Beam Finite Element Model Research Articles

Aeroelastic Optimization of Aircraft Wings Using a Coupled Three-Dimensional Panel-Beam Model

This work introduces an aeroelastic optimization framework with a coupled three-dimensional panel method and Timoshenko beam finite element model. The method allows for optimization of both the exterior surface of the wing and interior structural properties. We investigate the effects of curved wall spars on the aeroelastic performance of converged designs, which have been shown to provide an improved performance due to the ability to create tradeoffs between bending and torsional stiffnesses. Studies also highlight the importance of calculating aerodynamic loads in the deformed configuration and solving the coupled aeroelastic problem to convergence.

Experimental and numerical investigations on the nonlinear aeroelastic behavior of high aspect-ratio wings for different chord-wise store positions under stall and follower aerodynamic load models

This study performs an experimental and numerical investigation on the nonlinear aeroelastic response of cantilever high-aspect-ratio beam-like wings with a ballast at their free tips, emulating the effects of a store. As an extent, the effects of different chord-wise ballast positions are experimentally examined for two highly flexible rectangular wings. Furthermore, the numerical model proposed brings forward a nonlinear finite element beam model accounting for aerodynamic nonlinearities, via stall and follower forces models, along with geometrical nonlinearities due to large displacements and rotations. A great variety of analyses were performed: First, the flutter boundaries of the wings were analyzed; second, the limit cycle oscillation amplitudes and frequencies in the oscillating wings were evaluated; third, the coupling behavior and the nonlinear responses obtained were discussed under several attributes. The geometrical nonlinearities were taken into account by a total Lagrangian formulation based on a straightforward and consistent interpolation field in order to describe the exact kinematics of a Timoshenko’s beam. Nonlinear aerodynamic loads were computed via an unsteady strip theory in the time-domain with the Jones approximation for the Wagner’s function along with a follower aerodynamic loads assumption. Additionally, a non-usual stall model based on an experimental quasi-static stall curve for flat plates was used to interpolate the lift-curve slope. The experimental and numerical results indicated a minimum flutter speed for ballast positions about of −5 mm toward the leading edge. Next, different nonlinear post-flutter LCO behaviors were obtained for the different ballast positions tested. To conclude, the good correlation between model and experiments indicated that the nonlinear modeling approach proposed herein was capable to predict the aeroelastic behavior of the tested high aspect-ratio wings.

Finite Element Modeling of Steel-concrete Composite Beams with Different Shear Connection Degrees

In order to study the behavior of Steel-concrete composite beams with different shear connection degrees, using finite element software ABAQUS, four models with different numbers of headed studs are established, all of which apply appropriate concrete and steel constitutive models, and contact relationship. The accuracy of finite element models is verified by comparing the simulation results with corresponding beam tests in multiple aspects, for instance, the interface slip, the ultimate capacity, the failure modes and the load-strain distribution. The analysis focuses on the interface slip development of composite beams with different connection degrees, and the results show that the interface slip seldom becomes the control condition when designing composite beams. A further parametric study is performed to investigate the effect of various parameters on the static response of composite beams. Finally, the applicable conditions and limitations of different modeling methods are discussed. The modeling method used in this paper is suitable for simulating the static performance of composite beams, especially in the investigation of the interface slip development.

Multi-fidelity analysis and uncertainty quantification of beam vibration using co-kriging interpolation method

In this paper, a multi-fidelity surrogate model is created using co-kriging methodology to determine the natural frequencies of beams by combining the fidelities of Euler-Bernoulli (low-fidelity) and Timoshenko (high-fidelity) beam finite element models. This study of free vibration of beams involves uncertainties in material properties. The sampling space for the co-kriging surrogate model is created using an optimal latin hypercube sampling technique. It is shown that the co-kriging surrogate model predicts the natural frequencies with high computational efficiency and accuracy, in the entire design space. The computational efficiency and utility of the multi-fidelity model is demonstrated through its application to a problem of quantifying uncertainties in the natural frequencies of a tapered beam using Monte Carlo Simulation.

Topology optimization of structural frames considering material nonlinearity and time-varying excitation

An approach for the topology optimization of structures composed of nonlinear beam elements under time-varying excitation is presented. Central to this approach is a hysteretic beam finite element model that accounts for distributed plasticity and axial-moment interaction through appropriate hysteretic interpolation functions and yield/capacity function, respectively. Nonlinearity is represented via the hysteretic variables for curvature and axial deformations that evolve according to first order nonlinear ordinary differential equations (ODEs), referred to as evolution equations, and the yield function. Hence, the governing dynamic equilibrium equations and hysteretic evolution equations can thus be concisely presented as a system of first-order nonlinear ODEs that can be solved using general ODE solvers without the need for linearization. The approach is applied for the design of frame structures with an objective to minimize the total volume in the domain, such that the maximum displacement at specified node(s) satisfies a specified constraint (i.e., drift limit) for the given excitation. The maximum displacement is approximated using the p-norm and thus permits the completion of the analytical sensitivities required for gradient-based updating. Several numerical examples are presented to demonstrate the approach for the design of structural frames subjected to pulse, harmonic, and seismic base excitation. Topologies obtained using the suggested, nonlinear approach are compared to solutions obtained from topology optimization problems assuming linear-elastic material behavior. These comparisons show that although similarities between the designs exist, in general the nonlinear designs differ in composition and, importantly, outperform the linear designs when assessed by nonlinear dynamic analysis.

A kNN algorithm for locating and quantifying stiffness loss in a bridge from the forced vibration due to a truck crossing at low speed

This paper proposes a k-Nearest Neighbours (kNN) algorithm for locating and quantifying bridge damage based on the time-varying forced frequencies due to a moving truck. Eigenvalue analysis of a simplified vehicle-bridge coupled system, consisting of a three-axle rigid truck model and a simply supported finite element beam model, shows how the eigenfrequencies of the coupled system vary with the locations of the vehicle and with the damage represented by a stiffness loss. The computational efficiency of eigenvalue analysis is exploited to generate a vast sample of patterns for training a kNN algorithm. In the field, acceleration due to the crossing of a test vehicle would be measured and analysed using a time–frequency signal processing tool to obtain the instantaneous frequencies. The crossing must take place at a low speed to achieve sufficiently high resolution and to minimise deviations from the eigenvalue solution. Then, the kNN algorithm searches for the patterns of forced eigenfrequencies that are closest to the on-site instantaneous frequencies to determine the location and severity of the damage. For theoretical testing purposes, field measurements are simulated here using coupled equations of motion and dynamic transient analysis.

Расчёт критических частот ротора центробежного насоса на ос-нове его дискретной математической модели

Calculations of the centrifugal machines critical frequencies of the rotors are currently carried out on the basis of the finite element method using multi-functional software as same as ANSYS and other similar, that work with finite elements of the three-dimensional type, as well as some specialized computer programs working with the beam-type finite elements. Anyway, the finite element method is used. But in this case an user needs a lot of time for prepation of the initial data. Therefore, this article presents a calculation of the critical frequencies of the rotor of a centrifugal fuel pump of a liquid-propellant engine based on its discrete model. This calculation also includes an algorithm of results clarification. This model has been verificated by comparing the critical frequencies obtained in calculations based on the finite element beam model and discrete model with using the algorithm of results clarification and without it.

Damage detection in structures using modal curvatures gapped smoothing method and deep learning

This paper deals with damage detection using a Gapped Smoothing Method (GSM) combined with deep learning. Convolutional Neural Network (CNN) is a model of deep learning. CNN has an input layer, an output layer, and a number of hidden layers that consist of convolutional layers. The input layer is a tensor with shape (number of images) × (image width) × (image height) × (image depth). An activation function is applied each time to this tensor passing through a hidden layer and the last layer is the fully connected layer. After the fully connected layer, the output layer, which is the final layer, is predicted by CNN. In this paper, a complete machine learning system is introduced. The training data was taken from a Finite Element (FE) model. The input images are the contour plots of curvature gapped smooth damage index. A free-free beam is used as a case study. In the first step, the FE model of the beam was used to generate data. The collected data were then divided into two parts, i.e. 70% for training and 30% for validation. In the second step, the proposed CNN was trained using training data and then validated using available data. Furthermore, a vibration experiment on steel damaged beam in free-free support condition was carried out in the laboratory to test the method. A total number of 15 accelerometers were set up to measure the mode shapes and calculate the curvature gapped smooth of the damaged beam. Two scenarios were introduced with different severities of the damage. The results showed that the trained CNN was successful in detecting the location as well as the severity of the damage in the experimental damaged beam.

Enriched beam finite element models with torsion and shear warping for the analysis of thin-walled structures

This paper presents three beam Finite Element (FE) formulations developed for the analysis of thin-walled structures. These account for out-of-plane cross-section warping by removing the classical rigid body cross-section hypothesis and capture the interaction of axial/bending stress components with shear and torsion.The beam FE models rely on different kinematic assumptions to describe out-of-plane cross-section deformations. Indeed, warping displacement field is interpolated in the element volume according to different approaches, with increasing level of accuracy and detail. First two models adopt a coarse warping description, where warping displacement field is defined as the linear combination of assumed warping profiles and unknown kinematic parameters. In the first model, these are considered as equal to the generalized cross-section torsional curvature and shear strains and a classical displacement-based formulation is adopted to derive the element governing equations. In the second model, warping parameters are assumed as independent kinematic quantities and a mixed approach is considered to derive the FE formulation. Third model, also relying on a mixed formulation, independently interpolates warping by introducing additional degrees of freedom on the cross-section plane, thus, resulting in a richer description of the out-of-plane deformations. This latter is also adopted to propose a numerical procedure for the warping profile evaluation of thin-walled beams subjected to torsional and shear forces, for general cross-section geometry.The efficiency and accuracy of the proposed FE formulations are validated by simulating the response of thin-walled structures under torsion and coupled torsion/shear actions and the influence of the kinematic assumptions characterizing each formulation is discussed.

Method to Evaluate Effect of Spudcan Penetration on Adjacent Jacket Piles

When a jack-up drilling rig operates near an adjacent jacket platform, the effect of the large-diameter spudcan penetration on adjacent platform piles should be evaluated if the spudcan-pile clearance is less than one spudcan diameter. In this study, a method is developed to calculate the response of a pile subjected to spudcan penetration-induced load and pile head load transmitted from upper structure. The spudcan penetration-induced lateral pile deflection is first determined by large deformation finite element calculation. The spudcan penetration-induced load along pile shaft is then determined by transforming the pile lateral deflection into equivalent nodal loads in a nonlinear foundation beam finite element model. The pile response is finally calculated using an isolated pile finite element model subjected to penetration-induced loads and pile head loads transmitted from the upper structure or an overall finite element model which includes the upper structure and piles. Centrifuge model tests under 50g condition are conducted to verify the validity of the proposed method. To further investigate the applicability of the proposed method, the effects of pile head constraint, lateral pile head load magnitude and its direction, spudcan-pile clearance and undrained shear strength are studied. The effect of spudcan penetration on an adjacent pile is found to increase with rotation stiffness at the pile head. Spudcan penetration affects the adjacent piles most when the lateral pile head load is facing back to the spudcan. The effect of spudcan penetration decreases significantly when the spudcan-pile clearance is larger than the diameter of the spudcan and decreases with increasing undrained shear strength. Furthermore, the spudcan penetration has more influence on the pile deflection than the bending moment.

Design of wave-like dry friction and piezoelectric hybrid dampers for thin-walled structures

This paper proposes a wave-like hybrid damper containing both dry friction and piezoelectric damping mechanisms for thin-walled structures. The idea is to distribute piezoelectric material on the wave-like friction plate, so that the elastic deformation of the plate can be further utilized to generate additional shunted piezoelectric damping. The proposed damper has the following advantages: simple structure, easy installation and maintenance, convenient to adjust the normal preload, and feasible to mount piezoelectric materials. Combined with damped nonlinear normal modes (dNNMs), the nonlinear modal electromechanical coupling factor (nonlinear MEMCF) is proposed, and its relationship with piezoelectric damping is established for electromechanically coupled systems with contact nonlinearities. Based on the extended periodic motion concept (E-PMC) of dNNMs for non-conservative systems, the preliminary design guidelines of wave-like hybrid dampers are given through nonlinear modal analyses. The modal damping ratio and the nonlinear MEMCF are used to evaluate the damping generated by friction and piezoelectric mechanisms, respectively. The damping effect is also verified by steady-state response analyses through the Multi-Harmonic Balance Method (MHBM). By using a cantilever beam finite element (FE) model, the spatial distribution of piezoelectric material is optimized for a single wave-like hybrid damper. Four optimized hybrid dampers are then implemented to an industrial thin-walled structure. Taking the normal preload as an example, the influence of parameter distribution patterns at different interfaces on the damping effect is also discussed. Compared with the underlying friction damper, the wave-like hybrid damper not only provides greater damping, but is also less sensitive to the variation of excitation amplitude and the normal preload. Whether friction or piezoelectric damping is inactive, the proposed damper can still generate considerable damping.

A Multiobjective Perspective to Optimal Sensor Placement by Using a Decomposition-Based Evolutionary Algorithm in Structural Health Monitoring

The objective of optimal sensor placement in a dynamic system is to obtain a sensor layout that provides as much information as possible for structural health monitoring (SHM). Whereas most studies use only one modal assurance criterion for SHM, this work considers two additional metrics, signal redundancy and noise ratio, combining into three optimization objectives: Linear independence of mode shapes, dynamic information redundancy, and vibration response signal strength. A modified multiobjective evolutionary algorithm was combined with particle swarm optimization to explore the optimal solution sets. In the final determination, a multiobjective decision-making (MODM) strategy based on distance measurement was used to optimize the aforementioned objectives. We applied it to a reduced finite-element beam model of a reference building and compared it with other selection methods. The results indicated that MODM suitably balanced the objective functions and outperformed the compared methods. We further constructed a three-story frame structure for experimentally validating the effectiveness of the proposed algorithm. The results indicated that complete structural modal information can be effectively obtained by applying the MODM approach to identify sensor locations.

Comment to “Skeletonization-based beam finite element models for stochastic bicontinuous materials: Application to simulations of nanoporous gold” by C. Soyarslan et al. [J. Mater. Res. 33(20), 3371 (2018)

Abstract

Temperature increase on folded solar sail membranes

All currently considered solar sail designs require the deployment of a thin reflective membrane. This membrane is stowed using some folding technique and sometimes coiled onto a spool. The temperature of the deployed sail membrane is a critical aspect for solar sail design. Depending on the geometry of the imprinted folding lines, sunlight may be reflected inside folding lines which would locally increase the temperature of the membrane. The analysis presented here aims for a quantification of that temperature increase. Microscope images of a 7.5μm thick polyimide membrane reveal the geometry of folding lines for different tensioning states. In addition, the opening of folding lines are analysed with a finite-element beam model. After the determination of the geometry as a function of the tensioning state, it is analysed how many reflections may appear in a folding line depending on its opening angle for a sail that is oriented perpendicular to the Sun. Two cases are investigated, deep space and low-Earth orbit. It is shown that, even for small tensioning states, the membrane geometry does not allow more than only two reflections. Depending on the material, this can cause a slight temperature increase that also depends on the investigated case (deep space or low-Earth orbit).

Finite beam element with 22 DOF for curved composite box girders considering torsion, distortion, and biaxial slip

Experimental and numerical study on the mechanical performance of curved steel–concrete composite box girders is reported in this research. First, this research establishes a theoretical model for curved composite girders with 11° of freedoms (DOFs) for each node. The DOFs include the longitudinal displacement, transverse displacement, deflection, torsion angle, warping angle, and interface biaxial slip between steel and concrete. Based on the virtual work theorem, the equilibrium function, the stiffness matrix, the node displacement matrix and the external load matrix are proposed for the curved composite girders using the FE spatial discretization. Second, the authors conduct an experimental program on three large-scale curved composite girders with various interface shear connectors and central angles. The comparison between the developed finite beam element, the elaborate FE model and the test results indicates the developed finite beam element has an adequate level of accuracy in predicting the deflection, the torsion angle and the axial strain distribution of test specimens. Third, based on the developed finite beam element model, the effect of initial curvature, number of diaphragms, and the interface connector stiffness on the curved composite girder is examined. The simulation results showed that the initial curvature significantly contributes to the displacement and stress of composite girders. Applying more diaphragms can notably reduce the distortion angle and distortion displacement. The interface shear connector stiffness has a significant influence on the curved composite girder. With the increasing shear connector stiffness, the displacement and stress of curved composite girders decrease notably. Based on the parametric analyses, it is recommended to limit the central angle of simply supported composite girder below 45°, to apply an adequate number of diaphragms, and to design curved composite girders as fully shear connection specimens.

Hybrid Sandwich Panels: A Review

A high specific stiffness, high specific strength, and tailoring the properties for specific application have attracted the attention of the researchers to work in the field of laminated composites and Sandwich structures. Rapid use of these laminated composites and Sandwich structures necessitated the development of new theories that suitable for the bending, buckling and vibration analysis. Many articles were published on free vibration of beams, plates, shells laminated composites and sandwich structures. In this article, a review on free vibration analysis of shear deformable isotropic beams, plates, shells, laminated composites and sandwich structures based on various theories and the exact solution is presented. In addition to this, the literature on finite element modeling of beams, plates, shells laminated composites and sandwich structures based on classical and refined theories is also reviewed. The present article is an attempt to review the available literature, made in the past few decades on free flexural vibration response of Fiber Metal laminated Composites and Sandwich panels using different analytical models, numerical techniques, and experimental methods.

Design of dry friction dampers for thin-walled structures by an accelerated dynamic Lagrange method

The low inherent damping for thin-walled structures often leads to prominent vibrational problem. This paper proposes a friction patch to enhance the damping for thin-walled structures. The damping patch is simple in structure and easy to adjust the normal preload. Based on a beam finite element model, parameters including geometry, stiffness and position of the proposed damper are optimized numerically. The steady-state response of the system is calculated by the DLFT in the frequency domain efficiently with high accuracy. The damping performance of the friction patch is quantified by the resonant amplitude for the target mode. The design guidelines summarized from numerical simulation are experimentally verified through a cantilever beam. Four optimized friction patches are implemented to a complex industrial thin-walled structure. Results show that the well-designed friction patches provide over 40% vibration reduction with less than 0.83% additional mass of the host structure for different modes.

Probabilistic modelling of the robustness of reinforced concrete frames accounting for material property variability using a layered beam finite element approach

In this contribution the influence of material properties variability on the structural robustness of Reinforced Concrete (RC) frames is assessed using a computational approach. A layered beam finite element model is employed in a correlation reduced Latin Hypercube Sampling-based stochastic framework in which the material parameters driving the elastic, plastic and fracture behavior of both steel and concrete constituents are considered to be Random Variables (RVs). The probability characteristics of each RV are set to match relevant experimental data available in the literature. Structural robustness of each deterministic simulation is evaluated based on the outcome of a nonlinear dynamic progressive collapse computation using the Sudden Column Loss (SCL) scenario. The sensitivity of structural robustness and residual displacement to each material parameter is established first, considering their variations separately. The robustness of a RC frame designed following the European building code, incorporating all RVs simultaneously is assessed and critically compared to the results of the sensitivity analysis. The link between the structural degradation and failure mechanism and data extracted from the cross sectional behavior is established. The identification of structural mechanisms inducing failure or survival is attempted and a set of practically relevant recommendations for progressive collapse resistance is listed.

Numerical investigation on the creep response of concrete structures by means of a multi-scale strategy

In this paper, a multi-scale modelling strategy is proposed to investigate the creep behaviour of reinforced concrete structures. A Mean Field homogenisation procedure is adopted to compute the overall response of a high-strength concrete made of limestone inclusions embedded in a cement paste matrix. Finite element models of beams subjected to sustained bending loads are fully coupled to the time-dependant effective material law delivered by the homogenisation method. Furthermore, a Genetic Algorithm is used to improve the accuracy of the finite element predictions. The influence of relevant structural parameters, such as beam height, steel reinforcement ratio in tension and compression, and cement volume fraction, is assessed on the long term creep deflection over a period of five years. The long term multiplier factor, λΔ, defined as the creep deflection over the immediate deflection, is calculated numerically and discussed in detail. The above results provide further insight into the time-dependent deformation mechanisms present in concrete structures which are still not well-understood, and may shed more light on the improvement of current design equations and the development of complementary design guidelines.

Impact of back-end-of-line architecture on chip-package-interaction in advanced interconnects

Chip–package interaction (CPI) has become an increasingly important reliability issue in the microelectronics industry. In order to survive the thermally induced stresses during processing or working lifetime, the complex back-end-of-line (BEOL) layer stacks must have sufficient mechanical strength. The understanding of accelerated mechanical tests performed at wafer level, such as shear microprobing, is needed to early detect the risk of failure in the final IC device. In this study, the impact of the BEOL architecture in terms of via density and metal density on the failure location and the amount of observed BEOL failures is demonstrated by performing a large statistical amount of shear microprobing combined with post-mortem focused ion beam (FIB) cross sections. The experimental results are further supported by local bump pull tests, in-situ scanning electron microscopy (SEM) micro beam bending tests and finite element modeling (FEM). A clear correlation was found between the BEOL architecture and the amount of observed BEOL fractures. It was found that the cross sectional metal area in the topmost Z–group has a stronger impact on the amount of BEOL failures compared to the low or medium, X or Y–groups respectively. This trend was explained in terms of elastic shielding effect. Furthermore, both experimental results and FEM show that the via density may play a dominant role in both crack initiation and crack growth. These findings lead to a better understanding of the robustness of interconnect structures and the stresses they can tolerate and may serve as guidelines to develop a CPI-aware design of advanced nano-interconnects.