Influence Of Geometric Imperfections Research Articles

Additive manufacturing error quantification on stability of composite sandwich plates with lattice-cores through machine learning technique

Architected lattice structures are designed to achieve specific mechanical properties while maintaining relative lightweight. Additive Manufacturing (AM) facilitates the fabrication of lattice structures with complex geometries. However, manufacturing imperfections, e.g., node dislocation, radius variation, and waviness, inevitably affect the performance of composite structures, of which the impact is significant yet difficult to quantify. Herein, a virtual model-assisted AM error quantification scheme is proposed to alleviate this challenge. The influence of geometric imperfections on the static buckling behaviour for sandwich lattice-core panels is investigated. A recently developed Extended Support Vector Regression (X-SVR) is utilized to alternatively bridge multiscale analyses. By integrating the sampling and virtual modelling methods, the effect of AM errors can be comprehensively quantified with statistical moments, probability density function (PDF), cumulative distribution function (CDF), etc. Furthermore, high computational efficiency, robustness, and other inherent features highlight the applicability of the proposed AM error quantification scheme in engineering.

The influence of geometric imperfections on post-buckling behavior and free vibrations of a fiber-reinforced composite laminated plate under thermal loading

The influence of geometric imperfections on post-buckling behavior and free vibrations of a fiber-reinforced composite laminated plate under thermal loading

SLENDER COLUMN STRENGTH OF INNOVATIVE CONCRETE FILLED STEEL TUBE COLUMNS WITH HIGH‐PERFORMANCE BUILDING MATERIALS

AbstractThis paper presents a comprehensive experimental and numerical study on the load‐carrying behaviour of innovative high performance materials steel‐concrete composite columns: Namely concrete‐filled steel tube columns with solid steel core (CFSTCSC) and concrete‐filled double steel tube columns (CFDST). The experimental results exemplify the basic load‐carrying behaviour. In addition to that, the application range of high‐strength materials is evaluated in relation to the slenderness. Finally, the influence of geometric imperfections on the load‐carrying behavior is investigated based on the manufacturing tolerances of such multi‐component cross‐sections.

Structural analysis of unreinforced masonry spiral staircases using Discrete Element modelling

Unreinforced masonry spiral staircases have been built for more than two thousand years in castles, churches and palaces, and these staircases require structural assessment. For a few decades, the structural behaviour of “cantilever” staircases has been debated among scholars. Several structural methods have been used, but due to the complex 3D geometry and the substantial number of treads, a priori assumptions have been made about the magnitude and point of application of the contact forces between the treads and the wall-tread connections. These assumptions influence the calculation of torsional moment, which, in some methods, reaches high values that could generate shear stresses greater than the material’s strength. In this paper, a 3D model based on one helix of the “cantilever” spiral staircase of San Domingo de Bonaval, in Spain, has been analysed using the Discrete Element Method. The entire stair is analysed without making assumptions on the magnitude and location of the resultant contact forces, which are calculated for each tread using customised Python-based functions. The wall-tread connections have been modelled using rigid blocks, and several contact conditions have been investigated. Moreover, different friction angles and the influence of geometrical imperfections are analysed to simulate material tolerances and assembly imprecisions. The simulation results indicate that perfect wall-tread contact conditions lead to conservative predictions of the torsional moment. Instead, gaps and imperfections allow small displacements, which reduce the torque and increase compression forces in the inner helical ring of the stair. Low friction angles could increase the torsional moment values, while vertical settlements do not cause a significant effect. Cantilever situations could still occur due to not perfect contact conditions between consecutive treads, which suggests that the tread-tread contact area should be carefully inspected during restoration. More generally, this paper demonstrates the potential variability of the structural behaviour of highly indeterminate structures when boundary conditions are uncertain, while providing valuable context to inform restoration strategies.

Influence of geometric imperfections on the nonlinear forced vibration characteristics and stability of laminated angle-ply composite conical shells

The forced vibration characteristic of laminated composite truncated conical shell has been analyzed by including von Karman kinematic non-linearity. The geometric imperfection is included in the analysis by providing an initial doubly sinusoidal transverse displacement. The finite element analysis has been carried out using the displacement field of FSDT and the constrained strain terms are interpolated using field consistent modified shape functions in order to avoid membrane/transverse shear locking. The steady state periodic response has been obtained by solving the governing equations in time domain using modified shooting method and arc length/pseudo-arc length continuation techniques. The main aim of the paper is to explore the effects of initial imperfections, fiber-angle and curvature on the nonlinear periodic response characteristics. Further, the stability of the periodic response has also been investigated and the ensuing bifurcations resulting in loss/gain of stability has been discussed. The parameters affecting the softening/hardening nonlinear behavior of the conical shells have also been assessed. The nonlinear frequency response reveal greater amplitude during inward half cycle due to destabilizing nature of the nonlinear membrane stress resultants during inward motion at large amplitudes. Multiple stress reversals is observed during a periodic cycle which has large ramifications on the fatigue design.

Influence of imperfection sensitivities on postbuckling of laminated cylindrical panel under axial load: Numerical and experimental investigation

Influence of geometric imperfections on postbuckling of layered (laminated) composite cylindrical panels has been performed under axial compression load using finite element code, ANSYS and validated experimentally. Finite element code was initially validated with available literature for performing the further analyses on the panel. Eigen imperfection irregularities were considered for predicting postbuckling loads of layered composite cylindrical panels with SSSS and SFSF boundary conditions with different r/t ratio and ply sequence and compared the results. Glass-polyester laminated cylindrical panels were fabricated and tested using fixture which accommodates different boundary conditions for investigating the postbuckling phenomenon. Experimental postbuckling analysis was carried out to validate the finite element analysis results and found satisfactory. The influence of imperfections with different r/t, stacking sequences with SSSS and SFSF boundary conditions were carried out and compared. As the r/t ratio of the cylindrical panel increases the postbuckling load decreases for a given boundary conditions and with magnitude of imperfection sensitivities. It has been observed that SFSF boundary conditions with angle play layup sequences taking more axial loads than SSSS boundary conditions with same layup sequence and imperfection sensitivity.

Influence of geometric imperfections on the free vibrational response of the functionally graded material sandwich plates with circular cut-outs

The influence of circular cut-outs and geometric imperfection on the free vibration analysis of functionally graded material (FGM) sandwich plates with (2-1-2) plate configuration conditions has been investigated in this paper. Geometric imperfections, such as sine-type and global-type imperfections, are especially susceptible to plate vibration analysis, and these imperfections can be considered while studying plate vibration behavior. The governing equations are formulated based on the Lagrangian principle for the vibration analysis of the FGM sandwich plates subjected to the simply-supported and clamped boundary conditions. The results have been obtained using a C0-continuity isoparametric formulation with four noded elements having seven degrees of freedom per node. The accuracy of the present results has been confirmed by comparing the present results with the reported literature.

Research on Hysteretic Behavior of Cold-Formed Thin-Wall Rolled Edge Channel Steel Flexural Members

The finite element software ABAQUS is used to calculate and analyze the mechanical performance of cold-formed thin-walled curved channel steel members under horizontal reciprocating load. Double nonlinear finite element model needs to be considered, the influence of geometric imperfection and residual stress. The accuracy of the results was verified by comparing with the relevant test results. On the basis of controlling the main parameters such as width-thickness ratio, axial compression ratio, slenderness ratio and buckling mode, the numerical simulation results of 9 hysteretic specimens were selected to research the influence of the above factors on the hysteretic performance of the flexural members. The analysis results show that the width to thickness ratio, axial compression ratio and slenderness ratio have great influence on the hysteretic performance of the flexural members. The larger the three main parameters are, the worse the bearing capacity, ductility and energy consumption of the members will be. Therefore, the design should avoid as far as possible to choose a larger width-thickness ratio and slenderness ratio section components.

COMPUTER SIMULATION IN THE PROBLEMS OF STABILITY OF THIN-WALLED RODS OF AN OPEN PROFILE WITH SHAPE IMPERFECTIONS

The presented numerical methodology is based on the finite element method (FEM) and computational procedures of the NASTRAN software package. It allows to investigate the influence of geometric imperfections in the shape of thin-walled rods of open profile on the critical values of the load, the shape of the stability loss and the stress-strain state. It has been developed an algorithm for computer modeling of initial imperfections in the shape of thin-walled rods, which is implemented in the NASTRAN software package using a neutral NASTRAN PC file and a specially developed program written in FORTRAN language and adapted to this software package. Geometric imperfections of the rods can be represented as their form of loss of stability or the form of deformation from the action of the load with the possibility of varying the maximum value of the imperfections amplitude. Computational procedures for solving the Lanczos stability problem and the geometrically nonlinear static problem by the Newton-Rafson method can be used to model imperfections. The program developed by the authors allows to form new nodal coordinates of a finite-element model of rods and to visualize geometric imperfections in a given scale. The article provides a step-by-step description of finite-element construction models of thin-walled rod of open profile with an ideal surface and taking into account the imperfection of the form, which is presented as the first form of loss of rod stability from longitudinal load applied with eccentricity. With the help of the FEMAP NASTRAN preprocessor is forming the geometry of the middle surface of an ideal rod, and setting the mechanical characteristics of the material, boundary conditions and load. The middle surface of the rod is fed as a set of flat quadrangular finite elements with six degrees of freedom in the node. In the article, a linear calculation of the stability by the Lanzosch method is performed to obtain the form of rod geometric imperfection. Setting the maximum amplitude of imperfections was performed using the program developed by the authors. Using the Newton-Rafson method, the geometrically nonlinear problem of rod statics with a given shape imperfection is solved, the critical value of the longitudinal load is determined, and the corresponding form of the rod stability loss is obtained. The presented numerical technique and the developed algorithm of computer modeling of shape imperfections allow to investigate in nonlinear formulation the stability of open profile thin-walled rods taking into account geometric imperfections of different amplitude as different forms of rod deformation, including the form of stability loss, to assess the impact of imperfections on the critical value of the load, the form of stability loss and stress-strain state. The presented algorithm and numerical technique can be used to study the stability of such thin-walled structural elements as shells, plates and others.

Stability behaviour of stiffened curved plates subjected to pure compression

This paper investigates the stability behaviour and load carrying capacity of longitudinally stiffened, transversally curved steel plates under compressive stresses. The behaviour of stiffened, curved plates is a complex problem, especially due to the interaction of curvature, relative stiffness of the stiffeners and initial imperfections. A comprehensive parametric study is presented to investigate the effects of curvature, plate slenderness, size and shape of stiffeners on the ultimate resistance of stiffened curved plates. The aim of the study is to explain the behaviour of such structures and to demonstrate the benefits that can be obtained from bridge decks with curved plates. From the results some important conclusions are drawn regarding the structural behaviour and the positive effects of curvature on the cross-sectional resistance. A study on the influence of geometric imperfections on the load-bearing capacity is presented, which is based on the modification of nodal coordinates by means of sine-shape functions.

Microstructure/geometric imperfection sensitivity on the thermo-mechanical nonlinear stability behavior of functionally graded plates using four variable refined structural kinematics

The present work deals with the nonlinear stability characteristics of geometrically imperfect shear deformable functionally graded plates (FGP) subjected to thermo-mechanical loads. The equilibrium, stability, and compatibility equations are derived using trigonometric shear-strain function based refined shear deformation plate theory. The displacement field used in the present study has been employed for FGP for the first time. The in-plane and transverse displacements consist of bending and shear components, whereas the displacement field contains only four unknowns. Geometric nonlinearity has been incorporated in the formulation in a von-Karman sense. A generalized porosity model has also been developed to accommodate both even and uneven porosity distribution reported in the literature. Various models of geometric imperfection have been modeled using imperfection function. An exact expression for the critical buckling load and critical buckling thermal load of geometrically imperfect porous FGPs for various loading conditions have been developed. After ensuring the excellent accuracy of the developed expression, the influence of geometric imperfection, porosity inclusion, and geometric configuration on the nonlinear stability of FGPs has been discussed extensively. The results presented in this paper will be used as a benchmark for future research.

Influence of geometric imperfections on the efficacy of optimization approaches for grid-shells

The current literature provides a wide range of examples of structural optimization based on different strategies and mainly finalized to obtain light solutions safe toward strength and stability requirements. Recently, many studies focused the attention on the role of geometric imperfections that inevitably arise during the construction process by leading to an alteration of the ideal shape at the basis of the optimization process. This occurrence could particularly affect the safety level of the obtained optimized solution. Aim of the present paper is to assess the efficacy of some approaches previously carried out by the authors for the structural optimization of grid-shells here specifically considering the presence of geometric imperfections. To this purpose, numerical analyses are presented in the paper by introducing different geometric imperfection scenarios and also accounting for different case studies.

Influence of geometric imperfections on the axially loaded composite conical shells with and without cutout

The nonlinear stability analysis of a structure with initial geometric imperfections is very complex, difficult, and unsolved yet in designing. At present, there are no unified design guidelines for imperfection sensitive metal shells (spherical, cylindrical, conical, and so forth), and the study about composite shell structures is often for a specific ply parameter and therefore less adaptable. In this paper, the imperfection sensitivity analysis of orthotropic conical shells with and without cutouts under compression is investigated numerically. The eigenmode-shape imperfections and dimple-shape imperfections are introduced to conical shells with different cutout sizes. In order to find the worst imperfections that can reduce the buckling load as far as possible, an optimization framework based on the multiple perturbation load approach is developed by the present authors to search the possible positions of dimple-shape imperfections; the effectiveness of the algorithm has been proved by comparing with other conventional approaches.Mid-surface imperfections, a type of realistic imperfection, transferred from a cylinder are considered for a conical shell with a cutout at last. This work can provide a reference value for conical shell design for practical engineering applications.

Influence of Geometric Imperfections on Buckling Resistance of Reinforcing Bars during Inelastic Deformation.

This paper presents the results of numerical simulations on three main factors and their influence on the buckling resistance of reinforcing bars and on their behaviour in the range of postcritical deformations. These three factors are the shape of initial deformation, the amplitude of geometric imperfection and the slenderness of bars. The analysis was made of bars fixed on both sides for three initial shapes of deformation between adjacent stirrups, four amplitudes of geometric imperfections and eight bar slendernesses. The results of the numerical analyses carried out showed that the factors analysed have a very high influence on the inelastic buckling of the bars. The initial deformation shape, the radius of curvature and the slenderness of the bars have a significant influence on the buckling resistance of these bars and their longitudinal and transverse deformations. The research demonstrates that bars which are bent or compressed initially have a smaller resistance to buckling compared to straight bars, as the amplitude of geometric imperfections increases and the slenderness of the members increases. However, for the deformation shape of the bars, which is accompanied by shear forces, the drop in the buckling resistance of the members is small, and resistance to buckling for items with a small slenderness was higher than that of straight bars.

Influence of flange dimensions and geometrical imperfections on stress concentrations at welded flange necks

AbstractRing flange connections for tubular towers, like those for wind turbines or chimneys, are subjected to significant fatigue loading. Next to the bolts, the weld connecting the flange to the tower shell also needs to be checked against fatigue failure. The flange causes local bending moments in the shell, which increase the meridional stress, i. e. stress concentrations occur. In this paper, the influence of geometrical imperfections on such stress concentrations is quantified and the influence of flange geometry on resulting stress is investigated. Recommendations are given for flange dimensions and the design procedure.

Buckling of launch-vehicle cylinders under axial compression: A comparison of experimental and numerical knockdown factors

Metallic grid stiffened cylinders are often used as tank and interstage structures in launch-vehicle systems. When subjected to axial compression, these thin-walled shells are prone to buckling. The corresponding critical buckling load heavily depends on deviations from the ideal shell shape.In general, these deviations are defined as geometric imperfections and they can significantly reduce the critical load. Considering the influence of geometric imperfections into the design process of thin-walled shells poses major challenges for structural design.This article presents an overview regarding the modelling, analysis and design of metallic grid stiffened launch-vehicle cylinders. In comparison to commonly studied unstiffened cylinders, complex shells applied in aerospace engineering can have a completely different structural response to axial compression than their unstiffened counterparts. Advanced shell buckling design conceps like perturbation approaches and energy barrier criteria are applied and validated with experimental data. Finite element models are presented and described in detail. Important aspects like skin and weld buckling as well as the influence of cutouts are analyzed and discussed.

Critical buckling load of pile in liquefied soil

Buckling instability has been recently identified as a possible mechanism of pile failure in liquefiable deposits and this failure mechanism is not explicitly mentioned in most design codes. To carry out routine design and checking, it is necessary to reliably estimate the critical buckling load of pile for a given liquefiable site. However, the existing calculation methods for the critical buckling load of pile in liquefied soils do not consider the influence of geometric imperfections and nonlinear behavior of the pile. In this paper, an efficient approach using the Beam on Nonlinear Winkler Foundation (BNWF) model is proposed to calculate the critical buckling load of pile in liquefied soils considering geometric imperfections and nonlinear behavior of the pile. The method is verified and validated using the finite element method and results from centrifuge tests. Furthermore, parametric analysis has been carried out to understand the influence of buckling load for different soil relative density, initial geometric imperfections of pile, flexural rigidity of pile, and pier height. It is found that the critical buckling load of pile in liquefied soils increases with the increase of soil relative density and flexural rigidity of pile, and decreases with the increase of initial geometric imperfections of pile and pier height. Finally, a simplified estimation method based on Euler buckling theory is provided for predicting critical buckling load of pile in liquefied soils and an example is taken to show the application.

Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects

This paper studies nonlinear free vibration characteristics of nonlocal magneto-electro-elastic (MEE) nanobeams resting on nonlinear elastic substrate having geometrical imperfection by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All of previously reported studies on MEE nanobeams ignore the influences of geometric imperfections which are very substantial due to the reason that a nanobeam cannot be always perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric constituent in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam are dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and geometrical imperfection.

Influence of initial geometric imperfections on the 1:1:1:1 internal resonances and nonlinear vibrations of thin-walled cylindrical shells

The analysis of internal resonances in continuous structural systems is one of the main research areas in the field of nonlinear dynamics. Internal resonances enable the transfer of energy between the related vibration modes, usually leading to new phenomena that have a profound influence on nonlinear oscillations, bifurcations and dynamic instabilities. Shells of revolution usually exhibit internal resonances due to their inherent circumferential symmetry and dense frequency spectrum in the lower frequency range, which may lead not only to m:n internal resonances but also to multiple internal resonances. In this work, the nonlinear response of an imperfect circular cylindrical shell, simply supported at the edges, to harmonic excitation is studied. Geometries that have two modes with n and n+1 circumferential waves, corresponding to the lowest natural frequency, are identified. These two modes are driven to resonance, with each being in one-to-one internal resonance with its companion mode, thus leading to a possible 1:1:1:1 internal resonance, a topic rarely investigated in the technical literature. The investigation of internal resonances in continuous systems is usually conducted using low-dimensional discrete models. Here, using a perturbation procedure, a consistent modal expansion is derived for an arbitrary number of interacting modes, leading to reliable low-dimensional models. Using the discrete models derived in this way, the shell nonlinear dynamics is explored by using bifurcation diagrams of the Poincaré map, continuation techniques and the Floquet stability criterion. The importance of internal resonances to the nonlinear vibrations and instabilities of the shell is clarified. It is well known that small geometric imperfections in the order of the shell thickness have a strong influence on the buckling and post buckling behavior of a thin-walled shell. However, their influence on internal resonances, dynamic instability and energy transfer is largely unknown. Thus, a detailed parametric analysis that considers different types of modal imperfection is conducted in the present work, and the influence of such imperfections on the activation of energy exchanges between the modes involved is analyzed. The results confirm that the form and magnitude of initial geometric imperfections have a profound influence on the results, enabling or preventing the transfer of energy among the resonant modes being considered. • Derivation of a consistent modal expansion by a perturbation procedure considering arbitrary number of interacting modes. • The influence of geometric imperfections on internal resonances, dynamic instability and energy transfer between modes. • Analysis of 1:1:1:1 internal resonance considering four vibration modes with the same natural frequency. • The dynamic bifurcations are sensitive to the form and magnitude of initial geometric imperfections.

Prediction of the elastoplastic in-plane buckling of parabolic steel arch bridges

In this paper, a modified eigen-buckling algorithm based on eigenvalue analysis was presented for evaluating the in-plane buckling strength of parabolic steel arch bridges. The buckling strength of parabolic arches under uniformly distributed vertical loads was studied. The slenderness parameter was modified to unify the buckling curves. Parametric analysis was carried out to study the applicability of the new algorithm. Finally, a case study regarding the bearing capacity of a steel arch bridge was performed to verify the proposed method. The results showed that the influences of geometric imperfections, rise-to-span ratio, and material yield strength of parabolic arches were taken into account by modifying the slenderness parameter. The buckling strength results of the arches using the modified dimensionless slenderness agreed very well with the straight column buckling curves in the specifications. The modified eigen-buckling algorithm provided very high accuracy in buckling strength assessment for parabolic steel arch bridges when the span was less than 200 m. The modified eigen-buckling algorithm predicted the load-bearing capacities of the arch bridge very well. Hence, the proposed method can be used for preliminary buckling strength evaluations in the bridge design stage.