Presence Of Geometric Imperfections Research Articles

1/2 and 1/3 Subharmonic Resonance Behaviors of a Rotating FG-CNTRC Beam with Geometric Imperfections

This paper aims at investigating 1/2 and 1/3 subharmonic resonances of a rotating functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam in the presence of geometric imperfections. A general function is introduced to denote three types of imperfections containing sine, global, and local modes. At first, based on the von-Kármán geometric nonlinearity assumption, the forced vibration equation is set up. Then, the Galerkin method and multiple scale method are utilized to study subharmonic resonance behaviors. Finally, coupled effects of FG-CNTRCs, rotating motion, and geometric imperfections on subharmonic resonance responses are investigated. It is found that a specific range of the excitation amplitude and frequency motivates the subharmonic resonance behavior. The coupling of geometric imperfections and geometric nonlinearities generates the 1/2 resonance phenomena, and geometric nonlinearities result in the 1/3 resonance behavior. Both the imperfection mode and amplitude can affect the resonance response and resonance regions. Moreover, in contrast with the 1/3 subharmonic resonance, geometric imperfections produce greater influence on the 1/2 subharmonic resonance.

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.

Critical buckling load analysis on spherical shells under various geometric imperfections

The strength of shell structures is mainly determined by their ability to resist buckling. However, the presence of geometric imperfections – a condition which the geometry is no longer the same as the original condition – significantly deteriorates the critical load and often leads to catastrophic failure. Ratio between the actual critical buckling load to the theoretical prediction is called knockdown factor. The study aims to analyse the critical buckling load on spherical dome elastic shells under various geometric imperfections. This study was conducted into several thicknesses (10, 16, 20, 37, 50 mm) and fixed base radius of 4000 mm. Analyses of linear buckling and nonlinear static are performed and aided with finite element program using MIDAS FEA. The result of this study reveals that the critical buckling load decreases sharply in the beginning of imperfection, then reach for quite slow progression until a constant value of Kd = 0.1. In addition, the higher minimum knockdown factor is obtained as the shell thickness increases.

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.

Wind load effect on the lateral instability of precast beams on elastomeric bearing supports

Abstract The behavior of slender precast beams related to lateral stability in the transitional and in service phases is worrying. The presence of geometric imperfections aggravates and makes the problems of instability more susceptible. The main objective of this work is to evaluate the behavior of concrete beams on elastomeric bearings and to analyze the influence of variables such as: concrete strength, wind load and bearing compression stiffness. For the numerical nonlinear analysis the software ANSYS based on the Finite Element Method was used. The analyses show that the influence of the strength of the concrete is significant in the lateral stability of the beam. The wind load represents a considerable decrease in the contact (lift off) between the beam and the bearing. Finally, the combination of these factors can result in a critical stress situation in the beam, and it is not possible to have equilibrium, causing its toppling.

Comparative Study Concerning the Methods of Calculation of the Critical Axial Buckling Load for Stiffened Cylindrical Shells

As demonstrated in numerous theoretical and experimental studies [1], the buckling behaviour of stiffened cylindrical shells (SCS) is strongly influenced by the presence of geometric imperfections caused by the manufacturing process and/or exploitation. Therefore, the design norms recommend the use of reduction coefficients with very low values, resulting in a significant reduction of the maximum load applied. In order to calculate the critical buckling load as accurately as possible it is necessary to know the real geometry of SCS. In case of SCS, the structural analysis based on the use of the finite element method (FEM), using models that reflect the real geometry of the shell determined from measurements, lead to a better evaluation of the critical buckling load. The structural analysis with FEM is accepted more and more by standards, EN 1993-1-6:2007 [2] specifying the types of numerical analysis accepted for cylindrical shells. The aim of this study is to compare the results concerning the critical buckling load for SCS under axial compression, obtained with both the analytical and FEM methods for real geometries obtained from measurements. For this purpose, scale models of SCS were used, for which were determined, by measuring, the values of the deviations from the median radius at several points on the shells surface. These deviations were then incorporated in the numerical analysis with FEM and it was determined, for each cylindrical shell, the value of the critical axial buckling load, by using geometrically nonlinear analysis. In order to validate the results of the numerical analysis, the analysed SCS were subjected to axial compression within an experimental program and the experimental data were compared with the results established on the basis of analytical and numerical calculation.

Effects of plies orientations and initial geometric imperfections on buckling strength of a composite stiffened panel

The use of composite stiffened panels is common in several activities such as aerospace, marine and civil engineering. The biggest advantage of the composite materials is their high specific strength and stiffness ratios, coupled with weight reduction compared to conventional materials. However, any structural system may reach its limit and buckle under extreme circumstances by a progressive local failure of components. Moreover, stiffened panels are usually assembled from elementary parts. This affects the geometric as well as the material properties resulting in a considerable sensitivity to buckling phenomenon. In this work, the buckling behavior of a composite stiffened panel made from carbon Epoxy Prepregs is studied by using the finite element analysis under Abaqus software package. Different plies orientations sets were considered. The initial distributed geometric imperfections were modeled by means of the first Euler buckling mode. The nonlinear Riks method of analysis provided by Abaqus was applied. This method enables to predict more consistently unstable geometrically nonlinear induced collapse of a structure by detecting potential limit points during the loading history. It was found that plies orientations of the composite and the presence of geometric imperfections have huge influence on the strength resistance.

Application of Continuation Methods to Uniaxially Loaded Postbuckled Plates

Continuation methods are used to examine the static and dynamic postbuckled behavior of a uniaxially loaded, simply supported plate. Continuation methods have been extensively used to study problems in mathematics and physics; however, they have not been as widely applied to problems in engineering. When paired with a Galerkin approximation, continuation methods are shown to be well suited to solving nonlinear buckling problems. In addition to providing a robust solution method for nonlinear equations, the linearized Jacobians from the continuation steps will contain natural frequency and mode shape information for mechanical systems (provided inertia terms are included). Results for the primary buckling branch are compared to previously published results. Using the open-source continuation package Auto, stable, remote secondary buckling branches were discovered. These secondary stable equilibrium persist even in the presence of geometric imperfections and their existence is confirmed by experiment.

Stochastic inverse identification of geometric imperfections in shell structures

It is now widely known that the presence of geometric imperfections in shell structures constitutes an important contribution to the discrepancy between theoretical and experimentally realizable ultimate loads governed by buckling. The present paper describes a method by which an actual initial imperfection field may be estimated using the service load response of a shell structure. The approach requires solving a stochastic inverse problem wherein uncertainty regarding initial imperfection predictions is expressed within the context of a Bayesian posterior distribution. The proposed approach could be applied to condition assessment and performance evaluation activities in practice.

Measurement and assessment of geometric imperfections in thin-walled panels

Thin-walled members may be subject to performance limitations arising through local or distortional buckling of slender elements comprising the cross-section of the member, or overall buckling of the member. The effects of structural instability may be aggravated by the presence of geometric imperfections in these elements. An investigation is presented into methods of measuring and assessing geometric imperfections in cold-rolled thin-walled steel panels. These methods can be used to characterise the geometry of prismatic thin-walled members that exhibit performance sensitivity due to geometric imperfections. The measurement procedures investigated include close-range photogrammetry, precise optical levelling, and the use of a co-ordinate measurement machine. The assessment procedure comprises a least-squares spectral decomposition of the measurements to characterise the imperfections existent in the panels under investigation, and estimates of the precision of the derived Fourier coefficients are used to inter-compare the three measurement procedures. The investigation has demonstrated that statistically significant imperfections may exist in thin-walled members at short and medium wavelengths, leading to a reduction in the load carrying capacity. Both optical levelling and the co-ordinate measurement machine technique can yield desirable results, but for high precision work, use of the co-ordinate measurement machine is recommended.

Finite element analysis of wall pressure in imperfect silos

It is generally accepted that the pressures exerted by stored bulk solid on silo walls after filling are closely predicted by the Janssen theory. However, recent experimental observations of silo wall pressure have shown significant deviations from Janssen pressures even after careful symmetrical filling. Both meridional and circumferential variations from the Janssen values have been found, which induce bending of the wall in reinforced concrete silos and high membrane stresses in steel silos. It has been suggested that the presence of geometric imperfections in the silo wall is a likely cause of these pressure variations. However, no rigorous investigation of the effects of uneven surface profile on wall pressures appears to have been performed, though some simple calculations have been produced. This paper presents a finite element study of the effects of a local axisymmetric wall imperfection on pressures acting on the wall of a circular silo. The effects of imperfection height and imperfection geometry on wall pressures are also investigated.

Analysis of Geometric Imperfections Affecting the Fibers in Unidirectional Composites

The compressive strength of unidirectional composites is partly limited by the presence of geometric imperfections, mainly including undulation and general misalignment of the fibers. By examining a number of regularly spaced cut sections under an optical microscope, the fiber paths within the material can be reconstructed using image processing techniques to determine the coordinates of the fiber centers in each cut. For each fiber, these coordinates are projected in main planes in inertia to determine the overall misalignment angle and smooth the undulation using a sinusoidal waveform. Four carbon fiber composites were examined in this way. The complete analysis of the parameters relative to misalignment and undulation shows the magnitude of the imperfections affecting each composite. Main component analysis is performed to identify the interdependence between several of these factors. In addition, correlating the positions of the different fibers show that they interact only at very short distances. These results call into question the approximation generally applied up to now, which was to consider unidirectional composites as a series of mutual parallel fibers undulating in phase. This method therefore opens the way to more realistic modeling of geometric imperfections as is required both for numerical and finite element analyses of the compression behavior of such materials.

Minimum weight design of truss structures with geometric nonlinear behavior

The paper presents an optimization method based on optimality criterion for minimum weight design of structures with geometric nonlinear behavior. The nonlinear critical load is determined by finding the load level at which the Hessian of the potential energy ceases to be positive definite. A recurrence relation based on the criterion that at optimum the nonlinear strain energy density be equal in all the members is used to develop an algorithm. Sample problems are given to illustrate the application of the method to truss type structures with a large number of design variables. NUMBER of algorithms based on the optimality criterion approach have been developed to design a minimum weight structure with specified constraints on nodal displacements, element stresses, system stability, etc.1'2 The optimization algorithm consisted of analyzing the structure by the finite element method and using a recurrence relation derived from the appropriate optimality criterion to modify the design variables. The optimality criterion was derived by, differentiating the Lagrangian with respect to the design variables. The displacements were assumed to be small and, in the finite element analysis, linear equilibrium equations were solved to determine the response of the structure to the ap- plied loads. In the case of system stability the constraints were defined (see Refs. 3-6) by the associated linear eigenvalue problem. This definition of system stability for some structures may not be valid because of the nonlinear behavior of the structure which may be due to the geometry of the structure or the presence of geometric imperfections. The correct procedure for these structures would be to analyze the structure* by using nonlinear equilibrium equations. This will be particularly true for large space structures (LSS). In this paper an optimization method based on the optimality criterion approach is presented for structures with geometric nonlinear behavior. In the case of a structure optimized with constraints on linear stability the optimum structure can have more than one critical buckling mode. This design tends to become im- perfection sensitive and a small deviation in the geometry of the structure can reduce its load carrying capacity sub- stantially. The imperfection sensitivity of the optimized structure can be reduced by designing the structure so that buckling loads associated with the critical buckling modes are not equal (see Ref. 7). A real structure has geometric im- perfections and these structures tend to have nonlinear

Influence of Geometric Imperfections and In-Plane Constraints on Nonlinear Vibrations of Simply Supported Cylindrical Panels

This papers deals with the effects of initial geometric imperfections on large-amplitude vibrations of cylindrical panels simply supported along all four edges. In-plane movable and in-plane immovable boundary conditions are considered for each pair of parallel edges. Depending on whether the number of axial and circumferential half waves are odd or even, the presence of geometric imperfections (taken to be of the same shape as the vibration mode) of the order of the shell thickness may significantly raise or lower the linear vibration frequencies. In general, an increase (decrease) in the linear vibration frequency corresponds to a more pronounced soft-spring (hard-spring) behavior in nonlinear vibration.

Pressurized Ring-Stiffened Shells: A Model Study

ABSTRACT The complex problem of interaction between general buckling and interframe buckling in ring-stiffened shells under external pressure is studied in a simple way by use of a rigid link model. The model incorporates linear and bilinear compressive springs with special properties to represent the circumferential stiffness and the buckling characteristics of a long shell and its ring stiffeners. The model allows the possibility of a shift of stiffness (material, weight) from the shell to the stiffeners. The optimum weight distribution may therefore be found in a relatively simple manner. It is found that interactive effects in the presence of geometrical imperfections have a considerable influence on the buckling strength of such structures.

Buckling Analysis of Geometrically Imperfect Stiffened Cylinders under Axial Compression

The buckling analysis of an imperfect, thin, circular, cylindrical, stiffened shell under uniform axial compression and for various end conditions is investigated. A methodology is presented for predicting critical conditions for such configurations. This methodology is based on the smeared technique and the von KarmanDonnell nonlinear kinematic relations in the presence of geometric imperfections. The computational procedure employs a Fourier series type of separated solution, and through the Galerkin procedure the field equations are reduced to a system of ordinary differential equations. These equations are solved by the finite-difference scheme. Numerical results for numerous stiffened and unstiffened configurations are presented.