Finite Element Model Of Plate Research Articles

Estimation, tuning, and evaluation of propagation direction behavior in superimposed orthogonal two-dimensional structure-borne traveling waves

Abstract Structure-borne traveling waves (SBTW) are observed in nature as a means for propulsion and locomotion of creatures on land and in the ocean. Recently, various approaches have been investigated to replicate this phenomenon. Previous studies have successfully generated SBTWs suitable for propulsion applications and particle motion on active surfaces. Much recent literature has focused on generating traveling waves that propagate only along a single axis for 1D and 2D structures. This limits their potential and does not take advantage of the full potential of 2D structures.
This study examines the potential of employing superposition to control the propagation direction of 2D SBTW. This is investigated numerically using an experimentally validated Finite Element model of a 2D plate with piezoelectric actuators. The individual SBTWs are superimposed by simultaneously exciting two pairs of actuators that are aligned orthogonally on the surface of a plate. Traveling waves are excited in the plate using two-mode excitation. Structural intensity is utilized to develop quantifiable metrics to describe the overall propagation direction and uniformity, which are necessary for describing the complex propagation patterns encountered with 2D SBTW. The potential of the proposed approach along with developed tuning and evaluation methods are demonstrated through case studies of two plates, one square and one rectangular. For both cases, the overall direction of the SBTW is tuned to propagate for any direction between the individual SBTW. This was achieved while maintaining a high-quality overall SBTW. With this approach, 2D SBTW can be steered for wave-driven motion applications such as propulsion of the structure itself or conveying particles in any direction along the structure's surface without compromising the quality of the overall traveling wave.

Analysis and experimental verification of dynamic characteristics of cantilever plate with fatigue crack

Fatigue cracks in aero-engine blades seriously threaten the stability and reliability of the engine. It is very necessary to identify and diagnose the crack state through vibration signals, and predicting its vibration rules through dynamic analysis is the basis of crack identification. At present, the dynamic model of cracked blades with breathing cracks is mainly established by implanting cracks, and there is a lack of relevant experimental validation. To address the above deficiencies, this paper firstly obtains the real extension path of the cracked plate through the fatigue testing machine, and then introduces it into the cantilever plate finite element model. Then the correctness of the proposed model is verified by natural frequency obtained from hammering test and frequency sweeping test. Finally, the effect of different crack parameters such as crack depth, crack location and plate length on the crack vibration characteristics is investigated based on simulations and experiments. The results indicate that (1) the real fatigue crack obtained by tensile test has larger amplitude peaks under excitation frequency compared with wire-cut crack, and it has stronger nonlinearity to better reflect the vibration characteristics; (2) Specimens show obvious nonlinear characteristics that significant amplitude peaks occur at multiples of excitation frequencies in both experiments and simulations; (3) For the cantilever plate containing breathing cracks, the vibration amplitude totally increased by 18.5% with the increase of crack depth, and it decreased by 41.5% throughout as the crack location became further away from the plate root. This study provides a theoretical basis for detection and diagnosis of blade cracks.

A unified buckling formulation for linear and nonlinear analysis of laminated plates using penalty based [formula omitted] FEM-HSDT model

In this paper, the effect of pre-buckling boundary conditions and the type of nonlinearity for stress stiffening used in different linear and nonlinear buckling approaches is studied for laminated composite plates. The study is conducted using a C0 finite element (FE) plate model, employing a unified C1 higher-order shear deformation theory (HSDT). The set of governing equations is derived using the principle of virtual displacement and solved using the tangent-based arc-length method in conjunction with a simple branch switching technique. The performance of the present C0 FE model is assessed through a validation exercise and comparison with results obtained via the use of ANSYS and, for linear analysis, Navier solution, as well as solutions available in the literature. The influence of the different in-plane loads, boundary conditions, side-to-thickness ratio, fiber orientation, types of imperfection and penalty stiffness matrix are also examined. The results show that the same boundary conditions must be utilized in both pre-buckling and linear eigenvalue analyses for accurate and realistic predictions of critical buckling loads, as confirmed from the nonlinear buckling analyses. Furthermore, the critical buckling loads obtained using Green–Lagrange nonlinearity are observed to be more conservative than those obtained using von Kármán nonlinearity. The nonlinear buckling approach is a generalized approach while the nonlinear eigenvalue approach has a limited range of application.

Influence of Initial Structural Dimensions of Plates on Welding Distortion

Aiming at the complex full-field deformation problem that easily occurs when welding plates, this paper adopts the elastic–plastic finite element method with heat-force coupling to study the deformation law of plates in different initial states. First, a rectangular plate finite element model with an initial radius and Gaussian heat source model was established to obtain the welding temperature field and deformation field of the plate; then, the method based on digital image correlation technology was used to detect the full-field dynamic deformation of the plate to verify the accuracy of the finite element model; finally, the influence of the initial structural dimensions of the plate on the weld deformation was investigated. The study shows the following: the thermoelastic–plastic finite element model proposed in this paper has high accuracy in both static and dynamic deformation; plates with the same curvature, and different lengths and widths of the initial structure of the plate welding deformation are saddle-shaped, and the edge effect of the welding of the plate is evident, independent of the length of the plate; and the maximum out-of-face deformation of the welding of the plate is linearly related to the length and the closer the aspect ratio of the plate is to 1, the smaller the out-of-face deformation is.

Analysis of transversely isotropic compressible and nearly-incompressible soft material structures by high order unified finite elements

This work proposes high-order beam (1D) and plate (2D) finite element models for the large strain analysis of compressible and incompressible transversely isotropic hyperelastic media, defined within the Carrera Unified Formulation (CUF) framework. The strain energy density function adopted in fiber-reinforced hyperelastic materials modeling is presented and expressed in terms of invariants and pseudo-invariants of the right Cauchy-Green strain tensor. The explicit expression of the tangent elasticity tensor is derived through the assumption of coupled formulation of strain energy functions. Refined fully nonlinear beam and plate models are defined in a total Lagrangian formulation, deriving the governing equations of the nonlinear static analysis through the Principle of Virtual Displacements in terms of fundamental nuclei, in resulting expressions of internal and external forces vectors, and tangent stiffness matrix independent of kinematic models and approximation theories adopted. The iterative Newton-Raphson linearization scheme coupled with the arc-length constraint is adopted to obtain actual numerical solutions. Different benchmark analyses in hyperelasticity are performed to assess the capabilities of our proposed model, analyzing the three-dimensional stress field for moderate to large strain states and comparing actual numerical results with exact closed-form solutions or results available in the literature, demonstrating the capabilities and reliability of CUF models in the analysis of fiber-reinforced soft materials and structures.

Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment

An enhanced lightness and thinness is the inevitable trend of modern industrial production, which will also lead to prominent low-frequency vibration problems in the associated structure. To solve the vibration problem of thin plate structures in various engineering fields, the active constrained layer damping (ACLD) thin plate structure is taken as the research object to study vibration control. Based on the FEM method, energy method, and Hamilton principle, the dynamic model of an ACLD thin plate structure is derived, in which the Golla-Hughes-McTavish (GHM) model is used to characterize the damping characteristics of the viscoelastic layer, and the equivalent Rayleigh damping is used to characterize the damping characteristics of the base layer. The order of the model is reduced based on the high-precision physical condensation method and balance reduction method, and the model has good controllability and observability. An LQR controller is designed to actively control the ACLD sheet, and the controller parameters and piezoelectric sheet parameters are optimized. The results show that the finite element model established in this paper is accurate under different boundary conditions, and the model can still accurately and reliably describe the dynamic characteristics of the original system in the time and frequency domain after using the joint reduction method. Under different excitation and boundary conditions, LQR control can effectively suppress structural vibration. Considering the performance and cost balance, the most suitable control parameter for the system is: Q-matrix coefficient is between 1 × 104 and 1 × 105, the R-matrix coefficient is between 1 and 10, and the thickness of the piezoelectric plate is 0.5 mm.

A Verification and Validation Study on a Loosely Two-Way Coupled Hydroelastic Model of Wedge Water Entry

_ The interaction between the structural response and hydrodynamic loading (hydroelasticity) must be considered for design and operation purposes of high-speed planing craft made of composites that are prone to frequent water impact (slamming). A computational approach was proposed to study the hydroelastic slamming of a flexible wedge. The computational approach is a loose two-way coupling between a Wagner-based hydrodynamic solution and a linear finite element plate model. Verification and validation (V&V) was performed on this coupled model. It was found that the model overpredicts rigid-body/spray root kinematics by <15% and hydrodynamic loading/ structural response by <26%. Introduction One of the primary constraints on the operational envelope of high-speed craft is slamming (water impact). Slamming occurs between the hull body and the water surface when a portion/whole of the craft exits the water and then reenters at high-enough velocity (Lloyd 1989; Faltinsen 2005). The frequent water impacts, which work like “water hammers,” along with their induced acceleration pose great jeopardy on hull structures as well as crew and instrument on-board (Yamamoto et al. 1985; Ensign et al. 2000; Hirdaris et al. 2014). With the growing use of lightweight materials, the interaction between the structural deformation and the hydrodynamic loading (hydroelasticity) becomes more prevalent. The current design criteria of high-speed craft are based on empirical procedures with no regard to hydroelasticity due to the lack of understanding of this complex phenomenon (DNV 2013; ABS 2016). Therefore, a better comprehension of hydroelastic slamming is the first step to designing more high-performance craft (Fu et al. 2014; Judge et al. 2020).

Experimental investigation on minimizing degradation of solar energy generation for photovoltaic module by modified damping systems

With the rapid increase in solar energy generation, it is common to see solar photovoltaic modules mounted on structures subjected to dynamic loading. These dynamic loads induce vibration in solar photovoltaic modules, which generate cracks and micro-cracks. This deteriorates the solar photovoltaic modules' performance and life, effectively reducing solar energy generation. In this context, this paper deals with modal and harmonic response analysis of solar photovoltaic modules. The photovoltaic module's natural frequencies and mode shapes for ten different mounting configurations are determined using the composite plate Finite Element Model for three separate solar photovoltaic technologies. The finite element model is validated by comparing it with experimental and published results. Acceleration, velocity and displacement responses are determined in harmonic response analysis for base excitation and body acceleration inputs separately. Moreover, harmonic response analysis is performed, for which the amplitude and Frequency of induced vibrations are decided based on measured metro train vibrations levels in the vicinity of the metro rail. It is observed that mounted natural frequencies are considerably affected by the mounting configuration. A comparison of first mode natural frequency between the first and last mounting configurations shows a difference of 214.9%. Harmonic response analysis gives the resonant acceleration, velocity and displacement peak levels for all ten mounting configurations. Based on the least number of resonant peaks and lower value of response amplitudes, the best and worst mounting configurations are identified for all three solar photovoltaic technologies. This study provides a basis for selecting the best mounting arrangements to achieve the best solar energy conversion efficiency with minor degradation of the solar photovoltaic modules subjected to induced vibrations.

Sparse Bayesian learning for complex‐valued rational approximations

AbstractSurrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For models that show a strongly non‐linear dependence on their input parameters, standard surrogate techniques, such as polynomial chaos expansion, are not sufficient to obtain an accurate representation of the original model response. It has been shown that for models with discontinuities or rational dependencies, for example, frequency response functions of dynamic systems, the use of a rational (Padé) approximation can significantly improve the approximation accuracy. In order to avoid overfitting issues in previously proposed standard least squares approaches, we introduce a sparse Bayesian learning approach to estimate the coefficients of the rational approximation. Therein the linearity in the numerator polynomial coefficients is exploited and the denominator polynomial coefficients as well as the problem hyperparameters are determined through type‐II‐maximum likelihood estimation. We apply a quasi‐Newton gradient‐descent algorithm to find the optimal denominator coefficients and derive the required gradients through application of ‐calculus. The method is applied to the frequency response functions of an algebraic frame structure model as well as that of an orthotropic plate finite element model.

Phased array guided wave propagation in curved plates

For the monitoring of plate structures, phased array guided wave has great application prospects to effectively determine damage location and size. Locating damage via phased array focusing is a challenging task, especially in curved plates. Hence, a systematic understanding of the behavior of the phased array guided wave propagation in curved plates is needed. In this study, a phased array focusing method was proposed for the damage localization of curved plates. Different damage scenarios and phased array focusing schemes are investigated in the finite element plate models with different radii. A high-speed signal generation and acquisition system including PZT actuators and sensors is set up. Experimental tests are carried out on a curved aluminum plate with embedded piezoelectric elements to verify the finite element models. Parametric studies are then performed to evaluate the effect of different radii and damage scenarios on the behavior of phased array guided wave propagation in curved plates. Numerical simulations and experimental results show that the proposed PA method has the capabilities of wave focusing and damage identification in curved plates. The damage localization method using phased array guided wave has the potential to be applied to the real-time monitoring of structures with curved plates.

Finite element analysis of train speed effect on dynamic response of steel bridge

AbstractThe development of materials engineering has facilitated the design of slender, light bridges replacing standard construction materials with others, which fulfil their purpose both in terms of structural behaviour and safety. This article focuses on the presentation of the problems related to the modelling of bridges and their loads modelling train passages, as well as an analysis of the influence of load parameters on the dynamic response of a structure. The problem has become essential with the development of materials engineering which enabled the design of slender and light bridges according to the assumptions of sustainable development. The article contains a number of numerical analyses which allowed the verification of the developed finite element bridge model (frame and plate-frame types) in terms of the possibility of using them at the design stage. The load was modelled as a system of concentrated forces, the so-called moving load (ML) model. The results obtained from theoretical analyses were compared within situmeasurements of the existing bridge subjected to the load variable in time (set of locomotives ST43 and ST45 and locomotive EP09). It has been found that in dynamic analysis, modelling of the load is essential. A simplified load model such as ML can be used when displacement values are the only results analysed in detail. ML and finite element plate and frame models give high accordance of the displacement results.

Modelling the experimental seismic out-of-plane two-way bending response of unreinforced periodic masonry panels using a non-linear discrete homogenized strategy

A non-linear discrete homogenized strategy is used to reproduce out-of-plane two-way bending shake table tests on full-scale unreinforced masonry walls. The numerical strategy represents unreinforced masonry walls as an assemblage of rigid quadrilateral plates connected through non-linear interfaces represented. The material response laws for these non-linear interfaces are derived from a homogenization procedure performed at the meso-scale by a finite-element plate model. This discrete model can simulate masonry orthotropy, full softening behaviour and failure. Bending and torsional deformation modes are represented. The performance of the numerical models in describing the response of the experimentally tested full-scale specimens is presented. The numerical strategy is then used to study the behaviour of unreinforced masonry walls in configurations hitherto untested. Such numerical results are then compared to state-of-the-art analytical approaches. Potential avenues of improvement for the implemented analytical methods are also highlighted.

Multi-layered plate finite element models with node-dependent kinematics for smart structures with piezoelectric components

This article presents a type of plate Finite Element (FE) models with adaptive mathematical refinement capabilities for modeling laminated smart structures with piezoelectric layers or distributed patches. The p-version shape functions are used in combination with the higher-order Layer-Wise (LW) kinematics adopting hierarchical Legendre polynomials. Node-Dependent Kinematics (NDK) is employed to implement local LW models in the regions with piezoelectric components and simulate the global substrate structure with the Equivalent Single-Layer (ESL) approach. Through the proposed NDK FE models, the electro-mechanical behavior of smart structures can be predicted with high fidelity and numerical efficiency, and various patch configurations can be conveniently modeled through one set of mesh grids. Moreover, the effectiveness and efficiency of the NDK FE approach are assessed through numerical examples and its application is demonstrated.

Geometrically nonlinear flexural analysis of multilayered composite plate using polynomial and non-polynomial shear deformation theories

In this paper, the geometrically nonlinear bending analysis of multilayered composite plates is carried out through a rigorous comparative study employing Green-Lagrange and von Kármán nonlinearity. The responses are analyzed for various transverse loads and boundary conditions, and emphasized the impending structural condition, which requires the consideration of full geometric nonlinearity. The study is conducted using a C0 finite element plate model using third-order and non-polynomial shear deformation theories (TSDT and NPSDT). The principle of virtual work is utilized to formulate the weak-form of governing equations, and discretized using nine-noded Lagrange elements with seven degrees-of-freedom per node. The performance of the present model has been validated by comparing present results with those available in the literature and obtained ANSYS results. The results reveal that the consideration of Green-Lagrange nonlinearity is essential for plates with all sides subjected to movable simply supported boundary conditions or with one free edge. The present study also provides a clear idea about the utilization of TSDT and NPSDT for the anti-symmetric and symmetric cross-ply plate, respectively, to get more accurate solution. Further, the effect of penalty for various theories and problems is also highlighted, and its prominent impact is asserted for some cases.

Study on Mechanical behavior and equivalent calculation of GFRP- stainless Steel Composite Truss Bridge

GFRP is a kind of carbon fiber composite reinforced material, which has attracted wide attention in the engineering field because of its light weight, high strength, corrosion resistance and so on.The solid plate and shell finite element model of full GFRP truss bridge is established by ABAQUS, and its mechanical characteristics are analyzed. The study shows that the stress of each element is less than the material strength, but the mid-span deflection of the truss bridge exceeds the allowable value of the specification, so three kinds of stainless steel plate layout schemes are considered, and the structural gravity, mid-span deflection change and element stress are compared and analyzed. Finally, it is concluded that the upper and lower stainless steel plate has a great contribution to enhance the vertical stiffness of the GFRP truss bridge. The stainless steel plate largely replaces the upper chord under pressure and the lower chord is pulled. On this basis, the stainless steel plate beam filled between oblique bars is equivalent to the upper and lower chords by using the idea of average equivalence and the principle of equal mass. The finite element software analysis shows that the equivalent error is very small.

Development of thermal residual stresses during manufacture of wind turbine blades

Thermal residual stresses have a major impact on the bond line fatigue of wind turbine blades, which can initiate tunneling cracks in the adhesive layer of the bond lines early in the operational life of the blade. This work investigates the simulation accuracy for predicting thermal residual stresses within a thick bond line. The trailing-edge bond line strip of a 34 m blade was modeled with classical laminated plate theory (CLT) on the one hand and with finite element (FE) plate models of different fidelities on the other. For the model benchmark, the thermal residual stresses were on the basis of a thermal simulation. These develop during the cooling after a typical curing cycle of a wind turbine blade manufacturing process. It was found that the analytical model on the basis of CLT was in good agreement with the plate models of higher fidelity. Additionally, a full 3D FE blade model was used to calculate the shape distortion and the thermal residual stresses. It was found that the analytical model, which did not take into account effects stemming from the whole blade structure, underestimated the full 3D FE model.

Vibration Based Damage Detection in Plate-Like Structure Using Square of Mode Shape Curvature

In this current work, a new methodology based on the square of mode shape curvature (SMSC) is presented that relates the mode shapes and its curvature changes before and after the damage for localization and sizing of the surface crack in plate-type structures. The significance of this method is it has the capability to portray accurate shape and exact location of the surface crack in a plate-like structure which are related to low and high elastic modes on dense and coarse measurement grids. The efficiency of the proposed SMSC is examined using experimental and numerical data acquired from modal analysis on the aluminum plate containing single and multi-surface cracks with a fixed-free condition using non-contact measurement a scanning laser vibrometer and on simple finite element plate model. As evidence of experimental and numerical study results, highly accurate crack characterization has been attained through the proposed method. In implementing this method, only a few modes of the structure are required. Further, the impact of the mode order on the effectiveness of crack detection, boundary distortion treatment, and grid density analysis was also performed by the proposed method.

On the mitigation of shear locking in laminated plates through p-version refinement

This article presents an evaluation of higher-order p-version plate elements in the mitigation of shear locking phenomenon in the analysis of multi-layered structures. Carrera Unified Formulation (CUF) is employed to construct the refined plate finite element models. The decomposition of strain energy components is introduced and used in the assessment of shear locking. The evolution of the displacement and stress solutions and the strain energy components with the increase of the polynomial degree of the p-version elements are reported. Reduced and selective integration techniques on p-version plate elements to alleviate locking are explored. Numerical results show that plain p-version plate elements with sufficient, higher-order shape functions are capable of mitigating shear locking effectively.

Numerical Investigation on Weld-Induced Imperfections in Aluminum Ship Plates

The present work aims at better understanding and predicting the thermal and structural responses of aluminum components subjected to welding, contributing to the design and fabrication of aluminum ships such as catamarans, lifesaving boats, tourist ships, and fast ships used in transportation or in military applications. Taken into consideration the moving heat source in metal inert gas (MIG) welding, finite element models of plates made of aluminum alloy are established and validated against published experimental results. Considering the temperature-dependent thermal and mechanical properties of the aluminum alloy, thermo-elasto-plastic finite element analyses are performed to determine the size of the heat-affected zone (HAZ), the temperature histories, the distortions, and the distributions of residual stresses induced by the welding process. The effects of the material properties on the finite element analyses are discussed, and a simplified model is proposed to represent the material properties based on their values at room temperature.

Vertical Water Entry of a Flexible Wedge into Calm Water: A Fluid-Structure Interaction Experiment

Slamming water impact occurs frequently on high-speed craft and restricts the operating envelope of a vessel. One approach to understanding the hydroelastic nature of this phenomenon is to study the vertical impact of a V-shaped wedge on calm water, which models a single slamming event after a vessel has become partially airborne. The dynamic structural response of the bottom plate of a wedge dropped vertically (drop height = 7.9 cm) is investigated both experimentally and computationally. The experiments were conducted with a flexible bottom model at Virginia Tech. Pressure on the wedge bottom, rigid body motion (vertical acceleration and vertical position), and full-field out-of-plane deflection were measured. The out-of-plane deflection was measured using stereoscopic digital image correlation. Predictions on the hydrodynamic pressure field were made using Wagner's method, Vorus's method, and an unsteady Reynolds-averaged Navier-Stokes solver, all assuming a rigid plate. In the present work, the reconstructed pressure distribution from the experiment was used as the loading condition in a dynamic, linear finite element plate model (one-way coupled approach). Both the predicted pressure and predicted deflection were compared with the experiment. It was found that in the experiment, there is a slight reduction in the measured hydrodynamic pressure compared with predictions. This reduction in pressure leads to a reduction in the reactions at the plate edges, which get transmitted to the frames of the vessel. This slight reduction at small loading cases has the potential to be more noticeable when more severe slamming loads are encountered. 1. Introduction Slamming water impacts occur when a vessel impacts the water surface at high speed relative to the free surface. Water impact was first studied by von Karman (1929) with the application of seaplane landing. Water impact, as it pertains to slamming, gradually attracted increasing attention in the application of high-speed craft. The understanding of this phenomenon has been applied to the structural design and evaluation of the operational envelope of high-speed planing craft. Sailors also consider slamming a serious risk because it contributes to major injuries in addition to mission-related setbacks such as speed reduction or heading change. The present investigation of slamming can lead to the development of better design criteria for small craft.