Effects Of Geometric Imperfections Research Articles

Static Bending and Vibration of Composite Nanobeams Taking Into the Effect of Geometrical Imperfection

Static Bending and Vibration of Composite Nanobeams Taking Into the Effect of Geometrical Imperfection

Buckling and post-buckling analysis of three-layer shallow arches with geometric imperfections and interlayer slip

In this paper, a semi-analytical solution is derived to capture the nonlinear stability and equilibria of shallow three-layered arches with flexible bond, which also accounts for the interlayer slip (i.e., the relative displacement between the layers). The member axis can have arbitrary geometric imperfections. With the equations presented, for the first time, the complete stable and unstable equilibrium paths can be predicted including multiple remote equilibria, which may occur in the presence of an imperfect member axis but cannot be determined with finite element simulations. Expressions for the direct prediction of critical loads for limit point buckling and bifurcation buckling are also provided, which may also be on the remote unconnected equilibrium paths. In several application examples, the effect of geometric imperfection and interlayer slip on the critical loads and nonlinear equilibria is revealed. Comparative finite element analyses with plane stress continuum elements demonstrate the accuracy and computational efficiency of the presented theory.

Imperfection Sensitivity of Plastic Shear Buckling Behavior in Corrugated Web Stainless Steel beams

AbstractThe shear behavior of corrugated web beams can be highly sensitive to the presence of initial imperfections. The designer has, in general, no prior information about the mechanical and geometric imperfections of welded elements. As a solution, in a FEM‐based design, the eigen buckling deformations with an equivalent maximum magnitude are included as an equivalent initial imperfection in a nonlinear analysis to account for the simultaneous effects of geometric imperfections and residual stresses. Previous researchers investigated the effects of initial imperfections in the form of different eigenmodes found via linear buckling analysis. They concluded that the shear strength rises with mode number, with the first mode providing the most crucial condition. However, it is shown in this paper that such a methodology is not applicable to stainless steel corrugated web beams in the medium slenderness ratio range when shear yielding precedes shear buckling. It is observed that, unlike in elastic buckling, in plastic buckling the first buckling mode does not result in the minimum strength. The results show that in FEM‐based design, using the first mode instead of the critical mode as the shape of the initial imperfection can result in a maximum of 19% and 31% overestimation of the ultimate shear capacity for the imperfection amplitudes of tw and hw/200, respectively.

2D calculation of parasitic fields in misaligned multipole electron-optical systems

The effects of geometrical imperfections in electron-optical components are usually evaluated in 3D simulations. These calculations inherently take a long time, require a large amount of memory, and do not directly produce the necessary axial field functions. We present a 2D perturbation method to calculate parasitic fields in misaligned multipole systems. Our method is based on finding an equivalent potential perturbation, similarly to Sturrock’s method, but does not rely on the potential being differentiable. The method is directly applicable to both electrostatic and non-saturated magnetic problems. It does not require any 3D data and it is fully compatible with existing finite element method codes such as EOD. The proposed method produces axial field functions with an accuracy of units to a few tens of percents, depending on the number of unperturbed multipole field components used and the geometry. The results can then be used, for instance, to determine the parasitic imaging aberrations of the misaligned optical system using standard methods, in order to evaluate the effect of mechanical design tolerances.

Nonlinear dynamic modeling of geometrically imperfect magneto-electro-elastic nanobeam made of functionally graded material

Smart magneto-electro-elastic (MEE) structures with high performance are highly valuable across a vast range of aerospace and industrial applications like smart sensing, space robotics, energy harvesting and biomedical research. This work focuses on the nonlinear dynamic response of a functionally graded MEE nanobeam. Initial geometric imperfection including global and localized imperfection modes is considered to reflect the effect of undesired error during nanofabrication process. Such geometric imperfection is involved by the product of hyperbolic and trigonometric functions. The nonlinear dynamic model for the FG-MEE nanobeam is established according to Hamilton’s principle and nonlocal constitutive relation to derive its governing equations of motion. The interaction between the imperfect FG nanobeam and its multi-physical stimulus is numerically solved via differential quadrature method. After validating the proposed model with existing works, the parametric study is conducted to fully reveal the coupling effect of geometric imperfection and numerous parameters including imperfection mode and amplitude, external electric and magnetic potentials, functionally graded index, boundary constraint and size-dependent parameter on nonlinear dynamic response of the FG-MEE nanobeam. Simulation results have demonstrated the significance of the MEE coupling effect, which can be used as a guide to design smart and advanced devices for aerospace and industrial applications.

Large scale fire resistance tests of prestressed continuous steel–concrete composite beams to evaluate the effects of geometric imperfections

Little attention has been devoted to exploring the effect of geometric imperfections under fire conditions. To bridge this knowledge gap, this paper presents findings from five large scale fire tests on prestressed continuous steel–concrete composite beams (PCCBs) designed to investigate the effect of initial geometric imperfection (IGI) on the fire resistance of PCCBs. The examined parameters include several IGI modes, load levels, and prestress levels. Various fire responses were monitored and recorded during these tests, such as cross-sectional temperature rise, mid-span deflection, prestress in the cable strands, and side-support reactions. The results of these fire tests indicate that PCCBs with the initial mode of flexural–torsional buckling at the middle support applied as an IGI had larger mid-span deflection and lower critical temperature relative to that of the beams without IGI. The same beams also underwent a larger degree of relaxation in prestress levels, thus reaching failure at a faster pace. Our findings also indicate that while the end-support reactions were redistributed when exposed to fire, the side-support reactions decreased at the first stage of fire exposure and then gradually increased toward the final stage of the fire exposure. Evidently, for PCCBs with IGI, the side-support reaction towards the end of the fire tests is larger than the initial reaction. To complement the conducted fire tests, a series of finite element (FE) models were developed to further study the effect of IGIs in terms of the fire response of PCCBs.

Highly efficient mesh-free approach to simulate the non-linear bending analysis of FG porous beams and sandwich beams with FG face sheets

The main objective of the present work is to propose a coupling of the Radial Point Interpolation Method (RPIM) with variable shape parameter to High Order Continuation Method (HOCM) for analyzing the geometrically non-linear behavior of porous Functionally Graded (FG) isotropic and sandwich Timoshenko beams by taking into account the non-linear shear deformation. The FG and FG Sandwich Beams (FGSB) effective material properties are assumed to vary continuously in the thickness direction according to a power-law index. The porosity is modeled as the stiffness reduction criteria and included in the mixture rule. The strong form of the non-linear equations governing porous FG and FGSB beams are obtained using the principle of virtual displacements in the framework of First-Order Shear Deformation Theory (FOSDT). The HOCM is used to compute the solution of the non-linear problem by a transformation to recursive succession of linear problems using Taylor series expansion. The continuation technique is used to obtain the complete solution path in a step by step manner. The effectiveness and accuracy of the proposed coupling is brought out through numerical examples which concern porous FG isotropic and FG sandwich beams. The optimal parameters have been defined according to the stability analysis of the proposed solver, and then used to investigate the effect of boundary conditions, showing the effect of the power-law index, effect of geometric imperfections, and face sheet-core-face sheet thickness ratios on deflections. The validation is done by comparing the obtained results to those available in the literature and/or those computed using Finite Element Method (FEM).

The effect of geometric imperfections on the mechanical response of isotropic closed-cell plate lattices

Cubic+octet plate-lattices, whose unit cell comprises plates aligned along simple-cubic and face-centered-cubic planes of crystal structures, have attracted scientists and engineers because of their isotropic, near-optimal mass-specific performance that reaches theoretical upper bounds on stiffness and strength at low density. While their structural efficiency has been recently examined analytically, numerically and experimentally, their sensitivity to geometric imperfections has remained elusive. Here, using finite element simulations, we present sensitivity of the macroscopic mechanical properties of the plate-lattices to two types of geometric imperfections: namely, periodically distributed defects, characterizing plate waviness and displaced intersections, and randomly dispersed defects, representing missing plates, observed in their additively manufactured samples. Our results show that the randomly dispersed imperfections lead to a greater reduction in the Young's modulus and yield strength than its counterpart across all relative densities under consideration, while their scaling relations with the relative density remains linear, confirming their structural efficiency attributed to stretching-dominated behavior even with the presence of the imperfections. This study sheds light on previously elusive sensitivity of the plate-lattices to the geometric imperfections and provides understanding of their defect-dependent mechanical performance.

An FFT-based method for estimating the in-plane elastic properties of honeycomb considering geometric imperfections at large elastic deformation

The geometric imperfections in honeycomb cells inevitably arise during the manufacturing process and can affect the honeycomb’s mechanical performance. Hence, it is critical to identify and quantify the geometric imperfections and characterize the effects of these imperfections on the effective mechanical properties of honeycomb. In this study, the geometric imperfections inside the honeycomb were identified from micro-CT scan data. Using the obtained geometric topology, a Fast Fourier Transform (FFT) based method was employed in combination with the composite pixel method to predict the effective in-plane elastic properties of honeycomb at large elastic deformations. The results of the nonlinear homogenized prediction were compared with the experimental data and the prediction values from analytical models to investigate the effects of geometric imperfections. It was found that the predictions from the FFT-based method agreed well with the experimental results. However, the predictions from the analytical models significantly overestimated or underestimated the elastic properties, indicating that the geometric imperfections inside the honeycomb significantly influence its in-plane elastic properties.

Auxetics and Other Systems with Unusual Characteristics

Auxetics and Other Systems with Unusual Characteristics

Bending Performance and Failure Behavior of Wooden Sandwich Panels with Corrugated Cores

Wooden sandwich panels with a corrugated core have not been the subject of scientific research so far. The anisotropic properties of the wood make it challenging to form corrugated shapes. Therefore, it is decided to determine the effect of geometric imperfections of the corrugated core made of wood veneers on the stiffness and strength of sandwich panels and the core elasticity modulus. The beams are manufactured in industrial conditions and subjected to three‐point bending. The research is carried out in the form of tests and numerical calculations. It is demonstrated that geometric imperfections of the core affect the stiffness and strength of sandwich panels. The modulus of elasticity can reach values lower by up to 37% and the strength by up to 24% compared with reference panels with an ideal, symmetrical core geometry. However, their average linear elasticity modulus (1449 MPa) indicates excellent construction properties. Under the tests, four stages of beam bending are revealed. The last stage means that panels can increase stiffness even after the core is destroyed. The corrugated core's modulus of elasticity is also determined.

Wind fragility assessment and sensitivity analysis for a transmission tower-line system

Wind fragility is essential to performance-based wind engineering, risk, and resilience assessment for transmission towers. However, it has not been sufficiently studied due to the key issues in performance evaluation and uncertainty treatment for transmission towers. The performance of high-rise structures can be severely weakened by geometric imperfections, but these impacts have not been well addressed for transmission towers. Besides, the current uncertainty treatment only considers the tower itself although the transmission tower is part of an interconnected tower-line system that has complex interactions with wind environment. Therefore, this paper provides a systemic solution for geometric imperfections of transmission towers, where the users can clearly observe the effect of geometric imperfections on the capacity and failure positions of transmission towers. On this basis, a wind fragility framework that incorporates the uncertainties of each line component, wind environment, and aerodynamic parameters is proposed for transmission towers. Finally, sensitivity analysis was conducted to identify the significant uncertainty parameters for tower capacity and demand by sensitivity diagram. It is found that in addition to the uncertainties of the tower itself, the uncertainties of wind profile exponent, outer diameter and aerodynamic parameter of conductors have significant effects on the fragility of transmission towers.

Thermo‐mechanical nonlinear stability analysis of geometrically imperfect functionally graded plates with microstructural defects using logarithmic structure kinematics: An unified expression

AbstractIn the present paper, thermo‐mechanical stability analysis of geometrically imperfect porous functionally graded plates (FGP) with geometric nonlinearity is presented. The equilibrium, stability, and compatibility equations are derived using Logarithmic structural kinematics in conjunction with the von‐Karman type of geometric nonlinearity. A logarithmic‐based shear‐strain function has been used for the first time for the buckling response of functionally graded material (FGM) plates. Generic imperfection function has been implemented to incorporate the various imperfection modes like sin‐type or global type in the formulation. The effective materials properties of the plates with porosity inclusion have been computed using modified power law. The plate is subjected to uniaxial and biaxial compression as well as combined compression and tension along with thermal loading. An exact expression for the critical buckling load and critical buckling thermal load of geometrically imperfect porous FGM plate for each loading case has been developed. After confirming the excellent accuracy of the current exact solutions, the effect of geometric imperfection, porosity inclusion, and geometric configurations on the nonlinear stability of the FGM plate have been discussed extensively. The results presented in this paper will be used as a benchmark for future research.

Modal localization in vibrations of circular cylindrical shells with geometric imperfections

The present study aims to investigate the effect of geometric imperfections in circular cylindrical shells on the vibration characteristics. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wave-length in the circumferential direction. However, in the presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. The present study has been carried out by means of a semi-analytical approach. Theoretical formulation were derived based on Sanders–Koiter thin shell theory. The analytical results have been compared with those of standard finite element analyses. The results corresponding to the analysis of modal localization are novel and can be used as a benchmark for further studies.

Variability in the Nonlinear Modelling Parameters of Steel I‐shaped Beams Subjected to Cyclic Loading Considering Manufacturing Tolerances

AbstractThis paper focuses on the probabilistic characterization of the cyclic behaviour of steel deep members with European I‐shaped profiles. The variability of the behaviour of the member depends on several factor such as the material variability and geometrical imperfections. The effect of material variability is well recognized by the scientific community and has been considered in international design codes such Eurocode 8. European hot rolled profiles may be produced with some tolerable deviation from the nominal section in terms of shape and dimensions, which are limited by the European standard EN10034. The effect of geometrical imperfections received considerable research attention in the past. However, to the best knowledge of the authors, there are no studies that investigated the effect of the manufacturing tolerances on the behaviour of I‐shaped steel members. The tolerance range on the dimensions of the profile can be significant. The change in the dimensions of the profile changes the web and flange slenderness which may have a significant influence on the flexural behaviour. Thus, the characterisation of the effect of the manufacturing tolerances on the behaviour of the members is of paramount interest. For this purpose, an advanced finite element model, validated with past experimental data, was developed and an extensive parametric study is conducted. Then, statistical methods are used to characterise the variability using different distributions

Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads

This paper presents an investigation on thermo-electro-mechanical nonlinear low-velocity impact behaviors of the geometrically imperfect functionally graded (FG) graphene-reinforced composite (GRC) beam with surface-bonded piezoelectric layers. Both uniformly distributed and FG patterns of graphene nanoplatelets (GPLs) are considered along the thickness of the GRC host beam. The effective Young’s modulus is calculated by the Halpin–Tsai model. The Poisson ratio and mass density are calculated by the rule of mixture. The modified nonlinear Hertz contact law is employed to predict the impact force between the spherical impactor and the geometrically imperfect GRC piezoelectric beam during impacting. By considering the first-order shear deformation theory and von Kármán nonlinear displacement–strain relationship, the nonlinear governing equations are obtained by Hamilton principle and dispersed by differential quadrature (DQ) method. The Newmark-β method associated with Newton–Raphson iterative process is adopted to parametrically identify the impact force and the dynamic response of the system. The effects of geometric imperfection, weight fraction and distribution pattern of GPLs, temperature variation, thickness of piezoelectric layer and impactor’s initial velocity on nonlinear low-velocity impact behaviors of geometrically imperfect GRC beams are discussed in detail. Our results illustrate that the coupling effect of geometric imperfection and thermo-electro-mechanical load has a significant effect on the nonlinear low-velocity impact behavior of GRC beam, and GPLs distributing into the piezoelectric layers is better for reducing the impact response of geometrically imperfect GRC piezoelectric beam.

Modeling and analyze of behaviors of functionally graded graphene reinforced composite beam with geometric imperfection in multiphysics

This paper establishes a mathematical model to analyze the static and dynamic behaviors of functionally graded graphene reinforced composite (FG-GRC) beam with geometric imperfection subjected to thermo-electro-mechanical load. Three different geometric imperfections are considered. Four different distribution patterns of graphene nanoplatelets (GPLs) are taken into consideration. The effective properties of the geometrically imperfect FG-GRC beam are estimated by the modified Halpin-Tsai model and rule of mixture. The nonlinear partial differential governing equations are deduced based on first-order shear deformation theory, von Kármán nonlinear displacement-strain relationship and Hamilton principle, and discretized as ordinary differential forms through the differential quadrature (DQ) method. Newmark-β method and iteration method are employed to numerically solve the governing equations. The effects of geometric imperfection, GPLs and piezoelectric actuators on bending and vibration of the geometrically imperfect FG-GRC beam subjected to thermo-electro-mechanical load are comprehensively investigated. The results clearly demonstrate that the coupling effect of geometric imperfections and thermo-electric-mechanical loads can introduce an additional transverse load acting along the length of the geometrically imperfect FG-GRC beam, and hence makes a significant difference on its static and dynamic behaviors.

On the buckling load estimation of grid-stiffened composite conical shells using vibration correlation technique

In this paper, the vibration correlation technique (VCT) has been used as a nondestructive method for predicting the buckling load of grid-stiffened composite conical shells. This technique is capable of predicting the buckling load of structures without reaching failure point through modal testing. The grid-stiffened composite conical shell has been fabricated using the filament winding process. To perform the experiment, the fundamental natural frequency of the specimen is measured under stepped axial compression loading. The procedure is followed up without actually reaching the instability point when the structure collapses and is no longer usable. A finite element model has been built using ABAQUS software considering the effect of geometric imperfection in order to determine the correlation between natural frequency and applied compressive load. A comparison of the experimental and numerical approaches indicated that the difference between numerical buckling loads and those obtained via the VCT is negligible. Moreover, the VCT has provided a reliable estimate of the buckling load, especially when the maximum applied load is greater than 67% of the experimental buckling load.

Влияние геометрических несовершенств сжатого пояса на несущую способность подкрановых балок с усталостными трещинами в стенке

In order to evaluate the effect of geometric imperfections of the compressed belt on the bearing capacity of crane beams with fatigue cracks in the wall, the authors present the results of numerical studies that were carried out using finite element modeling. There has been developed and implemented an algorithm for taking into account the imperfections of the compressed belt using the finite element method. There have been obtained dependences of the change in the average normal stresses in the compressed belt on the type of imperfection, the length of the crack, its position in the beam section and the flexibility of the wall. Recommendations are offered for assessing the reduction in the bearing capacity of crane beams with fatigue cracks in the wall.

Coupled dynamics of axially functionally graded graphene nanoplatelets-reinforced viscoelastic shear deformable beams with material and geometric imperfections

This paper is the first to explore the coupled dynamics of geometrically and material-wise imperfect axially functionally graded (AFG) graphene nanoplatelets-reinforced viscoelastic third-order shear deformable beams. Four AFG graphene nanoplatelets distribution patterns are considered. Porosity, as the material imperfection, is modelled using a Gaussian Random Field model. Four thickness-wise functionally graded porosity distribution patterns are modelled. Effects of geometric imperfection are included by assigning an initial curvature to the beam. To consider the influences associated with energy dissipation caused by internal friction, the Kelvin-Voigt model for viscosity is used. External dissipative energy is modelled using a transverse damper. The effective material properties of the AFG beams are calculated using a modified Halpin-Tsai micromechanics model, together with a rule of mixture. Coupled axial, transverse, and rotational motion equations are obtained by employing a Hamiltonian approach and third-order shear deformation. The natural frequencies are obtained using a modal decomposition method. A simplified version of the graphene nanoplatelets-reinforced AFG structure is verified by a computer code-based finite element method. This novel study on the effects of geometrical imperfection on the sensitivity of beams towards porosity imperfections demonstrates the significance of scrutinising the effects of one imperfection on another.