Static Structural Response Research Articles

An optimization-based rigid block modeling approach to seismic assessment of dry-joint masonry structures subjected to settlements

A rigid block modeling approach is presented for rocking dynamics and nonlinear static analysis of dry-joint masonry structures subjected to settlements and earthquake excitations. For the different types of analysis, a unified optimization-based formulation is adopted, which is equivalent to the system governing the static and dynamic structural response. Sequential solution procedures are used for time integration and for pushover analysis which take into account the effects of large displacements under the combined action of support movements and lateral loads. No-tension elastic contacts with finite shear strength are considered at block interfaces for time-history analysis and to obtain the elastic branch of pushover curves in nonlinear static analysis. A unilateral rigid contact behavior is also considered to obtain the descending post-peak branch of pushover curves corresponding to the activation of the rigid-body rocking motion, according to displacement-based assessment methods of failure mechanisms adopted in the standards. Comparisons with numerical models and experimental tests on a rocking block and on a buttressed arch are presented to show the accuracy of the developed approach. Simple tests on dry-joint tuff panels on the tilting table were also carried out to show the effects of imposed movements at support on the response to lateral loads. Finally, an application is presented to a full-scale triumphal arch subjected to the combined action of support movements and earthquake excitation to discuss, on the basis of the developed model, the effects of settlement-induced damage on seismic performance. The numerical analyses showed that the lateral force, the displacement capacity and the rocking response can be significantly affected by support movements, pointing out the relevance of the current building condition in the seismic safety assessment.

Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

In the present manuscript, a Layer-Wise (LW) generalized model is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads. The unknown field variable is modelled employing polynomials of various orders, each of them defined within each layer of the structure. As a particular case of the LW model, an Equivalent Single Layer (ESL) formulation is derived too. Different approaches are outlined for the assessment of external forces, as well as for non-conventional constraints. The doubly-curved shell is composed by superimposed generally anisotropic laminae, each of them characterized by an arbitrary orientation. The fundamental governing equations are derived starting from an orthogonal set of principal coordinates. Furthermore, generalized blending functions account for the distortion of the physical domain. The implementation of the fundamental governing equations is performed by means of the Generalized Differential Quadrature (GDQ) method, whereas the numerical integrations are computed employing the Generalized Integral Quadrature (GIQ) method. In the post-processing phase, an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations. A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes, calculated by the present methodology, have been successfully compared to those ones obtained from refined finite element three-dimensional simulations. Even though the present LW approach accounts for a two-dimensional assessment of the structural problem, it is capable of well predicting the three-dimensional response of structures with different characteristics, taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.

STATIC BENDING ANALYSIS OF NANOPLATES ON DISCONTINUOUS ELASTIC FOUNDATION WITH FLEXOELECTRIC EFFECT

In this study, rectangular plates subjected to static loads and supported on a discontinuous two-parameter elastic foundation are analyzed. The formulae for the computations are developed from improved shear deformation theory, where the displacement w is divided into bending and shear strain components. The results obtained from this article and other publications are evaluated to prove the accuracy of the proposed theory and the calculation program. Then, a parameter study is carried out to capture the effect of some material and geometrical parameters on the static response of structures. Especially the influence of the flexoelectric effect and discontinuous foundation is investigated. As two elastic foundation parameters and flexoelectric coefficient are increased, the non-dimensional maximum deflection of the plate decreases, indicating that these factors improve the plate's stiffness.

Analytical study on the inflated shape of a super pressure balloon covered with a diamond-shaped net

In the last two decades, extensive efforts have been made to develop a large super pressure balloon (SPB) capable of carrying heavy payloads for scientific observations of long durations. Due to recent achievements by the NASA Balloon Program Office, practical operations of large-scale lobed-pumpkin SPB will be realized in the near future. Meanwhile, the research team initiated the development of a lightweight SPB with an alternative design concept, in which the entire balloon is covered by a diamond-shaped net. In this work, the static structural response of the proposed SPB is analyzed by establishing a mathematical model to predict its inflated shape. This model is validated by comparing the generated results with those obtained from nonlinear finite element analysis. Excellent agreement between the analytical solutions and the corresponding finite element results was obtained. On the basis of the mathematical model, the inflated shape of the SPB is investigated and unique structural characteristics are deduced, i.e., the balloon inflates into a cylinder-like shape for a certain geometry of the cover net. This structural feature can be explained by considering the equilibrium of forces applied to the cover net.

Design and development of large scale FDM based 3D printer

Additive Layer Manufacturing (ALM) is one of the fabricating methods because it permits outrageous customization, quick prototyping of wanted designs and low volume creation of items. FDM printer goes under the material expulsion class. The filament is constrained into the hot extruder. The filament is warmed first and afterward stored, through the spout, onto a form stage layer-by-layer to frame the total 3D structure. A printer equipped for printing a 1.5-meter cubic-sized object was designed in SOLIDWORKS CAD software and manufactured into a functioning model. The Frame, Linear guide rail, and Z-axis rails were subjected to static structural, modal and harmonic response analysis with ANSYS Workbench. The designed parts were investigated by modal analysis to get the natural frequency. The effect on the guide rails and frame due to external forces, stepper motor, and extruder were examined with harmonic response analysis. The frequency at which the amplitude rises drastically from a phase angle of 0 degrees to 180 degrees was obtained using harmonic response analysis as well. The model was further subjected to motion analysis using ADAMS dynamic software.

Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories

In this novel work, applying boundary shape function differential quadrature hierarchical finite element method (DQHFEM) will be employed to analyze frequency, damping, bending, and buckling of an embedded sandwich nanoplate using different plate theories such as refined zigzag theory (RZT), sinusoidal shear deformation theory (SSDT), first-order shear deformation theory (FSDT) and classical plate theory (CPT). The face sheets as well as the core layer of the sandwich structure respectively are formed by porous material and nanocomposites reinforced with graphene platelets (GPLs) considering various dispersion. According to the Halpin–Tsai micromechanics model, Young’s modulus, as well as the rule of mixture for density as well as Poisson’s ratio related to the face sheets, can be obtained. Further, for modeling the mentioned sandwich structure much more realistic, Kelvin–Voigt model is applied. In order to gain motion of equations, D’Alembert’s principle is utilized where size influences can be contemplated as well using higher-order strain gradient nonlocal theory. In this comprehensive research, diverse parameters featuring the influences of structural damping, strain gradient parameters, GPL volume percent, dispersion, viscoelastic medium, porosity, boundary edges, and geometric variables upon vibration, buckling, and bending behaviors correlative to this structure. It is ascertained that RZT is the most accurate theory among other mentioned theories in estimating the static and dynamic response of structure which needs no shear correction factors. Moreover, the presence of GPLs can make the entire sandwich structure stiffer and dispersion patterns of pores, as well as GPLs, can affect the vibration, buckling, and bending of the structure.

Condition assessment of high-speed railway track structure based on sparse Bayesian extreme learning machine and Bayesian hypothesis testing

ABSTRACT Aiming at condition assessment of ballastless high-speed railway track structures, in this study, a probability prediction model of the structural static responses under temperature loads based on sparse Bayesian extreme learning machine (SBELM) is constructed. Utilizing the probabilistic predictions of the structural static responses, a Bayesian hypothesis testing-based condition assessment method for track structures is proposed. This method is employed for long-term monitoring data analysis of a high-speed railway track structure with a small-radius curve. Implicit mappings between the temperature loads and the structural static responses are obtained by training a SBELM model, and reliable predictions of the subsequent structural static responses based on the monitored temperature data are yielded. Subsequently, the probabilistic predictions of the structural responses are compared with measured data by Bayesian hypothesis testing for effective condition assessment. The illustrative application validates that the proposed method can realize the condition assessment of high-speed railway track structures effectively.

Effect Stress and Vibration Analysis at NACA Airfoil towards Axial Fan Blade Performance

Axial fans are widely applied in the industrial sector. Axial fans are used for ventilation systems and other cooling systems. The blade design of the axial fan requires an airfoil study. Unfortunately, there are not many articles that discuss in detail about airfoils, especially on noise and vibration that can have an impact on axial fan performance using computational fluid methods or software. This study performs axial fan analysis using computational methods with ANSYS Fluent, Static Structural, Modal and Harmonic Response software to obtain the values of stress, vibration and fluid flow. The experimental design used is using NACA 1412, 4142, and 6412 airfoils on the tip with variations in angles of 60, 74, and 80. While on the hub uses NACA 9312, 9412, and 9512 airfoils with angle variations of 20, 30, and 60 and simulated to find the value of vibration and stress analysis. The 3D axial fan design is imported into the ANSYS Fluent, Static Structural, Modal and Harmonic Response software. The simulation results using Ansys Fluent, shows the pressure contour with a maximum value of 198.424 Pa and Velocity streamline with a maximum value of 28.8669 m/s. the results of the Ansys Static Structural simulation show that the average total deformation is 9.9275e-008 m. The simulation results using Ansys Modal, show that there is a natural frequency of 287.8 Hz and the simulation results of Ansys Harmonic Response obtained an average total deformation of 5.0809e-012 m and the equivalent stress value with a maximum value of σ y, max = 0.20186 Pa.

Direct convolution integration method for random vibration analysis of structures subjected to nonuniformly modulated nonstationary excitations

A comprehensive direct convolution integration method is presented in this study for the random vibration analysis of linear structures subjected to multiple nonuniformly modulated nonstationary excitations. The structural unit impulse responses with respect to each independent excitation are first identified and stored by a few time-history analyses. Then the structural response statistics are calculated by the direct convolution integration of unit impulse responses and excitation statistics. Further, two fast Fourier transform algorithms are presented to speed up the convolution integration. Because the convolution expressions are explicit, the presented method can be used to only calculate the responses at some specific degrees of freedom of interest in engineering. Furthermore, it can only calculate the responses at a small number of sparse moments in consideration of the time slow-varying property of nonstationary processes. Finally, the random vibration analysis of a frame structure excited by the fully coherent and incoherent nonstationary excitations is utilized to demonstrate its high accuracy and efficiency. Some suggestions of application are given.

Topology optimization of proportionally damped structures under harmonic excitations: Analysis of velocity and acceleration responses

Topology optimization of proportionally damped structures subjected to harmonic excitations within a frequency interval is a challenging task. In this work, we consider the structural velocity and acceleration responses in a frequency interval as the optimization objectives. The optimized structures will be significantly different from those with the displacement response only due to the influence of excitation frequencies. In particular, if the acceleration amplitude of structural frequency responses in a frequency interval is considered, the optimization process usually converges to a configuration that is unable to ensure engineering feasibility. An optimization model that takes the structural static response of the structure as a weighted part of the objective function is proposed, it can make the optimized configuration more applicable for engineering design. An efficient method for calculating frequency responses over a frequency interval is also introduced. The derivatives of the objective function are derived by the adjoint method and can be calculated in a manner similar to the frequency response. Two illustrative examples are given to examine the accuracy and validity of the proposed method.

Experimental Study on Static and Dynamic Response of Aluminum Honeycomb Sandwich Structures.

Honeycomb aluminum structures are used in energy-absorbing constructions in military, automotive, aerospace and space industries. Especially, the protection against explosives in military vehicles is very important. The paper deals with the study of selected aluminum honeycomb sandwich materials subjected to static and dynamic compressive loading. The used equipment includes: static strength machine, drop hammer and Split Hopkinson Pressure Bar (SHPB). The results show the influence of applied strain rate on the strength properties, especially Plateau stress, of the tested material. In each of the discussed cases, an increase in the value of plateau stresses in the entire strain range was noted with an increase in the strain rate, with an average of 10 to 19%. This increase is mostly visible in the final phase of structure destruction, and considering the geometrical parameters of the samples, the plateau stress increase was about 0.3 MPa between samples with the smallest and largest cell size for the SHPB test and about 0.15 MPa for the drop hammer test.

Aerodynamic shape optimization of large-span coal sheds for wind-induced effect mitigation using surrogate models

Large-span coal sheds commonly used in thermal power plants are particularly vulnerable to wind loads, and the aerodynamic performances are largely affected by their external shapes. The search for the best performing shape through an aerodynamic optimization is still of importance for the mitigation of the design wind loads and responses. This study investigated the possibility of using surrogate models combined with genetic algorithm to carry out the aerodynamic shape optimization of large-span roof structures. The approach is applied to tri-centered coal sheds with closed and open gables, respectively. The shape optimization is numerically performed to minimize the vertical displacement of the shed model while subjecting to one normal and two oblique wind directions, 0°, 30° and 45°. The aerodynamic forces acting on coal sheds immersed in turbulent flow are obtained by the CFD simulation with RSM turbulence model, and the results are validated with wind tunnel tests. Kriging model is used to establish a global mapping between design variables and objective function by conducting a set of CFD and structural static response analyses. Results show that the aerodynamic loads and the optimal geometry are sensitive to the selection of gable types and wind directions. The optimal design presents a reasonable performance improvement compared with the near-optimal and original designs. Several compromised designs are finally provided in order to seek a balance between the effects of wind directionality and construction cost.

Experimental Aeroelastic Benchmark of a Very Flexible Wing

The paper presents the design, analyses, and testing of the Pazy wing, a very flexible wing model that was designed to study aeroelastic phenomena associated with geometrically nonlinear deflections and to provide data for validation of nonlinear aeroelastic simulation models. The Pazy wing is made of a main thin aluminum spar and a Nylon 12 printed ribs chassis providing the NACA0018 aerodynamic airfoil shape. The wing was covered entirely with a polyester film that serves as the skin. Static loading tests were used for model adaptation and to assure that the wing can deform to over 50% of its span without failing. Ground vibration tests were also used for model adaptation. Because there are uncertainties in the characteristics of the polyester skin under loads, both the static and ground vibration tests were used to asses the contribution of the skin to the wing’s stiffness and determine the stiffness bound with and without the skin. Wind-tunnel tests were conducted at conditions that lead to static and unsteady structural responses. The wing deformations were tracked by a motion recovery system, and the strains over the wingspan were recorded with a Bragg-grating fiber-optics system. In the static wind-tunnel tests, the aerodynamic loads were recorded by a force balance. The wind-tunnel tests included angle-of-attack sweeps in constant airspeed and velocity sweeps in fixed angle of attack. The largest wing-tip static deformation recorded in test was of 50% span. In the velocity-sweep tests, the wing showed strong oscillations at a velocity at which the wing-tip deformation was approximately 25% of the span and became stable again at higher speeds. The wing models and test data are publicly available through the 3rd Aeroelastic Prediction Workshop (https://nescacademy.nasa.gov/workshops/AePW3/public).

Fuzzy Finite Element Analysis for Static Responses of Plane Structures

Abstract In this paper, a fuzzy finite element algorithm is investigated to determine static responses of plane structures. This algorithm concerns finite element method, fuzzy sets theory, and response surface method. Firstly, the notion of a standardized triangular fuzzy number is developed and utilized to replace original fuzzy numbers in the surrogate models. Then, the error estimations between the training and the test sets are performed to select the suitable response surface model amongst the regression models. Lastly, a good performance combination of complete and non-complete quadratic polynomial regression models is proposed to define the responses of structures. The merits of the proposed algorithm are illustrated via numerical examples.

A comparison of two neural network architectures for fast structural response prediction

AbstractIn this contribution, we compare two different neural network architectures to predict the response statistics of structures. The overall goal is a significant speed‐up of the numerically expensive Monte Carlo simulation. The first approach is based on a convolutional neural network that learns from the whole excitation history, whereas the second approach is based on a feed‐forward network architecture learning from hand‐designed features. Both procedures use supervised learning: The neural networks learn from an initial subset before the prediction of the response statistics of the Monte Carlo simulation is possible.

Tuning of Static and Dynamic Mechanical Response of Laser Powder Bed Fused AlSi10Mg Lattice Structures through Heat Treatments

The use of additive manufacturing allows the production of complex designs, including metallic lattice structures, which combine lightness and good mechanical properties. Herein, the production of AlSi10Mg lattice structures by laser powder bed fusion is explored and consistent processing parameters are selected. Thereafter, it is demonstrated that heat treatments, specifically designed on the basis of the alloy's metallurgy, can be used to selectively induce different microstructural modifications and, consequently, finely tune the static and dynamic mechanical behavior of the aluminum lattice structures. In particular, removal of residual stresses results to be the dominant factor in allowing a smooth quasistatic compressive behavior and improving the structure's ability to absorb energy during collapse. On the contrary, the increase in ductility connected to the spheroidization of the Si network is shown to be of paramount importance in improving the structure's dynamic damping ability by allowing local plasticization.

Seismic performance improvement of underground frame structures by changing connection type between sidewalls and slab

Seismic failure mechanism of underground frame structures presents that the collapse of underground structures attributes to the insufficient seismic resistance of central columns. Therefore, researches have been conducted to improve the seismic performance of underground structures by enhancing the loading-carrying capacity of the central columns or decreasing the seismic loads transmitted to central columns. For this purpose, this study proposed a new approach by changing the connection type between sidewalls and slab: setting shock absorbing gap (SAG) between sidewalls and ceiling slab, which aims to decrease seismic loads transmitted to central columns. The proposal and working mechanism of SAG were illustrated detailedly. Afterwards, nonlinear finite element models, in which a developed elastoplastic constitutive model was used to simulate the 3D strength and softening behaviour of surrounding soils, were built for simulating the static and dynamic responses of underground structures. Based on the numerical results, SAG affecting the internal forces of structural components before earthquakes were discussed firstly. Then the seismic efficiency of SAG updating the seismic performance of underground frame structures was analyzed by discussing earthquake-induced damage mode of overall structures, soil pressure on structures, earthquake-induced deformations and internal forces of structural components. Finally, the seismic performance of underground frame structures influenced by the width of SAG and frictional coefficient of the sliding surface was investigated, and advice for reasonably using SAG was suggested.

A Monte Carlo Simulation Approach in Non-linear Structural Dynamics Using Convolutional Neural Networks

The evaluation of the structural response statistics constitutes one of the principal tasks in engineering. However, in the tail region near structural failure, engineering structures behave highly non-linear, making an analytic or closed form of the response statistics difficult or even impossible. Evaluating a series of computer experiments, the Monte Carlo method has been proven a useful tool to provide an unbiased estimate of the response statistics. Naturally, we want structural failure to happen very rarely. Unfortunately, this leads to a disproportionately high number of Monte Carlo samples to be evaluated to ensure an estimation with high confidence for small probabilities. Thus, in this paper, we present a new Monte Carlo simulation method enhanced by a convolutional neural network. The sample-set used for this Monte Carlo approach is provided by artificially generating site-dependent ground motion time histories using a non-linear Kanai-Tajimi filter. Compared to several state-of-the-art studies, the convolutional neural network learns to extract the relevant input features and the structural response behavior autonomously from the entire time histories instead of learning from a set of hand-chosen intensity inputs. Training the neural network based on a chosen input sample set develops a meta-model that is then used as a meta-model to predict the response of the total Monte Carlo sample set. This paper presents two convolutional neural network-enhanced strategies that allow for a practical design approach of ground motion excited structures. The first strategy enables for an accurate response prediction around the mean of the distribution. It is, therefore, useful regarding structural serviceability. The second strategy enables for an accurate prediction around the tail end of the distribution. It is, therefore, beneficial for the prediction of the probability of failure.

Numerical and Experimental Investigation of Static Four-point Bending Response of Honeycomb Sandwich Structure: Failure Modes and the Effect of Structural Parameters

The aim of this study is to characterize and assess failure modes and the effect of structural parameters of honeycomb sandwich structure. The semi-finite element model of honeycomb sandwich structure under four-point bending load is established by a parametric method. Laminate delamination is exhibited by a contact algorithm with the mixed-mode damage model. Experiments are conducted to obtain load-displacement curves of honeycomb sandwich structure and thereby verify the applicability of finite element model. The failure modes of honeycomb sandwich structure have also been identified by comparing the experimental results with the numerical results. The effects of structural parameters on the mechanical properties of honeycomb sandwich structure are discussed. Results demonstrate that the overall stiffness of honeycomb structure is closely related to the honeycomb cell size such as length, height and foil thickness. In addition, the strength of honeycomb sandwich structure is sensitive to stacking sequence of composite laminate with different fiber orientation. The main failure modes of honeycomb sandwich structure are laminate fracture, delamination, core buckling and wrinkling. The achievements in this study have guiding significance to design high-performance sandwich structure.

Machine‐learning‐enhanced tail end prediction of structural response statistics in earthquake engineering

AbstractEvaluating the response statistics of nonlinear structures constitutes a key issue in engineering design. Hereby, the Monte Carlo method has proven useful, although the computational cost turns out to be considerably high. In particular, around the design point of the system near structural failure, a reliable estimation of the statistics is unfeasible for complex high‐dimensional systems. Thus, in this paper, we develop a machine‐learning‐enhanced Monte Carlo simulation strategy for nonlinear behaving engineering structures. A neural network learns the response behavior of the structure subjected to an initial nonstationary ground excitation subset, which is generated based on the spectral properties of a chosen ground acceleration record. Then using the superior computational efficiency of the neural network, it is possible to predict the response statistics of the full sample set, which is considerably larger than the initial training sample set. To ensure a reliable neural network response prediction in case of rare events near structural failure, we propose to extend the initial training sample set increasing the variance of the intensity. We show that using this extended initial sample set enables a reliable prediction of the response statistics, even in the tail end of the distribution.HIGHLIGHTSA new Monte Carlo method is developed that provides the response statistics of a nonlinear system in the tail end of the distribution.A nonstationary filter is applied to a Gaussian white noise to generate realistic artificial earthquake records.An extended training strategy using neural networks is proposed to improve the reliability of the method in the tail end of the distribution.The new strategy reveals a significant speedup as well as a prediction of the response statistics in the tail end with high confidence.