Vibration analysis of two-dimensional micromorphic structures using quadrilateral and triangular elements

PurposeThe paper aims to presents a numerical analysis of free vibration of micromorphic structures subjected to various boundary conditions.Design/methodology/approachTo accomplish this objective, first, a two-dimensional (2D) micromorphic formulation is presented and the matrix representation of this formulation is given. Then, two size-dependent quadrilateral and triangular elements are developed within the commercial finite element software ABAQUS. User element subroutine (UEL) is used to implement the micromorphic elements. These non-classical elements are capable of capturing the micro-structure effects by considering the micro-motion of materials. The effects of the side length-to-length scale parameter ratio and boundary conditions on the vibration behavior of 2D micro-structures are discussed in detail. The reliability of the present finite element method (FEM) is confirmed by the convergence studies and the obtained results are validated with the results available in the literature. Also, the results of micromorphic theory (MMT) are compared with those of micropolar and classical elasticity theories.FindingsThe study found that the size effect becomes very significant when the side length of micro-structures is close to the length scale parameter.Originality/value The study is to analyze the free vibrations of 2D micro-structures based on MMT; to develop a 2D formulation for micromorphic continua within ABAQUS; to propose quadrilateral and triangular micromorphic elements using UEL and to investigate size effects on the vibrational behavior of micro-structures with various geometries.

RECONSTRUCTION OF THE TWO VARIABLES DISCONTINUOUS FUNCTION BY DIFFERENT INFORMATION OPERATORS USING TRIANGULAR ELEMENTS

The paper examines methods for constructing mathematical models of two variables discontinuous functions using various information about them: one-sided values at points and one-sided traces along a given system of lines. The case is considered when the domain of the required function is triangulated by right-angled triangles. If interpolation or approximation methods are used, then for their construction the values of the function at given points must be given; if we use interlination methods, then traces of the desired function along a given system of lines. In this work, we construct a discontinuous interpolation and approximation splines for approximating a discontinuous function of two variables with given one-sided values in a given system of points (in our case, at the vertices of right-angled triangles), and prove theorems on the estimation of the approximation error by constructed discontinuous structures. In the paper a discontinuous interlination spline, which uses completely different information about the discontinuous function, namely one-sided traces along a given system of lines (in our case, along the sides of right-angled triangles) is also built. Interlination of functions can find wide application in the aircraft and automobile body design automation; when receiving and processing the results of sonar and radar, when solving problems of computed tomography, in digital signal processing and in many other areas. In the paper theorems on the integral form and an estimate of the approximation error by the constructed discontinuous interlination operator are also proved. Computational experiments that compare the results of the approximation of a discontinuous function of two variables by different information operators using triangular elements are presented. In the future, it is planned to apply the constructed operators of discontinuous approximation and interlination to solve a two-dimensional problem of computed tomography with a significant use of the inhomogeneity of the internal structure of the body, which must be reconstructed.

spyro: a Firedrake-based wave propagation and full waveform inversion finite element solver

In this article, we introduce spyro, a software stack to solve acoustic wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing the finite element framework from Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite element method. The capability of the software is demonstrated by using a continuous Galerkin approach to perform FWI for seismic velocity model building, considering realistic geophysics examples. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to discretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process, a fully-explicit, variable higher-order (up to degree k = 5 in 2D and k = 3 in 3D) mass lumping method is used. We show that, by adapting the triangular elements to the expected peak source frequency and properties of the wavefield (e.g., local P-wavespeed) and by leveraging higher-order basis functions, the number of degrees-of-freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both 2D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material properties.

Galerkin finite element study for mixed convection (TiO2–SiO2/water) hybrid-nanofluidic flow in a triangular aperture heated beneath

Fluidity and thermal transport across the triangular aperture with lower lateral inlet and apply placed at the vertical outlet of the chamber which filled with efficient TiO2–SiO2/water hybrid nanofluid under the parametrical influence. Several parameters are tested like the numbers of Hartmann ($$0 \le Ha \le 100$$ 0 ≤ H a ≤ 100 ), Richardson ($$0 \le Ri \le 5$$ 0 ≤ R i ≤ 5 ), and Reynolds ($$10 \le Re \le 1000$$ 10 ≤ R e ≤ 1000 ) were critiqued through streamlines, isotherms, and Nusselt number ($$Nu$$ Nu ). Numerical model has to be developed and solved through the Galerkin finite element method (GFEM) by discretized with 13,569 triangular elements optimized through grid-independent analysis. The Hartmann number ($$Ha$$ Ha ), exerts minimal impact over the flow and thermal aspects while the other parameters significantly manipulate the physical nature of the flowing and thermal aspects behaviors.

Numerical Simulation of Tidal Current in Majishan Sea Area of Zhoushan Based on SCHISM

Based on the SCHISM ocean model, this paper constructs a numerical model of the Majishan sea area in Shengsi County, Zhoushan City, and numerically simulates the tidal and tidal current conditions in the sea area. The non-structural triangular elements are used to construct the high-precision nearshore terrain to accurately simulate the tidal and tidal conditions. Yearly measured tidal current data. Have a deeper understanding of the tidal currents in the Majishan sea area of Zhoushan. The results show that the Majishan sea area of Zhoushan belongs to regular shallow sea currents dominated by recurrent currents. In the actual measurement, the speed of the rising and falling tides varies, and the maximum and average flow speeds are both the high tide is greater than the medium tide and the small tide. The tidal changes are mainly controlled by the forward waves of the East China Sea, and the direction of the current is basically the same as the direction of the rising and falling tides.

A 4-node quadrilateral element with center-point based discrete shear gap (CP-DSG4)

This work aims at presenting a novel four-node quadrilateral element, which is enhanced by integrating with discrete shear gap (DSG), for analysis of Reissner-Mindlin plates. In contrast to previous studies that are mainly based on three-node triangular elements, here we, for the first time, extend the DSG to four-node quadrilateral elements. We further integrate the fictitious point located at the center of element into the present formulation to eliminate the so-called anisotropy, leading to a simplified and efficient calculation of DSG, and that enhancement results in a novel approach named as "four-node quadrilateral element with center-point based discrete shear gap - CP-DSG4". The accuracy and efficiency of the CP-DSG4 are demonstrated through our numerical experiment, and its computed results are validated against those derived from the three-node triangular element using DSG, and other existing reference solutions.

Features in the Resonance Behavior of Magnetization in Arrays of Triangular and Square Nanodots

Collective modes of the gyrotropic motion of a magnetic vortex core in ordered arrays of triangular and square ferromagnetic film nanodots have been theoretically investigated. The dispersion relations have been derived. The dipole–dipole interaction of the magnetic moments of the magnetic vortex cores of elements has been taken into account in the approximation of a small shift from the equilibrium position. It is shown that the effective rigidity of the magnetic subsystem of triangular elements is noticeably higher than that of the subsystem of square elements of the same linear sizes. The potential application of the polygonal film nanodisks as nanoscalpels for noninvasive tumor cell surgery is discussed

A Second-Order Stabilized Control Volume Finite Element Method for Self-Heating Effects Simulation of Semiconductor Devices based on Triangular Elements

A second-order control volume finite element method combined with the multiscale flux approximation (CVFEM-MS) based on triangular elements is proposed to numerically investigate the self-heating effects of semiconductor devices. The multiscale fluxes are combined with a selected set of second-order vector basis functions to stabilize the discretization of carrier continuity equations with respect to triangular elements. Numerical results reveal that the proposed method is robust and accurate, even on the mesh of low-quality, where the detrimental impacts caused by the severe self-heating on the terminal currents can be obviously observed for a bipolar transistor model.

Simulation-based assessment of coupled frequency response of magneto-electro-elastic auxetic multifunctional structures subjected to various electromagnetic circuits

This article deals with the modeling of magneto-electro-elastic auxetic structures and developing a methodology in COMSOL Multiphysics® to assess the free vibration response of such structures when subjected to various electromagnetic circuit conditions. The triple energy interaction between elastic, magnetic, and electric fields are established in the COMSOL Multiphysics® using structural mechanics and electromagnetic modules. The multiphase magneto-electro-elastic material with different percentages of piezoelectric and piezomagnetic phases are used as the material. In the solid mechanics module, the piezoelectric and piezomagnetic materials were created in stress-charge and stress-magnetization forms, respectively. The electric and magnetic fields are defined in COMSOL Multiphysics® through electromagnetic equations. Further, the customized controlled meshing constituted of free tetrahedral and triangular elements is adapted to trade-off between the accuracy and the computational expenses. The eigenvalue analysis is performed to obtain the natural frequencies of the MEE re-entrant auxetic structures. Also, the efficiency of smart auxetic structures over conventional honeycomb structures is presented throughout the manuscript. In addition, the discrepancy in the natural frequencies of the structures considering coupled and uncoupled state is also illustrated. It is believed that the modeling procedure and its outcomes serve as benchmark solutions for further design and analysis of smart auxetic magneto-electro-elastic structures.

Development of a Combined-Ritz Method for Modeling 3D Acoustics in Candu Fuel Sub-Channels

A combined finite element-Ritz method is developed to effectively model the 3D lowfrequency acoustics in CANDU fuel sub-channels. The complex acoustic behavior of CANDU fuel sub-channels in the cross section is captured using the six-node isoparametric triangular elements; and the acoustic wave propagation in the axial direction is modeled using the polynomials of order n. The Lagrange equations are utilized to formulate the system equations of motion. The acoustic system considered in this study consists of pipe-like medium (water) with rigid and smooth walls. At the inlet of the fuel channel acoustic system, an acoustic pressure wave is prescribed to simulate the pulsation induced by the main feeder pumps. At the outlet, the acoustic system is assumed to interact with a reacting and absorbing material with prescribed acoustic impedance. The method was tested for several scenarios of interest. Numerical results obtained are in excellent agreement with the analytical and ANSYS solutions.