Geometric Imperfections Research Articles

Choice of the shape imperfections model in dynamics problems of a long flexible cylindrical shell subjected to force couples

The issue of modeling geometrical imperfections in the dynamics problems of thin-walled shells was little researched. In cases when the natural modes of shell coincided with its buckling modes, the issue of choosing a dangerous imperfection model did not arise. When these shell modes did not coincide, it was important to investigate and compare the effect of different imperfections models on the static and dynamic characteristics of such shells. The choosing the shape imperfections model of a long flexible cylindrical shell subjected to force couples, the natural and buckling modes of which did not coincide, was studied using procedures of the finite element analysis software NASTRAN. The shell wall as a set of plat rectangular elements with six degrees of freedom at the node in the cylindrical coordinate system was modeled. The action of force couples as the concentrated forces were distributed at the nodes of the shell edges in accordance to the presentation of A.S. Volmir. The linear buckling problem and the geometrical nonlinear static analysis of the perfect shell by the Lanzosh method and the Newton-Raphson one were performed, respectively. The long half-waves buckling mode was taken as the first shell imperfections model. The modeling of the second shape imperfections as the first natural mode of the perfect shell using the natural vibration analysis by the Lanzosh method was performed. The different amplitudes of geometrical imperfections in proportion to the shell thickness using a program adapted to this software were set. The results of the geometrical nonlinear static analysis of the imperfect shell by the Newton-Raphson method showed that the shape imperfection model in the form of long half-waves more reduced the values of critical buckling loads. Investigations of natural shell vibrations by the Lanzosh method revealed the same influence of different imperfections models on the natural frequencies and natural forms. We think that the shape imperfections model in the form of long half-waves in studies of forced vibrations and dynamic stability of a long flexible cylindrical shell subjected to force couples will be more effective.

Stability of Steel Columns with Concrete-Filled Thin-Walled Rectangular Profiles

This paper provides a numerical and experimental analysis of global stability of axially compressed columns made of thin-walled rectangular concrete-filled steel tubes (CFSTs), with the consideration of initial geometric imperfections. The presented work introduces the theory of stability and strength of composite structural members subjected to axial compressive force. Moreover, a numerical calculation method for the determination of column resistance under axial load is presented, taking into account the influence of second-order effects that are considered in the European standard for the design of such members. This paper also presents the method of creating 3D models using the ABAQUS software, numerical analysis, and comparison of the obtained numerical results with experimental tests. In addition to the actual boundary and load conditions, the real properties of the used materials were also taken into account during the creation of 3D models. The actual properties of the used materials were obtained experimentally. Based on the obtained results and their comparison, several new findings and proven facts about the design and assessment of axially compressed columns made of thin-walled rectangular steel tubes filled with concrete are presented in the conclusions of the paper.

Nonlinear thermomechanical vibration of initially stressed functionally graded plates with porosities

AbstractThe large‐amplitude vibration of initially stressed functionally graded material (FGM) rectangular plates with porosities is investigated in this paper. All edges of the plate are simply supported and uncompressed edges are tangentially restrained. Initial stresses are caused by in‐plane compressive load acting on freely movable edges or thermally induced forces at restrained edges. Pores present in FGM through even and uneven distributions. Material properties are assumed to be temperature‐dependent and, due to the presence of the pores, the effective properties of FGM are determined using a modified rule of mixture. Governing equations in terms of deflection and stress function are established based on the classical plate theory taking into account von Kármán nonlinearity and initial geometric imperfection. These equations are solved using approximate analytical solutions along with the Galerkin method to obtain a time differential equation containing quadratic and cubic nonlinear terms. Nonlinear frequencies are determined by means of numerical integration employing the fourth‐order Runge–Kutta scheme. Parametric studies are carried out to analyze the effects of material and geometry properties, porosity volume fraction and distribution, pre‐existent compressive and thermal loads, imperfection and degree of tangential constraints of unloaded edges on the natural frequencies and nonlinear to linear frequency ratio of FGM plates.

Flexural buckling of press-braked stainless steel Z-section columns: Testing, numerical modelling and design

The flexural buckling behaviour and resistances of press-braked stainless steel Z-section columns are investigated in this paper, based on experiments and numerical modelling. An experimental investigation was conducted on two press-braked stainless steel Z-sections and included material testing, initial geometric imperfection measurements and twelve fixed-ended column tests. Minor-axis flexural buckling was observed for all press-braked stainless steel Z-section column specimens upon testing. The key obtained fixed-ended column test results, including failure loads, load–deformation histories and failure modes, were fully reported. Following the experimental investigation, a numerical investigation was performed, with finite element models developed to validate against the fixed-ended column test results and then used to conduct parametric studies to generate additional numerical data. On the basis of the test and numerical data, the relevant buckling curves, as specified in the European code, American specification and Australian/New Zealand standard, were evaluated and shown to provide accurate and consistent flexural buckling resistance predictions for press-braked stainless steel Z-section columns.

Experimental and numerical investigations towards the lateral torsional buckling of cellular steel beams

This paper deals with the response of so-called “cellular members” against lateral torsional buckling. These beams comprising regularly-spaced circular web openings are especially used for their high resistance-to-weight ratio, the possibility to integrate service pipes within their height, and for aesthetics. Such profiles usually exhibit a complex behaviour and many potential failure modes, including interactional local/global instability modes. Regarding global instability, the members are usually designed by means of approximate design rules, which often lead to an unduly conservative solution, with beams sometimes showing up to 150 % resistance reserves.The present research works aim at improving this situation, through the development of adequate design formulae. In this respect, the present paper reports on investigations led towards improved solutions for cellular members at the experimental and numerical levels. This first paper focuses on experimental activities and on the development and validation of dedicated shell F.E. models. The results of three bending tests on members spanning from 7.5 m to 11 m are reported. Cross-sectional dimensions, material properties and accurate initial geometrical imperfections were measured for each specimen and further introduced in the corresponding F.E. models, which are shown to provide predictions in close agreement with the experimental results. The companion paper [1] further makes use of the F.E. models within extensive parametric studies and proposes a new set of design rules that could be proposed for integration in Eurocode 3.

Structural response of steel sandwich panels with PUR foam core subjected to edgewise compression: Experimental, numerical, and analytical considerations

With the objective of leading to innovative lightweight structural components in the construction sector using sandwich panels with polyurethane foam and steel face sheets, different studies were conducted on such structures, including experimental, numerical, and analytical campaigns. The experimental campaign includes the mechanical characterisation of the constituent materials and the edgewise compressive test of small-scale sandwich panels. The test protocols are detailed, and their influence on the results is assessed. Through the use of digital image correlation recordings, deformation patterns and failure mechanisms in the constituent materials and the composite structure are identified. Material constitutive models are calibrated based on the experimentally obtained results. The accuracy of such models is first evaluated against the stress–strain curves recorded during the experiments. In the second stage, the response of the sandwich panels subjected to edgewise compressive loading is simulated. A parametric analysis on the sensitivity of the numerical models to the initial geometrical imperfections is shown to be fundamental to capturing the behaviour of the sandwich panels. Furthermore, the experimental and numerical results are compared to analytical solutions of the problem of the edgewise compression of sandwich panels. Finally, a thorough discussion of the obtained experimental, numerical and analytical results is presented, along with comparisons to results available in the literature.

Micromechanics of kink-band formation in bimetallic layered composites

Bimetallic layered composites with ultrathin layers possess high strength and hardness, and excellent shock resistance and radiation damage tolerance. However, they are prone to deformation localization and readily form kink-bands when subjected to layer parallel compression. Following this, we carried out extensive plane strain finite element finite deformation analyses to understand and rationalize the experimentally observed kink-band formation in these composites. In the calculations, both constituent materials were assumed to follow a rate-independent isotropic elastic-plastic constitutive relation with an ad-hoc thickness dependent yield strength. Our results demonstrate that in these composites, layer refinement, together with the strength differential between the layers of the constituent materials, is sufficient to trigger kink-banding. Importantly, this phenomenon occurs even in the absence of elastically stiff layers, geometrical imperfections (such as waviness of the layers), and extreme plastic anisotropy within the layers. Additionally, we performed parametric studies to investigate the individual effects of layer thickness, strength differential between the two constituent materials, and strain-hardenability of the materials on kink-band formation. The outcomes of our parametric studies reveal that the strain-hardenability of the constituent materials stabilizes the formation of kink-bands. Furthermore, it leads to a transition from the abrupt formation of through-width kink-bands to the onset and propagation of stable inclined wedge-shaped kink-bands, similar to the experimental observations.

The Ultimate Strength of Fully Transparent Pressure-Resistant Spherical Cabins

The fully transparent cabin used in a manned submersible is typically made of the viscoelastic material polymethyl methacrylate (PMMA). The pressure-bearing capacity of a PMMA-manned cabin was investigated considering the effects of initial geometrical imperfections and large openings. Three types of cabins were studied within the failure mode of nonlinear buckling, including an intact spherical cabin, a spherical cabin with a single opening, and a spherical cabin with double openings. The initial geometrical imperfection ranges from 0.1% to 0.5% of the inner diameter. The ultimate strength decreasing tendency for the different types of cabins with increasing initial imperfection was obtained and the thickness of the hatch cover determined based on the principle of equivalence differed its effects on the strength of the cabin. The influence of the hatch cover stiffness was not linear and indicated the necessity of exploring the coordinated design between the PMMA shell and the metal hatch cover for the transparent cabin.

Experimental and numerical investigation of corroded cold-formed steel channel section columns subjected to in-plane compression and bending

This paper investigates the effect of corrosion on bearing capacity of corroded cold-formed steel (CFS) channel section columns subjected to in-plane compression and bending. Herein, 14 CFS columns with different column lengths and corrosion degrees were investigated. The mass loss rate, surface morphology, and initial geometric imperfections of corroded CFS columns were measured. The eccentric compression test of corroded CFS columns that were accelerated corrosion by the outdoor periodic spray test were carried out. The relationships among the failure mode, load–strain curves and load–axial displacement curves, and mass loss rate were analyzed, and then the deterioration laws of bearing performance of corroded CFS channel section columns were discussed. The non-linear finite element model for corroded CFS columns considering surface morphology was then developed by using Geomagic Studio and ABAQUS. The results indicated that the local and overall initial geometric imperfections of corroded specimens were greater than those of non-corroded specimens. With increasing mass loss rate, the distortional buckling deformation of corroded CFS columns occurred in advance and the failure locations were diversified. Corrosion exhibited a greater impact on the buckling critical load than on the ultimate load and post-buckling strength. The failure positions of corroded CFS channel section columns subjected to in-plane compression and bending were found to be mainly related to the areas with severe corrosion of the flange.

Experimental study on fire resistance of high strength Q960 steel columns under axial compression

In order to obtain the mechanical behavior of H-shaped high-strength Q960 steel column under axial compression in fire, the bearing capacity tests of two Q960 steel columns at ambient temperature and fire resistance tests of six Q960 steel columns at elevated temperature were carried out. By considering different slenderness ratios, load ratios, and heating rates of the test columns, the furnace temperature, column temperature, lateral displacement, and axial displacement were measured and recorded. Then, critical temperature, fire resistance, and failure mode of the columns were obtained. The thermal-mechanical coupling analysis model for the Q960 steel column was established by using ABAQUS finite element analysis software. After verifying the accuracy of the model, parameter analysis was carried out to investigate the effects of load ratio, slenderness ratio, geometric imperfection, thermal creep, residual stress, and steel strength on the fire resistance of steel columns. Based on the test data and analysis results, a fire resistance design method for high-strength Q960 steel columns under axial compression is proposed.

Geometric Imperfection Simulations in Cee-Shape Cold-Formed Steel Members Based on Newly Developed Machine-Vision Inspection Techniques

This paper insightfully studies geometric imperfection simulations of cee-section CFS members from laser-based measurements. A machine-vision imperfection inspection technique is first developed where an algorithm is implemented to automate imperfection characterization from volumetric data. The measured imperfections are statistically analyzed and resemble past measurements from other researchers. Two imperfection simulation approaches are studied, i.e., the modal imperfection simulation method and the 1D spectral simulation method, where strength performance and deformation are predicted from finite element analysis. The analysis results are compared with those of testing. The 1D spectral simulation method is superior where stochasticity and regularity of real im-perfection can be properly addressed. The study provides feasible access to imperfection simulations of cee-section CFS members that other researchers can directly apply. The prediction results can aid the future direct analysis and design of CFS members.

Local–flexural interactive buckling behaviour and design of press-braked stainless steel slender Z-section columns

The present paper reports an experimental and numerical study on the local–flexural interactive buckling behaviour and resistances of press-braked stainless steel slender Z-section columns. A testing programme adopted two press-braked stainless steel slender Z-sections and included material testing, initial geometric imperfection measurements and twelve fixed-ended column tests, with the experimental setups, procedures and results fully reported. The testing programme was accompanied by a numerical modelling programme, with finite element models developed and validated against the fixed-ended column test results; upon validation, parametric studies were conducted to generate additional numerical data over a wide range of cross-section dimensions and member lengths. The obtained test and numerical data were adopted to evaluate the relevant design rules for press-braked stainless steel slender Z-section columns susceptible to local–flexural interactive buckling, as set out in the American specification and European code. It was revealed from the evaluation results that the American specification led to accurate interactive buckling resistance predictions, while the European code resulted in relatively conservative interactive buckling resistance predictions. Finally, a revised Eurocode design approach was developed and provided more accurate and consistent interactive buckling resistance predictions for press-braked stainless steel slender Z-section columns than its original counterpart.

Advanced numerical simulations on S690 cold-formed square hollow sections under compression

Based on a number of numerical investigations into welding simulations, highly non-linear welding-induced residual stresses within high strength S690 welded H-sections have been evaluated successfully, and surface residual stresses along their flange / web junctions have been carefully calibrated against measured data. This modelling technique has been extended to cover residual stresses of cold-formed circular hollow sections recently, and also of cold-formed square hollow sections as described in this paper. Hence, a full presentation on the proposed approach of integrated and coordinated numerical simulations on various mechanical, heat transfer and thermomechanical, and stresses analyses on these cold-formed square hollow sections is described. Subsequent structural analyses of these models on both stocky and slender columns of these cold-formed square hollow sections are then carried out. Structural adequacy of the proposed approach is thoroughly demonstrated through a systematic calibration against various measured data – both temperatures and residual stresses of these sections induced during fabrication, and load-deformation curves of these sections under compression. It should be noted that the proposed approach provides a scientific mechanism to determine directly residual stresses due to transverse bending and longitudinal welding as initial materials imperfections in these high strength S690 cold-formed square hollow sections. With an adoption of the lowest eigenmodes of these columns as their initial geometric imperfections after adjusted with measured or design values of the member out-of-straightness, both the effects of initial materials and of initial geometric imperfections onto the structural performance of these columns are readily quantified separately.

Novel Imperfection Method for Post-Buckling Strength of C-Sectioned CFS Members

The overall behavior of cold-formed steel (CFS) members is significantly affected from existing geometric imperfections. In this work, a mode shape-based imperfection coefficient computation method is developed to investigate the effects of initial geometric imperfections on member behavior. The point clouds of CFS members are collected and used to extract imperfection distributions and coefficients. The computed coefficients are integrated into the numerical model for analysis. Finally, axial loading tests are conducted to compare the numerical and experimental results. The results obtained using mode shape-based imperfection coefficients are generally closer to the experimental results than the common method used in practice.

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.

Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection

Investigating the nonlinear transient responses of rotating annular plate is a worthy subject in aerospace and aeronautic fields. In this paper, the nonlinear transient response induced by pulse loads for the graphene platelets reinforced metal foams (GPLRMF) annular plate with rotating motion is illustrated by time history curves and phase trajectory. Three-dimensional displacement field is captured by employing the first-order shear deformation theory (FSDT). The modeling accuracy of nonlinear transient response for the annular plate resting on viscoelastic foundation is enhanced by using von-Kármán's nonlinearity. The assumed mode method is used to solve the highly coupled nonlinear governing equations, and the fourth order Runge-Kutta iterative algorithm is applied to track the nonlinear transient response path. Detailed parametric studies are performed to investigate the effects of initial geometrical imperfection, dispersion and weight fractions of graphene platelets (GPLs), distribution types and coefficients of porosity, geometric dimensions of annular plates, viscoelastic foundation, thermal effect, types and properties of uniformly distributed pulse loads as well as rotating motion on nonlinear transient response of the annular plates. It turned out that, the blast load can significantly affect the dynamic behavior of the annular plate. Additionally, the annular plate with larger initial geometric imperfection has better deformation resistance, and the presence of the rotating motion can increase the maximum vibration amplitude of the annular plate.

Creep behavior of titanium alloy used in deep-sea pressure shell considering tensile/compressive asymmetry: Experiments and numerical modeling

Titanium alloy pressure shell of deep-sea submersible suffers from room-temperature creep problem, which can affect the safety of the structure. There is currently a lack of research on the tensile/compressive asymmetry of the creep response of titanium alloy structures at room temperature. In this paper, room-temperature creep behavior and mechanism of titanium alloy were investigated by creep test of twisting of titanium alloy square plate. Taking cylindrical pressure shell with geometrical imperfection and multi-sphere pressure shell as examples, the creep mechanical behavior of titanium alloy pressure shells under complex stress states were investigated by numerical simulation. It is found that only under tensile stress can slip bands move across phase boundaries, resulting in tensile/compressive asymmetry in creep behavior. The proposed DTC model can accurately describe the room-temperature creep behavior of titanium alloy structures. For cylindrical pressure shell with geometrical imperfection, creep deformation results in a 121 % increase in the magnitude of geometrical imperfection. The results obtained with the tensile model towards the conservative side. For multi-sphere pressure shell, the evolution of physical quantities cannot be accurately described without considering the tensile/compressive asymmetry in creep properties. The range of relative error when using traditional models is between 5% and 33%.

Vibration Investigation of Circular Graphene Sheet with Geometrical Defect Considering Two-Phase Local/Nonlocal Theory Exposed to the Magnetic Field

In this work, the mixed local/nonlocal elasticity theory is developed for the investigation of the vibration of a circular graphene sheet with a structural defect located in a magnetic field. When graphene is placed in a magnetic field, the Lorentz force is applied to it, which is calculated using Maxwell’s equations. The insufficiency of Eringen’s nonlocal theory (ENT) caused some authors to employ the two-phase theory (TPT) to study nanostructures. Geometric imperfections can happen in the manufacturing process of graphene sheets. Lots of these imperfections can be modeled as a hole. So, in this work, an imperfection is considered as the centric hole. Governing equations, in Newtonian formulation, are extracted in the integrodifferential form. The boundary conditions are selected as clamped at inner and outer edges. To discretize the equation of motion we employ Galerkin’s approach. The solution is validated using a comparison study between the presented results and those that exist in the literature, and the accuracy of the suggested approach is verified. The effectiveness of the mixture parameter, magnetic field, radius of imperfection, and nonlocal parameter is examined on the natural frequency. The results exhibit that an increase in the mixture parameter and magnetic field increases the natural frequency of the graphene sheet.

Calculation method for local–global interaction buckling capacity of stainless steel C-columns

In this paper, based on the completed experimental research, the C-section stainless steel column was simulated in ABAQUS, and the FEM results were compared with the test results to verify the accuracy of the FE model. On this basis, the FE model was used to carry out a parametric analysis of the local–global interaction (L-G) buckling capacity of the C-section stainless steel column, and the effects of the initial imperfection distribution mode, the mechanical properties of the material, and the improvement of the material strength in the corner region were investigated. When the initial geometric imperfection distribution mode is local buckling or L-G buckling, the change of imperfection shape has less effect on the occurrence of L-G buckling and the ultimate capacity of the member. Within a certain range, the stainless steel hardening coefficient and the increase strength of corner region on the L-G buckling capacity of stainless steel columns is small. The nominal yield strength of stainless steel has a more significant effect on the L-G buckling capacity. Finally, based on the parametric analysis results and the direct strength method, the calculation formula for the local–global interaction buckling capacity of stainless steel C-columns under axial compression is proposed, and the accuracy of the calculation results were verified by comparing with the test results.

Experimental, numerical and analytical study on axial compression buckling of chopped glass fibre-reinforced polymer cylindrical shells

A series of experiments were carried out to investigate the buckling response of chopped strand mat glass fibre-reinforced polyester (CSM-GFRP) cylindrical shells when subjected to axial compression load. Finite element modelling by using ABAQUS was performed to verify the experimental results, then a parametric study was conducted to investigate the effect of wall thickness, shell height, radius, young’s modulus, fibre volume fraction, and geometric imperfections on the buckling load of the CSM-GFRP cylindrical shells. The findings revealed that the buckling load was decreased with increasing the radius-to-wall thickness ratio (r/t) and increasing the value of the imperfection amplitude-to-wall thickness ratio, Additionally the results indicated that the buckling load increased with increasing the fibre volume fraction. Finally, an equation was proposed to predict the buckling load of the CSM-GFRP cylindrical shells using nonlinear regression analysis.