constant thickness. The hybrid algorithm utilizes fast discrete wavelet transformation, energy approach and time of flight criteria for the purpose of the localization of single- and multi-damage problems inside or on the periphery of concrete plates. A brief theoretical background of the hybrid method as well as numerical procedures for modeling the piezoelectric smart aggregate and ultrasonic wave propagation are presented. Experimental and numerical verification of the damage localization were performed on square samples/models with one or two damages and with 16 positions of piezoelectric smart actuator/sensor aggregates. After the verification of the hybrid method, a numerical simulation was performed on models with one or two damages for plates of arbitrary geometric shapes. Based on the obtained results, it was concluded that the proposed method can be applied to damage localization in concrete plates of arbitrary geometric shapes. The presented method and numerical procedure can be further used in research through varying the geometry, number and position of damages as well as the number and position of piezoelectric smart aggregates.

Three-Dimensional Autonomous Guidance for Enclosing a Stationary Target Within Arbitrary Smooth Geometrical Shapes

Three-Dimensional Autonomous Guidance for Enclosing a Stationary Target Within Arbitrary Smooth Geometrical Shapes

The oscillatory fingerprints of self-prioritization: Novel markers in spectral EEG for self-relevant processing.

Self-prioritization is a very influential modulator of human information processing. Still, little is known about the time-frequency dynamics of the self-prioritization network. In this EEG study, we used the familiarity-confound free matching task to investigate the spectral dynamics of self-prioritization and their underlying cognitive functions in a drift-diffusion model. Participants (N = 40) repeatedly associated arbitrary geometric shapes with either "the self" or "a stranger." Behavioral results demonstrated prominent self-prioritization effects (SPEs) in reaction time and accuracy. Remarkably, EEG cluster analysis also revealed two significant SPEs, one in delta/theta power (2-7 Hz) and one in beta power (19-29 Hz). Drift-diffusion modeling indicated that beta activity was associated with evidence accumulation, whereas delta/theta activity was associated with response selection. The decreased beta suppression of the SPE might indicate more efficient sensorimotor processing of self-associated stimulus-response features, whereas the increased delta/theta SPE might refer to the facilitated retrieval of self-relevant features across a widely distributed associative self-network. These novel oscillatory biomarkers of self-prioritization indicate their function as an associative glue for the self-concept.

Groundwater mounding due to recharge from ephemeral streams

Recharge from ephemeral streams (called Masil in Farsi and Wadi in Arabic) is the main process of groundwater recharge in arid regions of the world where groundwater is the most important source of water supply. Despite advances in mathematical models of simulating infiltration from these streams, there is no versatile analytical model to simulate the groundwater mound due to recharge from an ephemeral stream. The goal of this paper is to present a semi-analytical model of the groundwater mound due to recharge from an ephemeral stream of an arbitrary geometric shape in aerial view. A three-dimensional anisotropic unconfined aquifer is considered, and a point recharge is imposed to the water table at first. The point- recharge solution is obtained via the Laplace and Fourier transforms. The image well method is employed to incorporate the lateral no-flow boundary that represents the margin of the unconfined aquifer. The point-recharge solution is then extended to simulate the groundwater mound due to recharge from the stream of an arbitrary shape by approximating the stream by multiple straight segments and integration of the point-recharge solution along the desired directions of those segments and the principle of superposition. A constant head variable discharge well is also placed near the stream to calculate the sustainable yield which is the average discharge of a constant-head well as compared to an equivalent constant-flux well. The results of this work are presented in the form of groundwater mound-time curve and groundwater mound spatial maps. The scaled sensitivity of groundwater head to recharge from the stream-time curves and depletion volume of the nearby well-time curve are also obtained. The influences of aquifer parameters on the groundwater mound and sustainable development of the aquifer near the ephemeral stream are analyzed. This study shows that: (1) Groundwater mound follows the shape of the stream and spreads spatially from the stream over time and the groundwater mound is higher inside the convex part of the stream due to interference from the neighboring stream segments; (2) The groundwater head collected from an observation well in a fine-grain aquifer is more valuable to estimate the recharge from the ephemeral stream than a coarse-grain aquifer; (3) The sustainable yield of a production well in an alluvial aquifer is maximum near the stream in a coarse-grain non-layered aquifer than the (coarse- or fine-grain) layered aquifer. The results of this work can be utilized as a valuable tool for managing the unconfined aquifers in the arid and semi-arid regions when ephemeral streams are the primary sources of recharge.

The effect of trait anxiety on the time course of self-relevant processing: Evidence from the perceptual matching task

Studies have widely reported that trait anxiety is associated with a range of cognitive biases toward external negative emotional stimuli. However, few studies have examined whether trait anxiety modulates intrinsic self-relevant processing. This study investigated the electrophysiological mechanism underlying trait anxiety’s modulating effect on self-relevant processing. Event-related potentials (ERPs) were recorded while participants performed a perceptual matching task that assigned an arbitrary geometric shape to an association with a “self” or “non-self” label. Results showed larger N1 amplitudes under self-association than under friend-association conditions, and smaller P2 amplitudes for self- than for stranger-association conditions in individuals with high trait anxiety. However, these self-biases in the N1 and P2 stages were not observed in those with low trait anxiety until the later N2 stage, in which the self-association condition provoked smaller N2 amplitudes than the stranger-association condition. In addition, both high and low trait anxiety individuals showed larger P3 amplitudes for the self-association condition than for the friend- and stranger-association conditions. These findings suggest that, although both high and low trait anxiety individuals showed self-bias, high trait anxiety individuals distinguished between self-relevant and non-self-relevant stimuli at an earlier stage, which may reflect hypervigilance to self-relevant stimuli.

A general multi-layered hyperelastic plate theory for growth-induced deformations in soft material samples

In this paper, we propose a general multi-layered hyperelastic plate theory to study the growth-induced deformations of soft material samples. First, by considering a multi-layered plate sample with an arbitrary geometrical shape and adopting a general hyperelastic constitutive model, the 3D governing system is established, which incorporates the growth effects of the different layers in the plate. Then, a series expansion-truncation approach is adopted to eliminate the thickness variables in the 3D governing system. An elaborate calculation scheme is applied to derive the iteration relations of the coefficient functions in the series expansions. Through some further manipulations, a 2D vector plate equation system with the associated boundary conditions is established. To show the efficiency of the plate theory, three typical examples regarding the growth-induced deformations and instabilities of multi-layered plate samples are studied, where the incompressible neo-Hookean constitutive model is adopted. Some analytical and numerical solutions to the plate equation system are obtained, which can provide accurate predictions on the growth behaviors of the plates. Furthermore, the problem of ‘shape-programming’ of multi-layered plates through differential growth is studied and the explicit formulas for some typical examples are derived. By using these formulas, the shape evolutions of the plates during the growing processes can be controlled accurately. The results obtained in the current work are applicable for the design of intelligent soft devices with multi-layered plate structures.

Discrete heat transfer model with space–time nonlocality

The study of processes occurring under locally non-equilibrium conditions is of great interest due to the intensive development of laser technologies and the emerging opportunity to carry out technological operations under extreme conditions (at ultrahigh temperatures, pressures and their gradients). This paper presents the results of the development for a discrete mathematical model of thermal conductivity that takes into account the inertia of the heat transfer process in solids. A computational algorithm using the APDL language has been developed on the basis of the finite element method. APDL (ANSYS Parametric Design Language) is a scripting language that you can use to automate common tasks or even create your own model expressed in terms of parameters (variables). Developed algorithm allows one to automatically calculate temperature fields in solids of arbitrary geometric shape taking into account the heat transfer inertia. The APDL algorithm is adapted for the ANSYS software product which makes it available to a wide range of users. Verification of the algorithm developed is performed by comparing the obtained numerical results with the exact analytical solution of the model task.

Reducing the Sim2Real-Gap in Extrusion Blow Molding using Random Forest Regressors

In plastics manufacturing, the extrusion of thermoplastic material and subsequent blow molding into a cavity is a common procedure to create hollow objects with arbitrary geometric shapes and sizes. To ensure reliability of the production process and satisfactory quality of the final product, several control parameters need to be adjusted to modify the process behavior. The appropriate parameter allocation is typically determined during product and process development using FEM simulations. The simulations provide the ability to estimate the expected geometric shape of the final product and adjust the control parameters accordingly. However, simulations are only as good as their underlying computational model and can reflect reality only to a restricted degree. Deviations between the simulated product quality and real quality measurements of the physically produced product, the so-called sim2real gap, cannot be entirely avoided and persist even after several optimization cycles. In this paper, we address this problem and propose a data-driven approach to correct the sim2real gap. At its core, our approach is based on a random forest regression model that predicts simulation deviations based on process and product characteristics. The input data for the model is composed of control parameters from the extrusion and blow molding process as well as data from intermediate simulation results. Given the multitude of different variables, we incorporate extensive feature selection and engineering to extract the most valuable information to predict the sim2real gap. We train and evaluate our approach in a real use-case in which several different product geometries are manufactured with differently configured control parameters. The results show that our approach successfully reduces the sim2real-gap significantly. In addition, we show that with carefully designed feature engineering and parameterization, a model trained on one set of products with certain geometrical characteristics can be transferred and applied to another set of products with distinctively different geometrical characteristics.

Flattop Beam Shaping Using Hybrid Gratings

A new method of laser beam shaping with hybrid gratings is presented. The hybrid gratings consist of a blazed grating and a gradient binary grating. The blazed grating is used to separate the incident Gaussian beam into zero order and nonzero diffraction orders. A filter is used to block the nonzero order beams and obtain the zero orders with the desired shape. The gradient binary grating is used to improve the energy distribution of the inside area of the geometric shape. A phase hologram designed with the desired shape and hybrid gratings, is loaded on a phase-only spatial light modulation to achieve arbitrary geometric flattop shapes with high uniformity. Squared and hexagonal shaping experiments demonstrated that the presented method can convert a Gaussian beam into a flattop beam with steepness edge and high uniformity. Experimental results show that the beam non-uniformity is less than 0.037.

The Ping-Pong Electromagnetic Algorithm for Reflecting Surface Antennas of Arbitrary Shapes

An efficient ping-pong algorithm is presented to deal with electromagnetic scattering from reflecting surface antennas such as the reconfigurable intelligent surfaces (RISs) of arbitrary geometric shapes. The proposed computational electromagnetics (CEM) algorithm does not require formation, storage, and inverse of the impedance matrix used by the method of moments (MoM). Instead, a rigorous formula is obtained for the computation of the surface current from the scattered electric field. Besides, the algorithm only contains convolution operations with the scalar Green’s function and second derivatives operations to iteratively update the surface currents and scattered electric field. Also, hypersingular integration arising from the singularities of the surface current and scattered electric field is properly regularized. Furthermore, the algorithm converges fast and satisfactory results are obtained after a few iterations, and it is about ten times as fast as the MoM. Besides, the first iteration gives the solution for reflecting surface antennas on substrates of perfect absorption. Numerical solutions are obtained for some typical antennas and comparisons are made to those in the literature and from the MoM.

Photonic metacrystal: design methodology and experimental characterization

We report a design methodology for creating high-performance photonic crystals with arbitrary geometric shapes. This design approach enables the inclusion of subwavelength shapes into the photonic crystal unit cell, synergistically combining metamaterials concepts with on-chip guided-wave photonics. Accordingly, we use the term "photonic metacrystal" to describe this class of photonic structures. Photonic metacrystals exploiting three different design freedoms are demonstrated experimentally. With these additional degrees of freedom in the design space, photonic metacrystals enable added control of light-matter interactions and hold the promise of significantly increasing temporal confinement in all-dielectric metamaterials.

Напряженно-деформированное состояние континуума с очагом пластической деформации

The paper describes a method for constructing a shear plastic band in an elastic plane using the Crouch solution in the problem of a constant discontinuity of displacement on a finite segment of an unbounded plane. Analytical equations are obtained for calculating the stress-strain state (SSS) of a plane with a band of homogeneous plastic deformation for the cases of simple and pure shear. The analysis of SSS was carried out and the features of the field of internal stresses in an elastic plane with a band of plastic deformation shear were revealed. It is shown that a zone of homogeneous plastic shear deformation can be used as an element for constructing a zone of arbitrary geometric shape with a given distribution of plastic shear deformation. In the general case, the proposed approach can also be applied to construct zone with a homogeneous distribution of the normal components of plastic deformation.

ТЕОРЕТИЧНИЙ АНАЛІЗ СИЛ ОПОРУ ПЕРЕМІЩЕННЮ УДОСКОНАЛЕНОГО ПІДКОПУЮЧОГО РОБОЧОГО ОРГАНУ КАРТОПЛЕЗБИРАЛЬНОГО КОМБАЙНА

The amount of energy required to perform technological processes in agriculture largely depends on the size of the resistance to the displacement of the working bodies of machines. The main factor of energy consumption performing the technological process of potato harvesting is the resistance to the displacement of the digestive working body. In order to reduce the resistance to displacement an improved design of the digging body is proposed. An analytical study was conducted to determine the problem of moving the working body in the soil environment. The strength of the soil resistance is determined and the regularity of the influence on its change of parameters and the shape of the blade and separation parts of the digging working body is established. Calculations are made using the Mathematica application programm. The graphic dependences and contours of the isoline of the traction flange of the working part of the working body are obtained. Analysis of the calculations allowed to set the parameters of the surface of the dashboard, which provide a minimum of traction resistance. The schedule and contours of isolines of the change of the total resistance to the displacement of the soil mass with the tubers by the separation surface of the working organ in the function of the distance between the bars and the size of their intersection are also obtained. Analysis of the dependence of soil resistance and tubers on the separation surface indicates that an increase in the size of the geometric size of the intersection of the rods leads to a significant increase in the resistance of the medium. The material presented in the article can be used for analytical determination of the resistance of the excavation working body of potato harvesting machines of arbitrary geometric shape in the soil medium with tubers.

Computational approach to solving problems of spatial processing of point sets on two-dimensional regular grids

The paper presents an approach to solving problems of spatial processing on sets of points on a plane. The presented method consists in plotting regions of an arbitrary geometric shape near given points of the set on a regular grid and determining the intersection points of the regions using spatial hash tables to improve the efficiency of operations. The proposed approach is implemented in the form of software for determining the spatial relationships between points as a sequence of operations with discretized sets and allows visualization of research results. Figs.: 2. Refs.: 13.
 Keywords: spatial processing task; point set; plane; regular grid; spatial hash table.

Beam shaping with high energy utilization and uniformity using gradient orthogonal gratings.

A flattop beam is useful in ultrafast laser processing. A laser beam shaping method for high energy utilization and uniformity is presented using a complex hologram displayed on a spatial light modulator. The hologram consists of a geometric mask, an external blazed grating, and internal gradient orthogonal gratings. The gradient orthogonal gratings can change the incident light energy distribution and obtain flattop beams with high energy utilization. Experimental results show that the presented method can obtain an arbitrary geometric shape with a steep edge and high uniformity. Meanwhile, the bigger the geometric mask size, the higher the energy utilization will be, and it is up to 78.70%.

Development of algorithms for the formation and placement of N-dimensional orthogonal polyhedrons into containers of complex geometric shape

The article is devoted to problems related with the development of algorithms for creating, optimizing and placing of orthogonal polyhedrons of arbitrary dimension. Under N-dimensional orthogonal polyhedron is understood a composite object represented as a set of N-dimensional parallelepipeds with a fixed position relative to each other, which is considered as a whole. The need to solve the problem of placing a set of objects in the form of orthogonal polyhedrons of arbitrary dimension arises when solving a large number of practical problems in the automation of design and production. In particular, solving the layout problems of equipment and space, problems of cutting materials, problems of designing very large-scale integrated circuits, and optimizing the distribution of resources in computing and production systems, as well as many other actual problems, can be reduced to solving the problem of packing orthogonal polyhedrons. To create a new N-dimensional orthogonal polyhedron, the operations of addition, subtraction and multiplication of orthogonal objects are implemented. With the aim to increase the placement speed of orthogonal polyhedrons which were created with using the voxel model, an algorithm for partitioning of an orthogonal polyhedron into many non-overlapping each other as large as possible large orthogonal objects is proposed. In the scientific literature, there are no solutions to the problem of partitioning an orthogonal polyhedron of arbitrary dimension. The proposed partitioning algorithm is based on the usage of a model of potential containers developed to solve the orthogonal packing problems of arbitrary dimension. To obtain a container of arbitrary shape, a possibility of setting its geometric constraints with an orthogonal polyhedron is implemented. The article presents an algorithm developed for packing an N-dimensional orthogonal polyhedrons inside containers of arbitrary geometric shape, based on the application of multiplication orthogonal polyhedrons operations to obtain the set of points of permissible placement of each considered object. The examples of solving the problems of cutting the industrial materials into objects of irregular shapes, as well as solving the problems of placement complex objects created with using the voxel model into containers of various geometric shapes (including sphere and cone) are given. The effectiveness of the application of the developed algorithms is shown on the example of solving the problem of generation a dense layout of details on a 3D printer platform.

АВТОМАТИЗИРОВАННОЕ ПРОЕКТИРОВАНИЕ ПРОСТРАНСТВЕННЫХ РЕШЕТЧАТЫХ СТАЛЬНЫХ КОНСТРУКЦИЙ ПОКРЫТИЙ СЛОЖНОЙ ФОРМЫ

The architecture of modern structures requires the use of structural systems in a wide range of both geometric and topological forms. Spatial steel structures are one of the most varied, complex and demanded types of structural forms of coatings for buildings and construction structures. The method of constructing spatial lattice structures of a complex geometric shape considered in the article is based on automated methods of computer modeling of the shell surface and the subsequent development of a separate spatial cell of a lattice of a certain type - a "family". The structural cell of the lattice is the basis for the topological structure of the building system, which is created using special software. The result of this development is a digital model of the megastructure of the entire spatial structure. Subsequent export of the constructed geometry to computational software systems allows one to estimate the stress-strain state of the system and select the cross sections of all its elements. The methodology developed in the article makes it possible to quickly and accurately design spatial structural structures of coatings of an arbitrary geometric shape. The speed and accuracy of modeling and calculation of shell lattice structures is achieved by optimizing the sequence of application of modern programs, using special modeling techniques.