Parallelepiped Elements Research Articles

Research on the Characteristics of Jacks Used to Rectify Tilted Buildings

One method of rectifying tilted buildings is by lifting them unevenly using hydraulic jacks. These jacks are loaded both monotonically and cyclically during the rectification process. It has been shown that the change in jack length is the sum of the change in the piston slide out and the change in the jack’s cylinder length, which is supported by a parallelepiped element. Laboratory tests were conducted to investigate the piston slide out and the change in the jack’s cylinder length under both monotonically and cyclically loaded conditions. The results indicated that the piston slide out forms a hysteresis loop. In contrast, the change in the jack’s cylinder length does not exhibit a hysteresis loop and is a non-linear function of the load. A structural model of the jack was proposed, consisting of three components: a linearly elastic component connected in parallel to the component where the frictional force occurs, and a component with non-linear elastic characteristics connected in series with them. Displacements of the linear elastic component, characterized by a constant stiffness, occur as long as the external load exceeds the internal frictional force. The value of the frictional force in this model increases with the load. The stiffness of the non-linear elastic component increases proportionally to the load.

Dual-Band Circularly Polarized Omni-Directional Biconical Antenna With Double-Circular Parallelepiped Elements for WLAN Applications

This research proposes a novel dual-band (2.45/5.80 GHz) omnidirectional circularly polarized (CP) biconical antenna with double-circular parasitic parallelepiped elements for wireless local area network (WLAN) applications. The proposed dual-band CP antenna scheme consisted of a biconical radiating structure surrounded by inner- and outer-circular parallelepiped elements that convert linearly polarized electric fields into CP fields. Simulations were performed to optimize the antenna parameters, and an antenna prototype was fabricated and experiments were conducted. The measured impedance bandwidths (IBWs) were 44.4% (1.84 – 2.89 GHz) and 4.56% (5.73 – 5.99 GHz) for the lower- (2.4 GHz) and upper-frequency (5.80 GHz) bands, respectively. The corresponding 3-dB axial ratio bandwidths (ARBWs) were 11.22% (2.27 – 2.54 GHz) and 10.49% (5.6 – 6.2 GHz). The radiation patterns of the dual-band antenna scheme were omnidirectional left-hand circular polarization, with the measured antenna gains of 3.2 dBic and 8.5 dBic at 2.45 and 5.80 GHz, respectively. The simulated and measured results were reasonably agreeable. Despite the narrow IBW and ARBW for the upper-frequency band, the bandwidths adequately covered the target upper frequency band, rendering the proposed CP omnidirectional biconical antenna scheme operationally suitable for WLAN applications. Furthermore, the novelty of this research lies in the use of a biconical radiating structure augmented with double-circular parasitic parallelepiped elements to realize circular polarization for dual-band WLAN applications.

Power Generation Efficiency of Thermoelectric Elements with a Trapezoidal Section

This article proposes a method to improve the thermoelectric conversion efficiency by controlling the heat flow direction of a thermoelectric element (TE) with a trapezoidal section. A thermoelectric generator (TEG) generally consists of a rectangular parallelepiped element. In theory, the thermoelectromotive force E can be easily estimated from the Seebeck coefficient α and the temperature difference ΔT, namely, E = αΔT. Seebeck coefficient α and resistivity ρ are known to have temperature dependence. We fabricated a TEG with a trapezoidal section which modified temperature distribution by TE shapes. It also provided many high Seebeck coefficient regions. As a result, the output power of TEG with a trapezoidal section was increased by 63% due to heat flow directions. It was also increased by 10% higher than the rectangular parallelepiped TEG at 400°C.

In Situ Experimental Study on the Active Support Used for Building Rectification.

There are many vertically deflected building structures in the world that require rectification. Temporary supports installed in the building bearing walls can be used to perform such a rectification. The supports consist of a hydraulic piston jack, a stack of parallelepiped steel elements, and a concrete grout. The structure is unevenly raised and reaches the desired vertical position using such supports. The support in which the piston extension is forced at the given time is an active support. The aim was to determine the stiffness of an active support. The investigations were performed in in situ conditions during experimental building rectification. No such investigations have been performed to date. It has been demonstrated that the stiffness of the investigated support results from the stiffness of the serially connected elements forming the support. In general, the support stiffness depends on the value of the force occurring in the support and is rising linearly along with the load for the investigated range. It was also shown that the force existing in the active support also depends on the stiffness of the building being rectified. The investigations carried out show that it is advantageous to use supports with smaller stiffness for rectification, as forces with smaller values must be induced in them. The application of forces with lower values also allows the avoidance of unfavorable penetration of the unlifted part of the building into the ground.

Examination of stiffness of stack of steel elements forming part of supports used for removal of building deflections

The removal of building deflections consists of uneven raising of buildings with piston hydraulic jacks. A stack of parallelepiped steel elements is situated under jacks during defl ection removal for technological reasons. The stack has decisive influence on the stiffness of the supports. Tests of the stack of parallelepiped elements loaded with increasing and decreasing force were designed and carried out. Three characteristic phases were identified based on the tests. The maximum stiffness in particular phases was, respectively 13.1, 63.1 and 10.1% of theoretical stiffness.

Scalable tensor-product preconditioners for high-order finite-element methods: Scalar equations

We present a tensor-product-based preconditioner for high-order discontinuous-Galerkin (DG) discretizations. The preconditioner is based on approximating the block diagonal of the Jacobian matrix corresponding to element-wise coupling with the sum of tensor products of small one-dimensional matrices. The preconditioner is obtained through an algebraic procedure which minimizes the error between the tensor-product approximation and the exact elemental block Jacobian.Inverting the full elemental block Jacobian requires O(Nd) memory storage and O(N2d) operations, while applying its inverse requires O(Nd) operations per degree of freedom, where N is the solution order and d is the dimension of the problem. Thus, traditional block preconditioners become impractical with increasing dimension, d, and order, N. The cost of forming, storing, or applying the current tensor-product-based preconditioner scales linearly with solution order (O(N)) per degree of freedom for arbitrary number of dimensions. Furthermore, the tensor-product-based preconditioner recovers the exact block-Jacobi preconditioner in the case of constant-coefficient scalar problems on right parallelepiped elements. Numerical results demonstrate the effectiveness of the preconditioner for solving 4D (3D-space+time) DG discretizations of scalar advection-diffusion problems up to 32nd order.

Hybrid energy converter based on swirling combustion chambers: the hydrocarbon feeding analysis

This manuscript reports the latest investigations about a miniaturized hybrid energy power source, compatible with thermal/electrical conversion, by a thermo-photovoltaic cell, and potentially useful for civil and space applications. The converter is a thermally-conductive emitting parallelepiped element and the basic idea is to heat up its emitting surfaces by means of combustion, occurred in swirling chambers, integrated inside the device, and/or by the sun, which may work simultaneously or alternatively to the combustion. The current upgrades consist in examining whether the device might fulfill specific design constraints, adopting hydrocarbons-feeding. Previous papers, published by the author, demonstrate the hydrogen-feeding effectiveness. The project’s constraints are: 1) emitting surface dimensions fixed to 30 × 30 mm, 2) surface peak temperature T > 1000 K and the relative ∆T < 100 K (during the combustion mode), 3) the highest possible delivered power to the ambient, and 4) thermal efficiency greater than 20% when works with solar energy. To this end, a 5 connected swirling chambers configuration (3 mm of diameter), with 500 W of injected chemical power, stoichiometric conditions and detailed chemistry, has been adopted. Reactive numerical simulations show that the stiff methane chemical structure obliges to increase the operating pressure, up to 10 atm, and to add hydrogen, to the methane fuel injection, in order to obtain stable combustion and efficient energy conversion.

Energy Converter with Inside Two, Three, and Five Connected H2/Air Swirling Combustor Chambers: Solar and Combustion Mode Investigations

This work reports the performance of an energy converter characterized by an emitting parallelepiped element with inside two, three, or five swirling connected combustion chambers. In particular, the idea is to adopt the heat released by H2/air combustion, occurring in the connected swirling chambers, to heat up the emitting surfaces of the thermally-conductive emitting parallelepiped brick. The final goal consists in obtaining the highest emitting surface temperature and the highest power delivered to the ambient environment, with the simultaneous fulfillment of four design constraints: dimension of the emitting surface fixed to 30 × 30 mm2, solar mode thermal efficiency greater than 20%, emitting surface peak temperature T &gt; 1000 K, and its relative ∆T &lt; 100 K in the combustion mode operation. The connected swirling meso-combustion chambers, inside the converter, differ only in their diameters. Combustion simulations are carried out adopting 500 W of injected chemical power, stoichiometric conditions, and detailed chemistry. All provide high chemical efficiency, η &gt; 99.9%, and high peak temperature, but the emitting surface ∆T is strongly sensitive to the geometrical configuration. The present work is related to the “EU-FP7-HRC-Power” project, aiming at developing micro-meso hybrid sources of power, compatible with a thermal/electrical conversion by thermo-photovoltaic cells.

Tilting plane tests on a small-scale masonry cross vault: Experimental results and numerical simulations through a heterogeneous approach

The seismic response of masonry vaults is discussed by presenting the results of an experimental campaign on a small-scale model and their numerical simulation though a heterogeneous full 3D non-linear Finite Element (FE) approach. The model relies into a discretization of the blocks by means of few rigid-infinitely resistant parallelepiped elements interacting by means of planar four-noded interfaces, where all the deformation (elastic and inelastic) occurs. In the framework of a heterogeneous approach, two typologies of interfaces are present, namely internal brick–brick interfaces, here assumed elastic, and mortar joints with zero thickness, behaving as a frictional (Mohr–Coulomb) material with infinite strength in compression and almost vanishing tensile strength. The model is incremental, non-linear elasto-plastic and exhibits softening at mortar interfaces. Each load step is solved by means of mathematical programming, i.e. through the formulation of a suitable constrained minimization problem where the objective function is represented by the energy of the mechanical system. The experimental and numerical results are compared and discussed in terms of both collapse mechanisms and force/displacement capacity.

Selective mass scaling for distorted solid-shell elements in explicit dynamics: optimal scaling factor and stable time step estimate

Summary The use of solid-shell elements in explicit dynamics has been so far limited by the small critical time step resulting from the small thickness of these elements in comparison with the in-plane dimensions. To reduce the element highest eigenfrequency in inertia dominated problems, the selective mass scaling approach previously proposed in [G. Cocchetti, M. Pagani and U. Perego, Comp. & Struct. 2013; 127:39-52.] for parallelepiped elements is here reformulated for distorted solid-shell elements. The two following objectives are achieved: the critical time step is governed by the smallest element in-plane dimension and not anymore by the thickness; the mass matrix remains diagonal after the selective mass scaling. The proposed approach makes reference to one Gauss point, trilinear brick element, for which the maximum eigenfrequency can be computed analytically. For this element, it is shown that the proposed mass scaling can be interpreted as a geometric thickness scaling, obtaining in this way a simple criterion for the definition of the optimal mass scaling factor. A strategy for the effective computation of the element maximum eigenfrequency is also proposed. The considered mass scaling preserves the element translational inertia, while it modifies the rotational one, leading to errors in the kinetic energy when the motion rotational component is dominant. The error has been rigorously assessed for an individual element, and a simple formula for its estimate has been derived. Numerical tests, both in small and large displacements and rotations, using a state-of-the-art solid-shell element taken from the literature, confirm the effectiveness and accuracy of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.

Full 3D homogenization approach to investigate the behavior of masonry arch bridges: The Venice trans-lagoon railway bridge

Some different procedures for the evaluation of the non-linear behavior of masonry arch bridges are here proposed. In particular, the Venice trans-lagoon masonry arch bridge is numerically analyzed by means of several 3D FE numerical strategies. The three dimensional behavior of the structure when subjected to train loads and pile foundation settlement is investigated. Focus is also posed to the stabilizing role played by the backfill.Both a non-commercial code and a standard commercial FE software are utilized. The non-commercial code properly takes into account for the orthotropic behavior of the barrel vaults and the stone arches, and allows performing non-linear static and limit analyses on complex 3D structures. Within the non-commercial FE approach, each material of the bridge (barrel vault, external stone arches, spandrels, piers, backfill) is suitably modeled using rigid parallelepiped elements and quadrilateral interfaces exhibiting an orthotropic constitutive law with either softening or rigid-plastic behavior in the non-linear and limit analysis version respectively. In both FE codes, mechanical properties of each material of the bridge (barrel vault, external stone arches, spandrels, piers, backfill) are modeled starting from suitable homogenization procedures in the elastic range (commercial software) and also beyond the linear limit (non-commercial FEM).The bridge is studied under service loads and up to failure for the passage of a standard train on either a single or both tracks. In the analyses, the stabilizing role played by the backfill, the strength increase obtained with stiff lateral stone arches on the barrel vault and the 3D effects induced by both load configurations are discussed. Results obtained with the incremental non-linear procedures are always compared with limit analysis predictions of collapse loads and failure mechanisms.Finally a uniform foundation settlement of one of the piles is simulated.

Singly-Fed Wideband 45&lt;formula formulatype="inline"&gt; &lt;tex Notation="TeX"&gt;$^\circ $&lt;/tex&gt;&lt;/formula&gt; Slant-Polarized Omnidirectional Antennas

Singly-fed 45 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> slant-polarized (SP) omnidirectional antennas without complex feed network are proposed in this letter. The antennas consist of a feeding probe that radiates monopolar omnidirectional vertically polarized (VP) fields and parasitic metallic/dielectric parallelepiped elements that convert omnidirectional VP fields into 45 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> SP fields. Two prototypes with metallic and dielectric parallelepipeds operating in C-band were designed. The bandwidths of the SP metallic and dielectric antennas are given by 15.1% and 31.9%, respectively.

Расчет железобетонных конструкций методом конечных элементов с учетом реального описания действующих физических процессов

It is well known, that buildings and their bearing structures are subject to ageing, including corrosion, deterioration, etc. When faults in bearing structure are detected, disposal-at-failure maintenance should be made. But before that, it is necessary to assess the rate of deterioration.The author suggests to use finite element method for calculation of the safety margin of reinforced concrete bearing structures, because the finite element method is widely used in engineering practice of structural design. In the process of engineering inspection of reinforced concrete structures all defects of the inspected structure should be clearly specified. The article suggests to create the FEM-Model of the inspected structure in view of the fact that this structure is defected. In order to achieve this effect, the stiffness matrix of some finite elements should be changed and the FEM-Model must be created of volumetric finite elements (the article speaks about eight-node parallelepiped elements).At first the FEM-Model will be created of eight-node parallelepiped elements with standard descriptions for the reinforced concrete; then finite elements in damage area must be changed. On the basis of integral estimation of the mode of deformation, deformation ratio will be calculated, which is essential for the description assignment of the changes in stiffness matrix. The formulation of the deformation ratio includes all the possible defects of structure through indexes, which must be analytically calculated depending on the concrete defect.The method described in the article is useful in the process of engineering inspection of the reinforced concrete structures. Using this method can sufficiently specify the safety margin of a defected structure and forecast the future operational integrity of this structure under the acting load.

Wideband Circularly Polarized Dielectric Bird-Nest Antenna With Conical Radiation Pattern

A wideband circularly polarized (CP) antenna with a conical radiation pattern is investigated. It consists of a feeding probe and parasitic dielectric parallelepiped elements that surround the probe. Since the structure of the antenna looks like a bird nest, it is named as bird-nest antenna. The probe, which protrudes from a circular ground plane, operates in its fundamental monopole mode that generates omnidirectional linearly polarized (LP) fields. The dielectric parallelepipeds constitute a wave polarizer that converts omnidirectional LP fields of the probe into omnidirectional CP fields. To verify the design, a prototype operating in C band was fabricated and measured. The reflection coefficient, axial ratio (AR), radiation pattern, and antenna gain are studied, and reasonable agreement between the measured and simulated results is observed. The prototype has a 10-dB impedance bandwidth of 41.0% and a 3-dB AR bandwidth of as wide as 54.9%. A parametric study was carried out to characterize the proposed antenna. Also, a design guideline is given to facilitate designs of the antenna.

A View on Stochastic Finite Element and Geostatistics for Resource Parameters Estimation

The resource parameter estimation using stochastic finite element, geostatistics etc. is a key point on uncertainty, risk analysis, optimization [1-5] etc. In this view, the paper presents some consideration on: 1) Stochastic finite element estimation. The concept of random element is simplified as a stochastic finite element (SFE) taking into account a parallelepiped element with eight nodes in which are given the probability density functions (pdf) on its point supports. In this context it is shown: a—the stochastic finite element is a linear interpolator, related to the distributions given at each nodes; b—the distribution pdf in whatever point x ∈ V; c—the estimation of the mean value of Z(x); 2) Volume integrals calculus; 3) SFE in geostatistics approaches; 4) SFE in PDE solution. Finally, some conclusions are presented underlying the importance of SFE applications

3D non-linear behavior of masonry arch bridges

In this paper, the static non-linear behavior of masonry bridges is numerically analyzed by means of a 3D FE numerical code. In particular, the three dimensional behavior of the structures when subjected to eccentric loads, the actual 3D geometry of the bridges (particularly important when skew arches are analyzed) and the strengthening effect induced by the backfill are considered.The code is non-commercial and is applied here for the first time in presence of a very large number of elements and different materials. It relies in a FE discretization of the structure by means of rigid infinitely resistant eight-noded parallelepiped elements and non-linear interfaces, exhibiting deterioration of the mechanical properties. Each material of the bridge (arch, buttresses, piers, and fill) is suitably modeled using interfaces having different constitutive behavior and mechanical properties.Two real scale masonry bridges are analyzed, namely a skew single span structure experimentally tested up to failure at the Bolton Institute, UK and a straight multi span bridge constituted by five circular arches and loaded with an eccentric load. Both 2D and 3D limit analyses are also performed to have full insight into the actual capabilities of the 3D approach to reproduce peak loads and deformed shapes at failure and, at the same time, to investigate limitations of 2D hypotheses when transversal effects induced by geometry and load eccentricity are not considered.

Efficient adaptive integration of functions with sharp gradients and cusps in n‐dimensional parallelepipeds

SUMMARYIn this paper, we study the efficient numerical integration of functions with sharp gradients and cusps. An adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions. The algorithm is based on a divide and conquer strategy and is independent of the location of the sharp gradient or cusp. The error analysis reveals that for a C0 function (derivative discontinuity at a point), a rate of convergence of n + 1 is obtained in . Two applications of the adaptive integration scheme are studied. First, we use the adaptive quadratures for the integration of the regularized Heaviside function—a strongly localized function that is used for modeling sharp gradients. Then the adaptive quadratures are employed in the enriched finite element solution of the all‐electron Coulomb problem in crystalline diamond. The source term and enrichment functions of this problem have sharp gradients and cusps at the nuclei. We show that the optimal rate of convergence is obtained with only a marginal increase in the number of integration points with respect to the pure finite element solution with the same number of elements. The adaptive integration scheme is simple, robust, and directly applicable to any generalized finite element method employing enrichments with sharp local variations or cusps in n‐dimensional parallelepiped elements. Copyright © 2012 John Wiley &amp; Sons, Ltd.

A New Class of Higher Order Mixed Finite Volume Methods for Elliptic Problems

We introduce a new class of higher order mixed finite volume methods for elliptic problems. We start from the usual way of changing the given equation into a mixed system using the Darcy's law, ${\bf u}=-{\cal K} \nabla p$. By integrating the system of equations with some judiciously chosen test spaces on each element, we define new mixed finite volume methods of higher order. We show that these new schemes are equivalent to the nonconforming finite element spaces used to define them. The Darcy velocity can be locally recovered from the solution of nonconforming finite element method. Hence our work opens a way to make higher order mixed method more practicable. Three-dimensional extensions to parallelepiped elements are also presented. This work can be viewed as a generalization of earlier works which were devoted to reducing the (lowest order) mixed finite element method to a corresponding nonconforming finite element method. An optimal error analysis is carried out and numerical results are presented which confirm the theory.

Numerical electroseismic modeling: A finite element approach

Electroseismics is a procedure that uses the conversion of electromagnetic to seismic waves in a fluid-saturated porous rock due to the electrokinetic phenomenon. This work presents a collection of continuous and discrete time finite element procedures for electroseismic modeling in poroelastic fluid-saturated media. The model involves the simultaneous solution of Biot’s equations of motion and Maxwell’s equations in a bounded domain, coupled via an electrokinetic coefficient, with appropriate initial conditions and employing absorbing boundary conditions at the artificial boundaries. The 3D case is formulated and analyzed in detail including results on the existence and uniqueness of the solution of the initial boundary value problem. Apriori error estimates for a continuous-time finite element procedure based on parallelepiped elements are derived, with Maxwell’s equations discretized in space using the lowest order mixed finite element spaces of Nédélec, while for Biot’s equations a nonconforming element for each component of the solid displacement vector and the vector part of the Raviart–Thomas–Nédélec of zero order for the fluid displacement vector are employed. A fully implicit discrete-time finite element method is also defined and its stability is demonstrated. The results are also extended to the case of tetrahedral elements. The 2D cases of compressional and vertically polarized shear waves coupled with the transverse magnetic polarization (PSVTM-mode) and horizontally polarized shear waves coupled with the transverse electric polarization (SHTE-mode) are also formulated and the corresponding finite element spaces are defined. The 1D SHTE initial boundary value problem is also formulated and approximately solved using a discrete-time finite element procedure, which was implemented to obtain the numerical examples presented.

The 3-D gravity inversion package GROWTH2.0 and its application to Tenerife Island, Spain

We present the gravity inversion software GROWTH2.0 and its application to recently obtained gravity data from the volcanic island of Tenerife (Canary Islands, Spain) to inform on its subsurface density structure. GROWTH2.0 is an inversion tool which enables the user to obtain, in a nearly automatic and nonsubjective mode, a 3D model of the subsurface density anomalies based on observed gravity anomaly data. The package is composed of three parts: (a) GRID3D to generate a 3D partition of the subsurface volume into parallelepiped elements, (b) GROWTH to perform the inversion routine and to obtain a 3D anomalous density model, and (c) VIEW for visual representation of the input data, the inversion model, and modeling residuals. The current version of the tool has been developed from an earlier code ( Camacho et al., 2002) and now incorporates several novelties: (1) a Graphical User Interface (GUI), (2) an optional automated routine for determination of parameter λ, which controls the balance between model fitness and smoothness, (3) optional determination of values for minimum density contrast, (4) a robust handling of outlier data, and (5) improved automated data reduction for terrain effects based on anticorrelation with topographic data. The new capabilities and applicability of GROWTH2.0 for 3-D gravity inversion are demonstrated by a case example using new gravity data from the volcanic island of Tenerife. In a nearly automatic approach, the software provides a 3-D model informing on the location and shape of the main structural building blocks of the island. Our model results allow us to shed light on the low-density structure of the islands dominant Pico Viejo–Pico Teide (PV–PT) volcanic complex and the identification of an intrusive structure (the east bulge volcano) embedded in Teide's east flank. A low-density body located at around 5.8 km depth beneath PT's summit may represent a current magma or hybrid reservoir.