Finite Structures Research Articles

A performance evaluation of a new flexible preconditioning method on a parallel finite element structure analysis program, FrontISTR

A performance evaluation of a new flexible preconditioning method on a parallel finite element structure analysis program, FrontISTR

Strategies to enhance the attenuation band in finite beams using periodic attachments

One-dimensional waveguides, such as beams are frequently found in structural engineering applications. A finite periodic structure composed of a beam with periodically spaced vibration absorbers is considered in this work. Additionally, the behaviour of the structure when a hinge condition is imposed between adjacent cells is investigated. Based on the dynamic stiffness matrix approach, the transverse displacement transmissibility is evaluated for a single cell. The effectiveness of using appropriately tuned vibration absorbers in the formation of a smooth super attenuation band is demonstrated. Prediction of the attenuation band is also discussed for a structure with several periodic cells. In addition, the effect of hinge connections between the cells on the boundary frequencies of the attenuation band and the minimum transmissibility is presented.

A deterministic energy method for predicting the response of coupled finite structures

The forced response of finite, thin rectangular plates coupled by a line joint can be predicted using well-established analytical methods. However, such methods become difficult to implement for thick panels coupled by complex joints. In these cases, the finite element (FE) method and conventional statistical energy analysis (SEA) are viable alternatives. However, the FE method can be time-consuming at mid/high frequencies while SEA involves various approximations and assumptions. This paper develops a deterministic energy method for predicting the forced response of coupled complex panels based on a hybrid finite element/wave finite element method (WFE), modelling the panels as coupled wave-bearing subsystems. Excitation of the structure by a time-harmonic point force is considered. The method involves meshing only a small segment of the panel and the joint using finite elements, and is able to model complex structures such as laminated panels and joints with low computational cost. An illustrative example of the method is presented - coupled thin, rectangular plates coupled by an "L" shaped joint.

Crystal plasticity finite element modelling and mechanical deformation mechanism of nanolaminated graphene reinforced metal matrix composites

Metal matrix composites with certain hierarchical structures are potential to break out the conflicts between strength and toughness. Nano-carbon like graphene (Gn) reinforced metal matrix composites with nanolaminated structures have been largely developed to overcome this issue. However, the plastic deformation mechanism hiding behind the nanolaminated structures is still lacking. In this study, crystal plasticity finite element simulations and composite structure modeling are combined in order to uncover the mechanical deformation behavior of nanolaminated Gn/Al composites. Different lateral Gn sizes of 180, 360 and 720 nm are considered, while the hybrid lateral Gn sizes of 180 and 720 nm are applied as well. Good consistency between experimental and numerical results indicates the reliability of performed simulations. It is found that the strengthening and hardening behaviors of Gn/Al composites are dominated by Gn rather than Al matrix. The edges of Gn serving as a major dislocation nucleation source produce localization of plastic deformation, while the interiors of Gn activate more slip systems but reduce total shear strains. The edges and interiors of Gn determine the stability of plastic deformation of Gn/Al composites; large edge vs. interior area of Gn will lead to early necking. The rule of mixture fails in predicting the peak tensile strength and tensile strain of Gn/Al composites with hybrid lateral Gn sizes, because the microscopic plastic deformation can largely localize around 180 nm Gn in these hybrid Gn/Al composites. This work is enlightening to design and develop novel smart metal matrix composites.

Products of Classes of Finite Structures

Products of Classes of Finite Structures

Propagation mechanism of low-frequency elastic waves and vibrations in a new tetragonal hybrid metamaterial

In order to achieve low-frequency vibration and noise reduction, artificial metamaterial with great potential in this field have been widely found. Based on previous studies, a new tetragonal hybrid metamaterial structure is proposed in this paper. It is exciting that the combination of inclusions with different material properties and sizes can affect the generation of band gaps. Then, based on the selected frequency, the propagation characteristics of waves in the structure were qualitatively analyzed using group velocity and phase velocity, and the potential for vibration reduction and noise reduction of the proposed structure was verified through finite element simulation of vibration in finite period structures. The results show that the proposed structure can open multiple broadband gaps, and the frequency range of the band gap can be flexibly adjusted according to needs. This study provides a new way for the design of low-frequency phononic metamaterial systems.

Elastic metamaterials with fractional-order resonators

Elastic metamaterials incorporating locally resonating unit cells can create bandgap regions with lower vibration transmissibility at longer wavelengths than the lattice size and offer a promising solution for vibration isolation and attenuation. However, when resonators are applied to a finite host structure, not only the bandgap but also additional resonance peaks in its close vicinity are created. Increasing the damping of the resonator, which is a conventional approach for removing the undesired resonance peaks, results in shallowing of the bandgap region. To alleviate this problem, we introduce an elastic metamaterial with resonators of fractional order. We study a one-dimensional structure with lumped elements, which allows us to isolate the underlying phenomena from irrelevant system complexities. Through analysis of a single unit cell, we present the working principle of the metamaterial and the benefits it provides. We then derive the dispersion characteristics of an infinite structure. For a finite metastructure, we demonstrate that the use of fractional-order elements reduces undesired resonances accompanying the bandgap, without sacrificing its depth.

Temporal logic of surjective bounded morphisms between finite linear processes

ABSTRACT In this paper, we study temporal logic for finite linear structures and surjective bounded morphisms between them. We give a characterisation of such structures by modal formulas and show that every pair of linear structures with a bounded morphism between them can be uniquely characterised by a temporal formula up to an isomorphism. As the main result, we prove Kripke completeness of the logic with respect to the class of finite linear structures with bounded morphisms between them.

Dynamic displacement estimation of structures using one-dimensional convolutional neural network

For large infrastructures, dynamic displacement measurement in structures is an essential topic. However, limitations imposed by the installation location of the displacement sensor can lead to measurement difficulties. Accelerometers are characterized by easy installation, good stability and high sensitivity. For this regard, this paper proposes a structural dynamic displacement estimation method based on a one-dimensional convolutional neural network and acceleration data. It models the complex relationship between acceleration signals and dynamic displacement information. In order to verify the reliability of the proposed method, a finite element-based frame structure was created. Accelerations and displacements were collected for each node of the frame model under seismic response. Then, a dynamic displacement estimation dataset is constructed using the acceleration time series signal as features and the displacement signal at a certain moment as target. In addition, a typical neural network was used for a comparative study. The results indicated that the error of the neural network model in the dynamic displacement estimation task was 9.52 times higher than that of the one-dimensional convolutional neural network model. Meanwhile, the proposed modelling scheme has stronger noise immunity. In order to validate the utility of the proposed method, data from a real frame structure was collected. The test results showed that the proposed method has a mean square error of only 5.097 in the real dynamic displacement estimation task, which meets the engineering needs. Afterwards, the outputs of each layer in the dynamic displacement estimation model are visualized to emphasize the displacement calculation process of the convolutional neural network.

Nonreciprocal vibrations of discretized finite elastic structures with spatiotemporally modulated material properties

Elastic waveguides with time- and space-dependent material properties have received great attention as a means to realize nonreciprocal propagation of small-amplitude mechanical waves in unbounded elastic media. Previous works have shown that propagating waves in a modulated medium violate reciprocity by means of asymmetric frequency and wave number conversion between two counterpropagating modes. We previously investigated nonreciprocal longitudinal and transverse vibrations in a finite elastic waveguide with time- and space-dependent material properties using a semi-analytical coupled-mode theory The model employs the mode shapes of the non-modulated beam as the orthogonal basis functions to describe the nonreciprocal vibrations of beams with spatiotemporally modulated properties. The present study extends previous work to consider vibrations of Euler beams with spatially discretized stiffness that are modulated in time and phased relative to each other to mimic spatiotemporal modulation. This is achieved by approximating the discretized stiffness and then employing the mode shapes of the beam with unmodulated discretized stiffness to predict the nonreciprocal vibrational response of the beam when subjected to spatiotemporal modulation. We perform a parametric study of the system parameters and discuss how this model can be used to define requirements of future systems that can be used for experimental demonstration.

Ranks and approximations for families of cubic theories

In this paper, we study the rank characteristics for families of cubic theories, as well as new properties of cubic theories as pseudofiniteness and smooth approximability. It is proved that in the family of cubic theories, any theory is a theory of finite structure or is approximated by theories of finite structures. The property of pseudofiniteness or smoothly approximability allows one to investigate finite objects instead of complex infinite ones, or vice versa, to produce more complex ones from simple structures.

Application of periodic structural wave impeding block for vibration isolation in foundation

The wave impeding board (WIB) is frequently integrated beneath dynamic machinery, tracks, and subgrades to counteract vibrations emanating from artificial sources. However, conventional WIBs have exhibited a limited isolation frequency band due to their dependence on the soil cut-off frequency of soil. Furthermore, the vibration sources typically encompass intricate frequency components spanning low, medium, and high frequencies. To overcome the technical limitations of WIBs relying on the cut-off frequency of soil, a new periodic structural wave impeding board (PSWIB) is proposed based on the principles of phononic crystals. Theoretical and numerical analyses demonstrate that PSWIB exhibits bandgap characteristics, with the attenuation range achieved by finite periodic structures aligning with the bandgap of an infinite PSWIB. Maximum amplitude reductions of 47 dB and 65 dB are achieved within the vibration attenuation range. Compared to traditional WIB, PSWIB surpasses the constraints imposed by the cut-off frequency of soil and allow for the design of constituent parameters based on the characteristics of the vibration source, enabling effective isolation of the target frequency vibrations.

Thermal conductivity at finite temperature and electronic structure of the ultra-wide band gap fluorinated 2D GaN

Passivation makes 2D hexagonal structure more stable than the planar variant. Surface fluorinated monolayer of GaN have been found to have ultra-wide band gap and have promising applications in optoelectronic conversion devices. In this work, using theoretical method, we have explored the thermal conductivity as well as the electronic structure of F–GaN. It has a low thermal conductivity of 7.67 W (mK)−1 due to the low group velocity and short phonon lifetime. The calculated direct band gap value is 4.63 eV, which could be modulated by strain and biaxial strain is found to more effective. Attractively, direct band gap can be maintained under tensile strain. Breakdown of symmetry by uniaxial strain lifts the band degeneracy of the VBM, which will lead to polarized light emission. The in-depth analysis shows that Ga–F as well as N–F bonds are strongly ionic, which is responsible for its low thermal conductivity and ultra-wide band gap.

A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data

This paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture structure adds flexibility and facilitates application and use in analysis. The family of distributions is exemplified using a mixture of negative binomial and shifted negative binomial distributions. Some basic and probabilistic properties are derived. We perform hypothesis testing for equi-dispersion and simulation studies of their power and consider parameter estimation via maximum likelihood and probability-generating-function-based methods. The utility of the distributions is illustrated via their application to real biological data sets exhibiting under-, equi- and over-dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM–Poisson distributions for handling under-, equi- and over-dispersion in count data.

Some Remarks on the Distribution of Additive Energy

The aim of this note is twofold. In the first part of the paper we are going to investigate an inverse problem related to additive energy. In the second part, we consider how dense a subset of a finite structure can be for a given additive energy.

A modified damage and fracture phase field model considering heterogeneity for rock‐like materials

AbstractDamage and fracture are the most extensive failure modes of rock materials, which may easily induce disaster and instability of engineering structures. This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks. The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations. Meanwhile, the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy. As for the numerical implementation, the three layers finite elements method structure was used in the frame of the finite element method. The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression.

Challenges and Solutions for Engineering Applications on Smartphones

This paper starts by presenting the concept of a mobile application. A literature review is conducted, which shows that there is still a certain lack with regard to smartphone applications in the domain of engineering as independent simulation applications and not only as extensions of smartphone tools. The challenges behind this lack are then discussed. Subsequently, three case studies of engineering applications for both smartphones and the internet are presented, alongside their solutions to the challenges presented. The first case study concerns an engineering application for systems control. The second case study focuses on an engineering application for composite materials. The third case study focuses on the finite element method and structure generation. The solutions to the presented challenges are then described through their implementation in the applications. The three case studies show a new system of thought concerning the development of engineering smartphone applications.

Finite element analysis and structure optimization of a gantry-type high-precision machine tool

The high-precision machine tool’s dynamic, static, and rigid nature directly affects the machining efficiency and surface quality. Static and dynamic analyses are essential for the design and improvement of precision machine to ensure good tool performance under difficult and demanding machining conditions. In this study, the performance of a high-precision machine tool was analyzed using its virtual model created using CAD. Static and model analysis using ANSYS Workbench software was conducted to establish the tool's static deformation and static stiffness. Furthermore, the static and dynamic characteristics of the tool were explored using a finite element modeling approach to study their performance. In particular, the structure, static force, modal, frequency spectrum, and topology optimization of machine tools were primarily analyzed. Using model analysis, we found the first four different frequencies (22.5, 28.9, 40.6, and 47.4 Hz) and vibration type, which suggested of a weak link. Further static structural analysis revealed that the deformation of the spindle was 67.26 μm. An experimental static rigidity analysis was performed, and the experimental deformation values of the tool and spindle were obtained. The static and dynamic characteristics, as well as the accuracy and efficiency of the finite element model, were verified by comparing the data with the finite element analysis (FEA) results. Subsequently, we modified the settings and analysis model to ensure that the analysis results were consistent with the experimental findings. The error between the two results was within 1.56%. For an applied load of 5000 N on the spindle nose, the tool nose transient response was 0.5 s based on transient analysis. Under the condition that the structural deformation is as constant as possible, the lightweight structure may achieve the minimum weight and enhance the natural frequency; thus, the ideal structure will be obtained, and finite element analysis will then be performed. The optimal conditions for topology optimization include a lightweight structure, reduced structural deformation, and increased natural frequency of the structure. The developed method improves structural optimization, increases the ability of the product to be manufactured, and offers designers a variety of price-effective options.

Signal Wrap-Around Free Spectral Element Formulation For Multiply Connected Finite 1-D Waveguides

This paper presents a novel spectral element formulation based on Numerical Laplace Transforms for the wave propagation of multiply connected finite 1-D waveguides, based on the first order shear deformation theory. The present formulation overcomes the severe short-comings of Fourier transform based spectral element formulation which has serious problems associated with the signal wrap-around while analysing finite domain structures. The real part of the Laplace variable which provides damping to the wavenumber solution, is characterized by Wilcox and Wedepohl approaches. The effect of this damping alters the wave dispersion and introduces certain interesting phenomenon that is not seen in the undamped waveguides. Problems involving wave propagation analysis are solved on finite multiply connected waveguides of varied complexity to demonstrate the efficiency of the formulated element. In most of the examples, the presence of signal wrap-around in Fourier domain based spectral element is brought out. With this approach, any large structural network, consisting of 2-D either metallic or composite finite length waveguides, under high frequency impact loading can be analyzed with very low computational cost.

Investigation of broadband damping and damping mechanism of quadrangular star-shaped ligament heterostructure

In this paper, a single-phase quadrangular star-shaped ligamentous heterostructure is constructed, and a two-phase structure is formed by attaching a resonator at the center of the structure. The lattice theory and finite element modeling are combined to analyze the band structure of the two structures, and the additional resonator at the center of the structure improves the bandgap range. Based on this, the bandgap can be widened and reduced by adjusting the resonator size. In the structural vibration modal analysis, it is explained that the coupling of traveling wave and vibration can open the omnidirectional bandgap, which provides guidance for the subsequent structural optimization. In addition, the relationship between bandgap opening and directional propagation of elastic waves is verified by a comprehensive analysis of group velocity, phase velocity, and other means. Finally, the transmission characteristics and stress distribution of the structure within the finite period structure are investigated, and it is further verified that the structure has a strong attenuation capability to vibration. This structure has good vibration isolation capability in a wide frequency range and has potential for application in complex vibration control.