Prismatic Elements Research Articles

Оптимізація теплообміну робочих поверхонь на основі локального контролю теплофізичних параметрів

The progressive trend of increasing the efficiency and operational reliability of equipment requires continuous improvement of methods for monitoring and managing work processes. One of the most promising methods for studying transport processes occurring in difficult conditions is physical modeling. The object of this research is heat-exchange prismatic surfaces, which are typical for many technical applications. The purpose of the work is to develop methods for optimizing heat transfer of working surfaces based on local control of thermophysical parameters in characteristic zones of the working environment. The studies were carried out in the ADS-1 aerodynamic stand using the methods of heat and mass analogy and hot-wire anemometry. The arrangement included four rows of prismatic elements. The essence of the local approach is to determine the average surface heat transfer coefficient from the local velocity, measured above each prismatic element, which makes it possible to estimate the spatial temperature heterogeneity of a specific arrangement and take measures to change the temperature in the desired direction by maneuvering the location of the elements. The proposed approach is fundamentally different from another widespread approach, which we called the channel one, in which information about the velocity and temperature fields is ignored, and the influence of the configuration and size of elements and their location on the hydrodynamic structure of the flow is insufficiently taken into account. The local approach allows, firstly, to more accurately diagnose the types of flow in the boundary layer of a streamlined element, determining laminar, turbulent, pseudolaminar, quasiturbulent, transition and separated flow regimes. Second, on the basis of a set of statistical data, make the transition to an arbitrarily specified arrangement of elements and thereby increase the accuracy of determining the temperature state of individual prismatic elements and the entire arrangement as a whole. Equations of similarity are proposed for calculating the local heat transfer of each face of the prism separately and the average surface heat transfer depending on the geometric and operating parameters. On the basis of the recommendations received, the thermal state of the elements of a specific arrangement was evaluated and measures were developed to improve it through targeted rearrangements of the elements.

Pengajaran Persiapan Ujian Nasional Mata Pelajaran Matematika di SMP Negeri 37 Samarinda

Community Service conducted at SMP 37 is teaching national math preparation tests for class IX. The method of community service in Samarinda 37 State Junior High School is by teaching using the junior high school national exam practice module. Activities carried out through the stage of providing material operations of fractions, value comparisons and reversals of values, ranks and roots, calculation of loan and savings interest rates, arithmetic sequences and sequences and geometry, linear and quadratic equations, sets, linear functions, line equations, line gradients, flat circumference and shape area, congruent and congruent triangles, circle angle, circle circumference, circle elements, prism and pyramid elements, volume and surface area of ​​prism and pyramid, statistics, sample space, and opportunity. After all the material has been submitted, it is continued with the prediction of the national mathematics exams in 2013, 2014, 2015, 2016, 2017, and 2018 with the development of the developed training modules. From the results of community service in Samarinda 37 Public Middle School, the level of student satisfaction found using modules was 41.52% very satisfied, 57.40% satisfied, 1.07% quite satisfied, and 0.00% dissatisfied. On the other hand, students also find it easier to understand learning if the teacher uses modules as teaching material in class

Study of Pavements of Concrete Paving Blocks with Ribbed Underside Surface

Improving the reliability and durability of sidewalks, footways, car parks and areas for various purposes, made of concrete paving blocks (CPBs), is an important task of construction. In order to improve the quality characteristics, new pavements consisting of concrete paving blocks with a ribbed underside surface are proposed. Hypotheses about the advantages of the developed structural solutions of pavements relative to traditional pavements of blocks with a flat underside surface were formulated. To confirm the hypotheses, studies of one of the developed pavement variants of in laboratory conditions were performed. The article describes the plan and methodology for implementation two series of experiments. In the first series of the experiment, a section of a traditional pavement of concrete blocks with a flat underside surface was investigated, in the second, a section from a pavement of concrete paving blocks with a ribbed underside surface consisting of three prismatic elements. Qualitative characteristics of the pavement are determined by various indexes. As a result of laboratory tests, the dynamics of settlement of experimental CPBs under the influence of vertically applied load was studied, and density index of a sand structural layer located under the tested CPBs was also obtained. The settlement indexes of the tested CPBs were investigated for three days. A comparative analysis of the experimental results confirmed the hypothesis about the advantages of pavements of concrete paving blocks with a ribbed underside surface. For the further implementation of the developed pavement variant in the construction industry, additional research is required. Further research directions of pavements of concrete paving blocks with a modified geometric shape of the underside surface are determined.

Why We Buy Books

Publishing is often characterized by instinctive decision-making with little attempt to apply a scientific methodology to an obvious question: why does one book sell and another not? The thesis of this paper is that, although there are aspects of a book’s publication history that one cannot predict in advance, one can know what these aspects are. A simple syllogism underlies the argument: if human behaviour can be understood through psychology and if book-buying is a form of behaviour, the motivations for book-buying can also be understood through psychology. This approach can be applied historically, through recourse to sales data, to trace the fossils of books published long ago and so discover the type and strength of the motivations that once drove people to buy them. History demonstrates that these motivations, once properly framed, can be understood to be influenced by context. Book-buying motivations also appear cyclically. This leads to a discussion of why it is that one book rather than another may satisfy a motivation and therefore sell better than another. Using the concept of prisms combining to reflect a motivational ‘light’, we see that books exist as constructs of a finite range of elements that cohere (or not) in a multiplicative way to enhance or diminish their effectiveness. Evidence is also given for what appears to be a universal ratio that dictates a natural entropy in the effectiveness of these prismatic elements.

Study of the Influence of Technological Parameters on Generating Flat Part with Cylindrical Features in 3D Printing with Resin Cured by Optical Processing.

The objective of this paper is to determine how the supporting structure in the DLP 3D printing process has influences on the characteristics of the flat and cylindrical surfaces. The part is printed by using the Light Control Digital (LCD) 3D printer technology. A Coordinate Measuring Machine (CMM) with contact probes is used for measuring the physical characteristics of the printed part. Two types of experiment were chosen by the authors to be made. The first part takes into consideration the influence of the density of the generated supports, at the bottom of the printed body on the characteristics of the flat surface. In parallel, it is studying the impact of support density on the dimension and quality of the surface. In the second part of the experiment, the influence of the printed supports dimension on the flatness, straightness and roundness of the printed elements were examined. It can be observed that both the numerical and dimensional optimum zones of the support structure for a prismatic element could be determined, according to two experiments carried out and the processing of the resulting data. Based on standardized data of flatness, straightness and roundness, it is possible to put in accord the values determined by measurement within the limits of standardized values.

Development of an embedded discrete fracture model for 2D and 3D unstructured grids using an element-based finite volume method

Recently, the unstructured gridding technique has been extensively used in reservoir simulation because of the high flexibility it provides to represent geologically realistic reservoirs. The embedded discrete fracture model (EDFM) has also attracted attention in recent years for the simulation of complex fractures in various types of computational grids. In this work, we develop a methodology to apply the EDFM in 2D and 3D unstructured grids using an element-based finite volume method (EbFVM). In this method, triangular and quadrilateral elements are used in 2D grids, and tetrahedron, prism, hexahedron, and pyramid elements are used in 3D grids. New approaches to addressing matrix-fracture connectivity and reducing the number of fracture unknowns in this type of grid are presented. The methodology is implemented in an EDFM preprocessing code.A series of case studies are presented to demonstrate the methodology in 2D and 3D simulations using an in-house compositional reservoir simulator. Different types of elements are used in the simulations to represent the reservoir geometries. Both primary and secondary recovery processes are simulated. The results show that when the number of control volumes is similar, the proposed method can obtain similar results on different grids with various types of elements, which confirms the effectiveness of the approach. Case studies with complex reservoir geometries are also presented to demonstrate the applicability of the model.This work demonstrates the extensiveness of the EDFM to unstructured matrix grids. It also shows the compatibility of the EDFM with various numerical approximation schemes. The use of unstructured gridding with mixed types of elements facilitates the representation of complex reservoir geometries, and through the combination with the EDFM, complicated gridding around fractures is avoided. Therefore, the approach in this work has high flexibility for simulating densely fractured media with complex geometries.

Efficient modelling of beam-like structures with general non-prismatic, curved geometry

The analysis of three-dimensional (3D) stress states can be complex and computationally expensive, especially when large deflections cause a nonlinear structural response. Slender structures are conventionally modelled as one-dimensional beams but even these rather simpler analyses can become complicated, e.g. for variable cross-sections and planforms (i.e. non-prismatic curved beams). In this paper, we present an alternative procedure based on the recently developed Unified Formulation in which the kinematic description of a beam builds upon two shape functions, one for the beam’s axis, the other for its cross-section. This approach predicts 3D displacement and stress fields accurately and is computationally efficient in comparison with 3D finite elements. However, current modelling capabilities are limited to the use of prismatic elements. As a means for further applicability, we propose a method to create beam elements with variable planform and variable cross-section, i.e. of general shape. This method employs an additional set of shape functions which describes the geometry of the structure exactly. These functions are different from those used for describing the kinematics and provide local curvilinear basis vectors upon which 3D Jacobian transformation matrices are produced to define non-prismatic elements. The model proposed is benchmarked against 3D finite element analyses, as well as analytical and experimental results available in the literature. Significant computational efficiency gains over 3D finite elements are observed for similar levels of accuracy, for both linear and geometrically nonlinear analyses.

The prismatic finite element with the interpolation procedure vector form for the engineering structures’ strength calculations

The technique of forming a stiffness matrix of a volume prismatic finite element with a triangular base and with six nodes located at the vertices of the prism is presented. The discretization element is formed on the basis of the interpolation procedure vector form with consideration as the interpolation object of the displacement vector of an arbitrary point of the engineering structure. It is proposed to improve the compatibility of the prismatic discretization element at the boundaries of the docking of the bases by using Lagrange multipliers as additional nodal unknowns, which are introduced in additional nodes located in the middle of the prismatic discretization element bases’ sides. The presented vector form of interpolation allows one to obtain the correct finite element solutions in the problems of determining the stress-strain state of engineering structures using curvilinear coordinate systems.

Comparing non-hydrostatic extensions to a discontinuous finite element coastal ocean model

The unstructured mesh, discontinuous Galerkin finite element discretisation based coastal ocean model, Thetis, has been extended to include non-hydrostatic (buoyancy-driven and free surface) dynamics. Two alternative approaches to achieve this are described in this work. The first (a 3D based algorithm) makes use of prismatic element based meshes and uses a split-step pressure projection method for baroclinic and barotropic modes, while the second (a 2D based algorithm) adopts a novel multi-layer approach to convert a 3D problem into a combination of multiple 2D computations with only 2D triangle meshes required. Model development is carried out at high-level with the Firedrake library, using code generation techniques to automatically produce low-level code for the discretised model equations in an efficient and rapid manner. Through comparisons against several barotropic/baroclinic test cases where non-hydrostatic effects are important, the implemented approaches are verified and validated, and the proposed algorithms compared. Depending on whether the problems are dominated by dispersive, baroclinic or barotropic features, recommendation are given over the use of full 3D or multi-layer 2D based approaches to achieve optimal computational accuracy and efficiency. It is demonstrated that while in general the 2D approach is well-suited for barotropic problems and dispersive free surface waves, the 3D approach is more advantageous for simulating baroclinic buoyancy-driven flows due in part to the high vertical resolution typically required to represent the active tracer fields.

Estimation of the interpolation error for semiregular prismatic elements

In this paper we introduce the semiregularity property for a family of decompositions of a polyhedron into a natural class of prisms. In such a family, prismatic elements are allowed to be very flat or very long compared to their triangular bases, and the edges of quadrilateral faces can be nonparallel. Moreover, the triangular faces of each element are either parallel or skew to each other. To estimate the error of the interpolation operator defined on the finite space whose basis functions are defined on the general prismatic elements, we consider quadratic polynomials as the basis functions for that space which are bilinear on the reference prism. We then prove that under this modification of the semiregularity criterion, the interpolation error is of order O(h) in the H1-norm.

Vibration and stress analysis of orthotropic laminated panels by active face prismatic finite element

In this paper a strategy for the stress analysis of sandwich plates and shells employing the active face triangular-based prismatic finite element is provided, which combines three-dimensional membrane elements (called active face) with solid elements providing stiffening cells, usually called honeycomb. The connection of solid and active face elements is done by direct nodal correspondence, keeping the total number of degrees of freedom unaltered, which makes the technique highly economical from the numerical point of view. Orthotropic properties are specially addressed, which are important for material failure criteria studies. The accuracy of the active face prismatic finite element is also evaluated in the calculation of natural frequencies of honeycomb sandwich panels for acoustic vibration isolation purposes, for instance. Results for orthotropic sandwich plates and shells are presented and compared with established commercial software and literature results.

Interface bond strength of lightweight low-cement functionally layered concrete elements

Production of cement accounts for around 5% of human-made carbon emissions. When the selection of a cement-intensive mix with low porosity is driven by durability requirements, the resulting low permeability of the material is only fully exploited in peripheral regions of the element where the material acts as a physical barrier against the penetration of aggressive substances. This paper explores the potential of casting layered prismatic elements composed of an external durability layer and a lightweight core section as a means to achieve cement and weight savings. Layered elements are traditionally obtained by casting new concrete layers onto already hardened older concrete layers. A major problem with this technique is that planes of weakness are obtained at the interfaces between the layers. The bond between the layers can be improved by casting the materials at approximately the same time. However, research to date has not yet demonstrated the viability of producing elements with wet cast external layers. Furthermore, the effects of delays between successive pours on the mechanical tensile performance of the interfaces in layered elements have not been quantified. An original method is presented to form prismatic elements composed of an external durability layer and a lightweight core section by casting two concrete mixes at approximately the same time. The approach is validated by realising a proof-of-concept prototype layered element. A set of additional layered elements are cast with various pour delays and cored across the interface between their layers to characterize the interlayer bond strength by direct tension. To interpret the mechanisms affecting the bond, the variation of tensile bond strength with the location of the sample and the impact of roughness are also investigated. When the pour delay was minimal, failure did not occur at the interlayer. The relationship between pour delay and bond strength is markedly nonlinear, with bond strength reductions of more than 30% for pour delays of only three hours. It was also found that the bond strength of the interface varies significantly with the considered location and that up to 40% of the bond strength reduction due to a delay between the castings can be recovered by roughening the surface of the older concrete prior to casting the newer mix. The successful realisation of wet cast prismatic elements with an external durability layer is an important step towards the realisation of light-weight layered concrete elements with low embodied energy.

Sum factorization for fast integration of DPG matrices on prismatic elements

Higher order finite element (FE) methods provide significant advantages in a number of applications such as wave propagation, where high order shape functions help to mitigate pollution (dispersion) error. However, classical assembly of higher order systems is computationally burdensome, requiring the evaluation of many point quadrature schemes. When the Discontinuous Petrov-Galerkin (DPG) FE methodology is employed, the use of an enriched test space further increases the computational burden of system assembly, increasing the relevance of improved assembly techniques. Sum factorization—a technique that exploits the tensor-product structure of shape functions to accelerate numerical integration—was proposed in Ref. [10] for the assembly of DPG matrices on hexahedral elements that reduced the computational complexity from order O(p9) to O(p7) (where p denotes polynomial order). In this work we extend the concept of sum factorization to the construction of DPG matrices on prismatic elements by expressing prism shape functions as tensor products of 2D simplex and 1D interval shape functions. Unexpectedly, the resulting sum factorization routines on partially-tensorized prism shape functions achieve the same O(p7) complexity as sum factorization on fully-tensorized hexahedra shape functions (as products of 1D interval shape functions) presented in Ref. [10]. Throughout this work we adhere to the theory of exact sequence energy spaces, proposing sum factorization routines for each of the 3D FE exact sequence energy spaces—H1, H(curl), H(div), and L2. Computational results for construction of the DPG Gram matrix on a prismatic element in each exact sequence energy space are presented, corroborating the expected O(p7) complexity. Additionally, construction of the DPG system for an ultraweak Maxwell problem on a prismatic element is considered and a partially-tensorized sum factorization for hexahedral elements is proposed to improve implementational compatibility between hexahedral and prismatic elements.

Experimental demonstration and performance evaluation of a complex fenestration system for daylighting and thermal harvesting

Two significant design strategies for mitigating building energy consumption are daylight redirection and solar energy harvesting. Effective daylighting implementation enhances the amount of useful natural light within a space and offsets the need for electric lighting. Solar energy harvesting systems can mitigate energy costs from mechanical systems by managing incoming thermal loads or capturing solar energy that can be used to supplement thermal systems in the building. While there are many available façade-based technologies that can perform daylighting or solar thermal energy harvesting, there remains a limitation in available systems that can perform both of them simultaneously. This paper, describes the design and experimental demonstration of a Liquid Filled Prismatic Louver (LFPL) system, which combines both energy-saving strategies. The LFPL system was installed in a south-facing room in New York City and evaluated for indoor daylight penetration and potential for thermal energy harvesting. Daylight redirection is achieved through the prismatic louver geometry and proper orientation, whereas thermal energy harvesting is achieved through IR absorption from the liquid (e.g., water) within the prisms. Daylighting performance was evaluated by illuminance measurements at key locations within the space, whereas thermal harvesting performance was evaluated through temperature measurements and thermal imaging analysis. We show that the LFPL system, with all prismatic elements oriented at the same angle, achieve a 2-fold and 8-fold enhancement in daylight redirection to the ceiling, for prism orientations of 10° and 20°, respectively. We also demonstrate the system’s capability to adjust to specific lighting needs, within the space, through the dynamic individual orientation of prismatic elements; thus, achieving a concentrated ceiling illuminance enhancement of ~100 times and ~200 times at 2.5 and 4.3 m away from the window sill, providing workplane illuminance enhancement of 6 and 2 times more than in the case of the control room with regular windows. Furthermore, we show a reduction of potential heating loads at locations close to the window from the combination of infrared absorption in the water volume and the redirection of the incoming solar radiation, leading to a reduction of the workplane temperature by an average of 7–10 °C.

Efficient Matrix-Free High-Order Finite Element Evaluation for Simplicial Elements

With the gap between processor clock speeds and memory bandwidth speeds continuing to increase, the use of arithmetically intense schemes, such as high-order finite element methods, continues to be of considerable interest. In particular, the use of matrix-free formulations of finite element operators for tensor-product elements of quadrilaterals in two dimensions and hexahedra in three dimensions, in combination with single-instruction multiple-data instruction sets, is a well-studied topic at present for the efficient implicit solution of elliptic equations. However, a considerable limiting factor for this approach is the use of meshes comprising of only quadrilaterals or hexahedra, the creation of which is still an open problem within the mesh generation community. In this article, we study the efficiency of high-order finite element operators for the Helmholtz equation with a focus on extending this approach to unstructured meshes of triangles, tetrahedra, and prismatic elements using the spectral/$hp$ element method and corresponding tensor-product bases for these element types. We show that although performance is naturally degraded when going from hexahedra to these simplicial elements, efficient implementations can still be obtained that are capable of attaining 50% through 70% floating point operations of the peak of processors with both AVX2 and AVX512 instruction sets.

Scientific-technical investigations for development of optical multifunctional components for deflection, splitting and shaping of light beams

Many optical applications require splitting or deflection of light beams. This usually is achieved by usage of standard plane optical elements such as mirror systems or prismatic elements. However, these components are usually limited to one certain function and the manufacturing process for achieving precise functionality is very demanding. The presented research topic shows the development of new optical multifunctional components that introduce certain advantages compared to existing plane optical components. The basic roof-element configuration is based on glass cuboids joined together under a certain angle that can be fine adjusted during the manufacturing process. The components are therefore rather simply built and robust, and can fulfil different optical functions simultaneously by modifications of the glass cuboids. A process chain was developed for efficient and flexible manufacturing of such plane optical elements. Technical investigations were made on novel manufacturing processes such as ultrasonic assisted grinding and ultrafine grinding for fabrication of the cuboid parts, as well as diffusion joining being one possibility to create the basic roof-element shape.

Analysis of a normal and aero helmet on an elite cyclist in the dropped position

Cyclists use to wear different helmets and adopt different body positions on the bicycle to minimize resistance. The aim of this study was to compare a standard helmet with the new aero road helmets in a bicycle-cyclist system by CFD on the dropped position. An elite level road cyclist volunteered to this research. The cyclist was scanned on his racing bicycle on the dropped position wearing competition gear and a standard helmet and an aero road helmet. A three-dimensional domain around the cyclist with 7 m of length, 2.5 m of width and 2.5 m of height and meshed with more than 43 million of prismatic and tetrahedral elements. The numerical simulations were conducted at 11.11 m/s. The numerical simulations outputs were viscous, pressure and total drag and coefficient of drag. The standard helmet presented a viscous drag of 10.52 N, a pressure drag of 16.51 N and a total drag of 21.98 N. The aero road helmet presented a pressure drag of 7.40 N, a viscous drag of 12.56 N and a total drag of 19.96 N. Moreover, the aero road helmet presented a lower viscous, pressure and total drag coefficient in comparison to the standard helmet. It is possible to conclude that an aero road helmet imposes less drag in comparison to a standard helmet.

Application of finite elements of various dimensions in strength calculations of thin-wall constructions of agro-industrial complex

The article presents a comparative analysis of the effectiveness of the use of finite elements of various dimensions in the study of the stress-strain state (SSS) of objects of the agro-industrial complex (AIC). To determine the strength parameters of the AIC objects, which can be attributed to the class of thinwalled, it is proposed to use a two-dimensional finite element in the form of a fragment of the middle surface of a triangular shape with nodes at its vertices. To improve the compatibility of a two-dimensional finite element at the boundaries of adjacent elements, it is proposed to use the Lagrange multipliers introduced in additional nodes located in the middle of the sides of the triangular fragment as additional unknowns. It is proposed to use a three-dimensional finite element in the form of a prism with triangular bases to study the SSS of agricultural objects of medium thickness and thick-walled. To improve the compatibility of the prismatic element, Lagrange multipliers in the middle of the sides of the upper and lower bases are also used. On the example of calculating a fragment of a cylindrical pipeline rigidly clamped at the ends loaded with internal pressure, the effectiveness of the developed two-dimensional and three-dimensional finite elements with Lagrange multipliers was proved. The validity of the use of a twodimensional element for researching the SSS of agricultural objects belonging to the class of thin-walled was proved.

Finit element model of pipeline discretization by prismatic elements

Using the shells of triangular finite elements in calculations with a choice of nodal unknowns in the displacements form and their first derivatives, the continuity between the elements is provided only by displacements. Continuity in the derivative values is performed only at the nodal points and is absent at the boundaries between the elements. This circumstance often leads to a very slow convergence of the computational process. In this article, when using a prismatic finite element with a triangular base, improvement of the computational process by ensuring the equality condition of the derivatives normal displacements in the sides middle of adjacent triangular bases using uncertain Lagrange multipliers. Correctness and efficiency of the developed algorithm are shown in terms of the calculation.

Evaluating the Effect of the Compressive Strength Development Factor on Concrete Creep Deformation in Bridge Construction

Abstract Excessive midspan deflection is often observed in large-span prestressed concrete girder bridges. In particular, the deformation caused by shrinkage and creep of concrete is an important part of deflection that often exceeds expectations. To achieve creep deformation control, extending the curing time and postponing the loading age are frequently adopted during construction. This article proposed an approach based on creep experiments with prismatic and beam specimens and viscoelastic model-based finite element analyses to evaluate the effect of the concrete strength development factor on the ultimate creep coefficient in the Comité Euro-International du Béton-Fédération internationale de la précontrainte (CEB-FIP) model. The concrete strength development factor ξcc(t/tu) is defined as the ratio of the mean compressive strength at the loading time to the maximum mean compressive strength obtained in the test. The strategies for targeted regulation and control of ξcc(t/tu) were discussed by establishing an artificial neural networks model for strength prediction from a database provided in our previous work. Uniaxial compressive prismatic specimens and pure bending beam specimens with a span of 5.0 m were used in the experiment for creep behavior observation. A viscoelastic finite element analysis (FEA) model was established based on solidification theory. The FEA model results were verified with measured data for capturing the creep behavior under ambient conditions to obtain reliable long-term creep deformation predictions. Finally, the proposed method was validated with the Xincheng bridge construction for the optimistic loading age determination, and the results indicated good feasibility in girder deflection control.