Element Nodes Research Articles

Influence of circular cutouts and elastic foundation on vibration characteristics of porous sandwich FGM plates under hygro-thermal environments

The present article investigates the effect of cutouts, porosity inclusion, and hygro-thermal environment on the vibrational characteristics of sandwich functionally graded material (FGM) plates resting on Pasternak elastic foundation. The governing equations for the sandwich FGM plates have been developed using the finite element method (FEM) with the conjunction of non-polynomial-based higher-order shear deformation theory (HSDT). The trigonometric shear-strain shape function has been used for the first time for sandwich FGM plates. The effective material properties with porosity inclusions have been computed using modified power–law distribution. The present results have been acquired by employing a C0 continuity isoparametric finite element (FE), using 4-noded elements with 7-DOF's per node. The accuracy of the current solution has been confirmed by convergence and validation studies. The influence of circular cutout, elastic foundations, hygro-thermal conditions, and geometric and boundary conditions on the vibrational frequency of porous sandwich FGM plates have been discussed in detail.

Nonlinear dynamic analysis of galloping of a single iced conductor with four degrees of freedom based on curved beam theory

Based on the nonlinear strain-displacement relationship of spatial curved beam theory, a finite element model for galloping analysis of iced transmission lines is established, which involves three translational degrees of freedom (DOF) and one rotational degree of freedom for each node. Considering the aerodynamic nonlinearity and the geometric nonlinearity of large amplitude motions of the iced transmission line, the nonlinear dynamic finite element equation is presented by using the virtual work principle. The equation is transformed into the sub-space according to the mode superposition method and a time integration algorithm is also performed in the sub-space. Then, the element independence and modal convergence are researched. Finally, the influence of aerodynamic forces on structural frequency is analyzed. The numerical results show that aerodynamic forces will greatly affect the torsional frequency of the transmission line, which accurately reflects the dynamic characteristics of transmission lines. Furthermore, the galloping calculation of the transmission line has reliable accuracy by using 4-DOF (per node) elements for the iced conductor. On the other hand, the model can predict the actual galloping response of the transmission line, which is convenient for the implementation of subsequent control design.

Aeroelastic control of delaminated variable angle tow laminated composite plate using piezoelectric patches

The free vibration and aeroelastic analysis of variable angle tow (VAT) laminated composite plate bonded with discrete piezoelectric patches are considered for investigation. A finite element (FE) model is developed using eight noded isoparametric elements to study the impact of delamination size and location on the dynamic response of smart VAT laminated plates. For aeroelastic analysis, the FE model is coupled with MSC. Nastran through Direct Matrix Abstraction Program (DMAP) and the structural parameters obtained with the FE model are supplied to MSC. Nastran solver to generate aerodynamic force matrix using Doublet Lattice Method (DLM). Various parametric studies are performed to find the most critical location of the delamination that severely affects vibration and flutter characteristics. The results showed that the delamination near the leading edge which faces free stream wind is found to be the most critical for the dynamic aeroelastic failure of structures. Further, the most effective location of the piezoelectric patches is identified to enhance the aeroelastic boundary of smart delaminated VAT composite plates using active displacement and velocity feedback gains.

Comparative performance of novel nodal-to-edge finite elements over conventional nodal element for electromagnetic analysis

In nodal-based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney spaces. Nodal elements impose both tangential and normal continuity of vector or scalar fields across interface boundaries. But in edge elements, only tangential continuity is imposed across interface boundaries, which is consistent with electromagnetic field problems. Therefore the required continuities in the electromagnetic analysis are directly obtained with edge elements whereas in nodal elements they are attained through potential formulations. Hence, while using edge elements, field variables are directly calculated but with nodal elements, post-processing is required to obtain the field variables from the potentials. Here, we present the finite element formulations with the edge element as well as with nodal elements. Thereafter, we have demonstrated the relative performances of different nodal and edge elements through a series of examples. All possible complexities like curved boundaries, non-convex domains, sharp corners, non-homogeneous domains have been addressed in those examples. The robustness of edge elements in predicting the singular eigen values for the domains with sharp edges and corners is evident in the analysis. A better coarse mesh accuracy has been observed for all the edge elements as compared to the respective nodal elements. Edge elements are also not susceptible to mesh distortion.

Convergence of restricted additive Schwarz with impedance transmission conditions for discretised Helmholtz problems

The Restricted Additive Schwarz method with impedance transmission conditions, also known as the Optimised Restricted Additive Schwarz (ORAS) method, is a simple overlapping one-level parallel domain decomposition method, which has been successfully used as an iterative solver and as a preconditioner for discretised Helmholtz boundary-value problems. In this paper, we give, for the first time, a convergence analysis for ORAS as an iterative solver—and also as a preconditioner—for nodal finite element Helmholtz systems of any polynomial order. The analysis starts by showing (for general domain decompositions) that ORAS is an unconventional finite element approximation of a classical parallel iterative Schwarz method, formulated at the PDE (non-discrete) level. This non-discrete Schwarz method was recently analysed in [Gong, Gander, Graham, Lafontaine, and Spence, Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation], and the present paper gives a corresponding discrete version of this analysis. In particular, for domain decompositions in strips in 2-d, we show that, when the mesh size is small enough, ORAS inherits the convergence properties of the Schwarz method, independent of polynomial order. The proof relies on characterising the ORAS iteration in terms of discrete ‘impedance-to-impedance maps’, which we prove (via a novel weighted finite-element error analysis) converge as h → 0 h\rightarrow 0 in the operator norm to their non-discrete counterparts.

Effect of delamination on natural frequencies of laminated FRP composite plate

De-lamination is a subtle kind of failure which might be induced during manufacturing or material handling, which causes the layers of a laminated composite plate to detach because of the failure of adhesion between the layers. The existence of de-lamination remains a major concern for design engineers as it affects the performance of the components, therefore its presence has to be detected in advance to take remedial action to avoid the malfunctioning of the structural component. The present work carries the investigation of free-vibration response of laminated FRP composite plate and a plate with de-lamination by developing numerical models in MATLAB environment based on the first order shear deformation theory and worked out through finite element procedure using a two dimensional 8 node element with a 5 degree of freedom for individual node. The effect of various parameters like boundary conditions, location of de-lamination, area of de-lamination, aspect ratio, number of plies and laminate stacking sequence on the free vibration behavior of the plate with an existing de-lamination is also investigated. Finally, the impact of de-lamination on the free vibrational behaviour of FRP laminated composite structures will be numerically identified and explored in depth.

A Low-Profile Ultra-Wideband Absorber Using Lumped Resistor-Loaded Cross Dipoles With Resonant Nodes

This article presents the design and analysis of a dual-polarized low-profile circuit analog absorber with wideband absorption characteristics. A lossy frequency selective surface consisting of cross dipole with central resonant node element is used as the top layer, while there is a continuous copper ground as the bottom layer. The novelty of the design lies in the use of the resonant node as it improves the absorption bandwidth by providing an additional resonance without compromising the low-profile nature of the design. It has a thickness of 0.077 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda_{L}$</tex-math></inline-formula> (where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda {\_}L$</tex-math></inline-formula> is the wavelength corresponding to the lowest operating frequency). The absorber also exhibits a stable absorption characteristics up to 30 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> angle of incidence and can avoid grating lobes within the operating bandwidth up to 40.79 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> angle of incidence. An equivalent circuit model is proposed to discuss the operating principles of the design. The validation of the design is done experimentally using the time-gating technique, and a good agreement between the measured and the simulated results is observed. The 10-dB reflection reduction bandwidth and the thickness-to-bandwidth ratio of the absorber are obtained as 108.67% (from 3.58 to 12.10 GHz) and 0.104 from full-wave simulation and 115.67% (from 3.5 to 13 GHz) and 0.098 from measurement, respectively.

A Model to Calculate the Current-Temperature Relationship of Insulated and Jacketed Cables.

This paper proposes and validates using experimental data a dynamic model to determine the current–temperature relationship of insulated and jacketed cables in air. The model includes the conductor core, the inner insulation layer, the outer insulating and protective jacket and the air surrounding the cable. To increase its accuracy, the model takes into account the different materials of the cable (conductor, polymeric insulation and jacket) and also considers the temperature dependence of the physical properties, such as electrical resistivity, heat capacity and thermal conductivity. The model discretizes the cable in the radial direction and applies the finite difference method (FDM) to determine the evolution over time of the temperatures of all nodal elements from the temperatures of the two contiguous nodes on the left and right sides. This formulation results in a tri-diagonal matrix, which is solved using the tri-diagonal matrix algorithm (TDMA). Experimental temperature rise tests at different current levels are carried out to validate the proposed model. This model can be used to simulate the temperature rise of the cable when the applied current and ambient temperature are known, even under short-circuit conditions or under changing applied currents or ambient temperatures.

Investigation on out-of-plane displacement measurements of thin films via a mechanical constraint-based 3D-DIC technique

Thin film is functioning as a key material in surface engineering, and accurate measurement of its deformation are particularly important for the reliability and stability assessment of coating-substrate structures. However, the displacement field measured by the conventional three-dimensional subset-based digital image correlation (3D-DIC) method has no spatial continuity; thus, it cannot precisely reflect the true deformation of thin films. To improve the measurement accuracy, a 3D-DIC method considering mechanical constraints (3DMC-DIC) was proposed in this paper. In this method, a mesh with 8-noded quadrilateral shell elements satisfying spatial continuity was employed to determine the out-of-plane displacements of all nodes based on trusted points, which are the speckle points with higher measurement accuracy obtained by the conventional subset-DIC method. The whole out-of-plane displacement field was then inversely obtained based on the optimized displacements of these nodes. A blister test was performed, and the results show that the out-of-plane displacement field of thin film with spatial continuity and high accuracy on specimen edge can be obtained by the 3DMC-DIC method.

A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method

Physics informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. Here, the training of the network is equivalent to the minimization of a loss function that includes the governing (partial differential) equations (PDE) as well as initial and boundary conditions. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering problems. The main contribution of the current work is to promote using the spatial gradient of the primary variable as an output from separated neural networks. Later on, the strong form (given governing equation) which has a higher order of derivatives is applied to the spatial gradients of the primary variable as the physical constraint. In addition, the so-called energy form of the problem (which can be obtained from the weak form) is applied to the primary variable as an additional constraint for training. The proposed approach only required up to first-order derivatives to construct the physical loss functions. We discuss why this point is beneficial through various comparisons between different models. The mixed formulation-based PINNs and FE methods share some similarities. While the former minimizes the PDE and its energy form at given collocation points utilizing a complex nonlinear interpolation through a neural network, the latter does the same at element nodes with the help of shape functions. We focus on heterogeneous solids and check the performance of the proposed PINN model against the solution from FEM on two prototype problems: elasticity and the Poisson equation (steady-state diffusion problem). It is concluded that by properly designing the network architecture in PINN, the deep learning model has the potential to solve the unknowns in a heterogeneous domain without any available initial data from other sources. Finally, discussions are provided on the combination of PINN and data from physical FE simulations for a fast and accurate design of composite materials in future developments.

Histopathology of the Shoot Apex of Sugarcane Colonized by Leifsonia xyli subsp. xyli.

Colonization of the xylem of sugarcane by Leifsonia xyli subsp. xyli results in the occlusion of the vessels by a gum-like compound and compromises the elongation of the stalk leading to stunted plants. However, no study has been performed in the apical tissue where the elongation of the stalks initiates at the intercalary meristem (IM). Microscopic and histochemical analyses were performed in plants with lower and higher bacterial titers and revealed that in both cases L. xyli subsp. xyli is present in this tissue and colonizes the forming xylem vessels in a similar way as observed in developed internodes. In both cases, it was observed adhering to the secondary walls, but only in plants with higher titers were a mild degradation of the walls and a granular material filling the vessels observed. The mixed composition of lipids, proteins, and pectin indicates that the filling is not a bacterial extracellular polymeric substance. Plants with higher bacterial populations also presented lower starch content in the ground parenchyma at the node elements, possibly resulting from the reported downregulation of photosynthesis and increased accumulation of phenolics. Their second and third IMs presented fewer cells and reduced expression of genes related to the cell cycle and to the synthesis of ABA in the apical tissue. These results indicate that increased L. xyli subsp. xyli colonization affects the development of the IM, which ultimately would reduce the length of the internodes, resulting in the main symptom of the disease.

A Green Infrastructure Planning Approach: Improving Territorial Cohesion through Urban-Rural Landscape in Vojvodina, Serbia

Spatial and urban planning are directed towards achieving territorial cohesion as one of the sustainable development goals. Considering the hybrid concept of green infrastructure, this paper aims to provide an “ecological model” of achieving territorial cohesion in spatial and urban planning. Based on the connectivity level analysis between green infrastructure elements (green infrastructure hubs, nodes, gateways and dots), application of the GI concept guides the development of spatial planning scenarios. The application of Voronoi diagrams and landscape graph-based principles contribute to defining the shortest distances between green infrastructure elements, which resulted in the definition of the significance of structural and functional arrangement of green infrastructure dots in the matrix of the urban rural continuum in the territory of the urban-rural landscape of three case studies in Vojvodina, Serbia (Novi Sad, Subotica, Zrenjanin). As a result of this study, green infrastructure dots showed a great potential of application at the local level by developing them through landscape design with creative and artistic elements in order to achieve higher level of cohesion through visual attractivity, multifunctionality and recreation. The level of connectivity between elements of green infrastructure should be considered as an indicator of the sustainable spatial development goals achievement, in the field of nature conservation and territorial and social cohesion.

Numerical Analysis of Steel Elevator Car Frame: Sensitivity to Element Connections

This is a preliminary study to assess the mechanical behavior of an elevator car frame made of steel components, through dynamic identification. Final element models considering different restraint conditions on element nodes are taken into account to evaluate how the whole performance of the structure is affected by local connections.

Investigation on model order reduction methods for flexible bodies with contact-impact based on partition modeling

The finite element method is widely used to solve the problem of flexible bodies with contact-impact. To express the high-frequency and high-transient characteristics of the impact process and the high stress distribution of the local contact region, the amount of the node coordinates will be very large, which brings great burden to the dynamic simulation. It is particularly important to reduce the degrees of freedom of the system in the contact-impact problem. However, as the impact itself is a strong nonlinear problem, the linear model reduction techniques cannot be used directly. The partition method is presented to solve this problem, in which the deformation of the contact region is described by finite element node coordinates to preserve the local nonlinear characteristic while the deformation of the non-contact region is described by the reduced elastic coordinates. Different model reduction techniques including modal truncation method and Krylov subspace method are used to reduce the degrees of freedom of the non-contact region of an experimental rod-plate impact case, and the results are compared with that of the finite element method and the experiment. The simulation results show that the partition method can effectively reduce the degrees of freedom of the system and maintain good accuracy. Moreover, the Krylov subspace method has an advantage over the modal method in the model reduction of contact-impact problem.

Element Differential Method for Computational Acoustics in Time Domain

In this paper, a new robust numerical method, named element differential method (EDM), is developed to solve computational acoustic problems in time domain. The key aspect of the method is the direct differentiation of shape functions of the isoparametric elements used to characterize the geometry and physical variables, which can be utilized to evaluate the spatial partial derivatives of the physical variables appearing in the governing equations and boundary conditions. Moreover, a unique collocation technique is proposed to form the system of equations, in which the governing equation is collocated at internal nodes of elements and the acceleration equilibrium equation is collocated at interface nodes between elements and outer surface nodes. EDM is a strong-form numerical method that doesn’t require a variational principle or a control volume to set up the computational scheme, and no integration is performed. Based on the Newmark difference technique, a time marching solution scheme is developed for solving the time-dependent system of equations. For the point sound source expressed in terms of the Dirac function, a sound source density function is proposed to approximate the point sound source to make it handleable in EDM. Three numerical examples are given to demonstrate the correctness and application potential of the developed method.

Dynamic instability analysis of perforated stiffened laminated composite panels subjected to non-uniform in-plane edge load under hygrothermal condition

A robust and computationally efficient finite element (FE) formulation has been developed in an effort to understand the parametric instability behaviour of a perforated stiffened composite panel subjected to a pulsating non-uniform edge load under a hygrothermal environment. The panel is modelled using a 9-noded heterosis element to avoid shear locking, whereas the stringer uses a 3-noded isoparametric beam element with a displacement compatibility condition employed at the skin–stringer​ interface. Due to the non-uniform distribution of stress in the perforated panel as a result of exposure to environmental and mechanical loading conditions, a unique dynamic technique has been implemented to account for the instability performance by employing two types of boundary conditions. In the current investigation, an unstiffened panel is initially obtained based on the highest value of the dynamic instability opening (DIO) and the unstable excitation frequency of the panel for different lamina schemes, cutout shapes, and loading conditions. The obtained unstiffened panel is further investigated for various stiffener configurations to determine a highly unstable perforated stiffened panel based on the DIO value and instability zone frequency range. Detailed parametric studies are then carried out considering the cutout sizes, cutout orientation, panel’s aspect ratio, and stiffener depth to understand the parametric instability behaviour of the panel in a hygrothermal environment. It is found that moisture significantly influences the dynamic instability behaviour of the perforated stiffened panel compared to the temperature exposure by shifting the instability zone towards the lower frequency. The width of the instability region of the stiffened panel broadens abruptly as the magnitude of the applied static in-plane edge load enhances. Also, for certain combinations of the dynamic and static load factors, the lower bound of the instability region reduces to zero, resulting in fluttering. In general, it is observed that stiffer the panel, wider is the instability zone with a higher unstable excitation frequency range.

Structural Behaviour of Metakaolin Geopolymer Concrete Wall-Type Abutments with Connected Wing Walls

This study work is related to exploring the role of connected wing walls in changing the behaviour of a metakaolin geopolymer wall type abutment when acted upon by all the forces that are generally applied on a short-span bridge. The modelling of abutment with connected wing walls is done using the STAAD Pro V8i SS6 software and all the loading applied for the analysis as per IRC: 6-2016. The modelling is done using the 4-noded plate elements for all the members, and the plate elements here are meshed using the quadrilateral meshing feature. The behaviour of the metakaolin geopolymer wall-type abutment is analyzed using various models with changing the basic parameters such as length of the wing walls, height of the walls, number of lanes on the bridge, and type of live load on the bridge. The various results are obtained in the form of bending moments from all the cases, which show us some really interesting behaviour of the abutment wall and the wing walls. As the length of the wing walls is increased, they take up more horizontal moments than the abutment wall and the deflection behaviour of the wing walls is way different than that of cantilever wall, and hence, it shows that the design aspects of the wing walls need to be checked. Also, the connected wing walls cause horizontal moments in the middle of the abutment wall, which is an interesting result; as now, it proves that after casting wing walls monolithically to the abutment wall, the design of the abutment wall cannot be done as cantilever wall, and we need to take care of this horizontal moment by providing required reinforcement. Also, as the length of the wing walls is short, the torsional moments become critical.

Nonlinear free vibration analysis of functionally graded plates and shell panels using quasi-3D higher order shear deformation theory

This paper presents the nonlinear free vibration behavior and response of functionally graded plates and shell panels under various boundary conditions. The displacement formulation followed uses a sinusoidal non-polynomial quasi-3D higher order shear deformation theory with six variables and, the parabolic transverse stress distribution functions are used to model stresses in the thickness direction. Present formulation employs the Green-Lagrange nonlinear strains along with Sander’s approximation to account for larger flexural response which could be experienced by the structure. An eight noded C0 continuous isoparametric finite element is used for numerical implementation of nonlinear finite element solver developed in MATLAB. Developed numerical formulation is employed to study and analyze the nonlinear free vibration response of the spherical, cylindrical and hyperboloid shell panels and the obtained results are seen to be consistent and good agreement with the literature thus establishing the effectiveness and accuracy of the present work.

Efficient Hyper-Reduced Small Sliding Tribomechadynamics

Abstract In the context of tribomechadynamics, hyper-reduction means that the deformations, as well as the contact and friction forces, are not computed based on all involved finite element nodes but in a reduced space. The goal is a reduction of the simulation time so that virtual tribomechadynamics becomes an efficient complement to test bench investigations and a useful tool for predictive simulation. In this work, an efficient hyper-reduction strategy for contact and friction forces is proposed. The available and a priori known space of possible gaps is used for the hyper-reduction of contact forces without using any snapshots. Friction forces on the other hand are computed based on snapshots stemming from a model order reduced simulation. After the theory has been explained, a generic example with bolted joints and different load cases is used to demonstrate the result quality of the method as well as the computational time savings.

Dynamic response of stiffened laminated composite plate in thermal environment

Composite materials are increasingly used in aerospace and automobile sectors. These materials are characterized by high stiffness and light-weight in comparison to conventional structural materials. During high-speed maneuvering of these vehicles, associated composite structures are subjected to dynamic loadings and are often exposed to varying thermal environments. To ensure high load carrying capacity and to avoid thermal buckling, stiffened laminated composite plates are preferred in some important structural components, e.g., aircraft’s fuselages, wings etc., than unstiffened laminated composite plates. For safe designing of these structures, it is thus necessary to investigate the dynamic behavior of stiffened laminated composite plates in thermal environment. In this paper, the dynamic response of stiffened laminated composite plates made of polyetheretherketone (PEEK) with intermediate modulus (IM7) carbon fibers in thermal environment has been investigated. Furthermore, development of a generalized finite element (FE) formulation using an 8-node isoparametric plate element employing first-order shear deformation theory (FSDT) has also been presented to analyze unstiffened and stiffened laminated composite plates in thermal environment. Detailed parametric study reveals that the dynamic deflection and the corresponding normal stress decrease with adding stiffener, and decreases further with increasing depth of the stiffener in thermal environment.