Effects Of Geometric Imperfections Research Articles

Effect of Geometric Imperfections on Anchor Loss and Characterisation of a Gyroscope Resonator with High Quality Factor

A critical functional part of a hemispherical resonator gyroscope (HRG) is the mechanical resonator, and a few million quality factor (Q-factor) is needed for the lowest resolution. This paper focuses on anchor loss of a HRG of a few millimeters in size. A detailed parametric study of dimensions and shell imperfections due to fabrication is carried out. A sensitivity study of the effect of shell mean radius, shell thickness, stem radius, stem height on the Qanchor is carried out. The effect of geometric imperfections such as shell offset, shell tilt, shell thickness variation, and unbalance is studied in detail. From the study, it is inferred that the anchor loss becomes very significant and approaches other loss mechanisms even with minor geometric imperfections in the hardware realisation. Based on the sensitivity study, the dimensional and geometric tolerances are arrived for precision fabrication. Precision resonator is fabricated as per the requirement of minimum anchor loss. The significance of other damping mechanisms such as air damping, excitationinduced damping, thermoelastic dynamic damping and surface dissipation is also discussed. Surface characterisation before and after surface treatment has been carried out using nanoindentation technique with regard to surface loss. Functional parameters of operating frequency and Q-factor are evaluated using laser Doppler vibrometry (LDV).

Effect of Geometric Imperfection on the Dynamic of Elevated Water Tanks

The elevated tanks are considered as very sensitive structures in seismic movement condition. Moreover, the conical steel tank manufacturing without local geometric imperfection seems to be too difficult. In generally, the latter is the most responsible factor to define the shell structures buckling capacity. For this reason, several theoretical and experimental researchers studied the performance of this type of structure under seismic loading. The present study aims to demonstrate the local geometric imperfection effect on dynamic buckling of elevated water tank. Using the three dimensions finite element technique to study the seismic response of perfect and imperfect elevated water tank was established taking into account the following factors; the interaction fluid structure (FSI), the wall flexibility, the local geometric imperfection, the nonlinear time history analysis, the material and geometric nonlinearity, and this by the application of three different instability criteria for the critical PGA estimate. The critical PGA of the imperfect elevated water tank numerical models decreased by 45, 45% compared to the elevated water tank numerical model without local geometric imperfection. The obtained results confirm the local geometric imperfection effect on dynamic buckling of elevated water tanks.

The Buckling Behavior of Vacuum-Infused Open-Hole Unidirectional Basalt-Fiber Composites Experimental and Numerical Investigations

Basalt-fiber-reinforced epoxy (BFRE) composite laminates fabricated using the vacuum infusion process were subjected to axial compression to assess their buckling behavior. The buckling responses of open-hole specimens were compared with those of plain ones. ABAQUS finite-element predictions of BFRE composite buckling agreed well with experimental results. A validated numerical model was used to perform a parametric investigation into the effects of open-hole specimen geometry and boundary conditions of specimens on their buckling behavior. A linear analysis was carried out to estimate the effect of geometric imperfections of specimens on their buckling. Also, glass-fiber-reinforced epoxy specimens were analyzed for their buckling response and compared with that of BFRE ones. The results of this study can be used for buckling-based designs of open-hole composite structures.

Effect of random geometric imperfections on the water-tightness of diaphragm wall

Diaphragm walls are commonly used as cut-off walls to prevent water from entering dewatered excavation pits, landfills and downstream water. However, due to the geometrical imperfections such as the positioning error of grab during trenching, small seepage passages through the diaphragm wall may occasionally occur, which will undermine its water-tightness and lead to significant leakages. This study therefore used a reliability-based approach to quantitatively estimate the effect of geometrical imperfections on the water-tightness of diaphragm walls using a three-dimensional discretised algorithm (TDA). This algorithm enables a rigorous examination of penetration of seepage passages and it further quantitatively estimates the flow rate through the diaphragm wall under certain circumstances. Finally, detailed design procedures and design graphs were provided, which may facilitate the choice of a rational grab model and construction parameters in the design of diaphragm walls.

Effect of Geometric Imperfections in the Shape of Buckling Form on the Reduction of Load Capacity of Cylindrical Shell

AbstractThe approach to numerical analyses was changed by the introduction of Eurocodes. The EN 1993-1-6 standard allows taking into account imperfections on the shape of a buckling form from a linear elastic bifurcation analysis. The article analyses the first ten forms of imperfection from a linear elastic bifurcation analysis on the reduction of the capacity of a cylindrical shell. Calculations were made using finite element methods.

Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

An assessment of the lateral-torsional buckling and post-buckling behaviour of steel I-section beams using a geometrically exact beam finite element

The goal of this paper is twofold. The first goal is to show that geometrically exact beam finite elements can be successfully employed to determine, accurately, the behaviour of steel I-section beams undergoing large displacements and finite rotations. For this purpose, a two-node geometrically exact beam element is presented and validated, which can handle arbitrary initial configurations (e.g. curved configurations), plasticity, geometric imperfections and residual stresses. The second goal is to employ the proposed element to assess the behaviour of I-section beams undergoing lateral-torsional buckling. In particular, the element is used to determine (i) elastic non-linear bifurcation loads (i.e., bifurcation loads accounting for pre-buckling deflections), (ii) large displacement elastic post-buckling paths including geometric imperfection effects and (iii) large displacement elastoplastic equilibrium paths accounting for geometric imperfections and residual stresses. Three support/loading cases are examined, namely: (i) simply supported beams under uniform moment, (ii) simply supported beams subjected to a mid-span vertical force and (iii) cantilevers subjected to a free end vertical force. Besides I-sections with standard height-to-width ratios, wider flange sections are also considered and it is demonstrated that, for the latter, the post-buckling behaviour is quite different from that of standard sections and an increase in the load carrying capacity is observed, which is not predicted by the current Eurocode 3 [1] provisions. Based on the results obtained, a set of relevant conclusions are drawn.

Probabilistic investigation on defective jet-grouted cut-off wall with random geometric imperfections

This study examines the effect of geometric imperfections arising from variations in both the diameter and orientation of jet-grouted columns on the water-tightness of a jet-grouted cut-off wall. A three-dimensional discretised algorithm is used to detect and measure the discontinuities in the wall. A statistical evaluation of the gross flow rate through the cut-off wall with random flow-through pathways is carried out using Monte Carlo simulations. Based on the statistical results, a dimensionless design chart is proposed which can help engineers to devise safe and economical wall designs through trade-offs among various parameters such as target diameter, column spacing and number of rows.

Numerical analysis of collapse load and specific strength for moderate-walled Ti6Al4V-laminate composite submersible vessel under external hydrostatic pressure

The effects of geometrical imperfections on the collapse load and specific strength of moderate-walled submersible vessel made of Ti6Al4V-laminate composites and Ti6Al4V alloy, respectively, have been investigated in this study. Two kinds of imperfections, which are the initial ovality along cross -section direction and the winding-induced waves along longitudinal symmetric axis, are considered. Two numerical analyses including the non-linear finite element (FE) and elastic-plastic buckling analysis are performed by the commercial software MSC Marc/Mant 2005. The obtained results indicate that initial imperfections have an obvious influence on the collapse loads of both the Ti6Al4V-laminate composite submersible vessel and the Ti6Al4V one. The collapse load is mainly governed by the elastic-plastic buckling critical load, which is conservative and safe for a vessel to bear the admissible failure load under the deepwater. Moreover, the Ti6Al4V-laminate composite submersible vessel has a better capability to resist imperfections than the Ti6Al4V one.

On the effect of geometrical imperfections and defects on the fatigue strength of cellular lattice structures additively manufactured via Selective Laser Melting

Porous structures have great potential in the biomedical field because, compared to traditional fully dense implants, prostheses with a porous structure show reduced stress shielding and improved osseo-integration. Selective Laser Melting (SLM) made possible to obtain metallic cellular materials with highly complex structures characterized by a wide range of cell morphologies that allow to finely tune the mechanical properties of the implant. Nevertheless, there are still several issues to address: among others, detrimental residual stresses and the discrepancy between the as-designed and the manufactured geometry. Micro X-ray computed tomography (µCT) combined with the Finite Elements (FE) method permits to carry out in-depth investigations on the effect of the number and severity of defects on the mechanical properties. In the current study, the results of fatigue and quasi-static tests were compared with FE calculations based on the as-designed geometry and on the as-built geometry reconstructed from µCT scans. Both the elastic modulus and the fatigue resistance resulted strongly correlated with the number and severity of defects. Moreover, predictions of the mechanical properties based only on the as-designed geometry were shown not to be accurate. The importance of considering the limitations in accuracy of the manufacturing technique when designing load bearing lattice structures was highlighted.

The Effects of Geometrical Imperfections on the Dynamic Characteristics of a Tapered Roller Bearing Cage

The Effects of Geometrical Imperfections on the Dynamic Characteristics of a Tapered Roller Bearing Cage

Marchant - Rankine’s - Murzewski approach for modelling of the buckling resistance of welded I-section columns

This paper discusses different aspects of analytical and numerical modelling of the buckling resistance of welded I-section columns subjected to axial compression. The section considered is of class 1 that implies no local buckling affecting the column performance. The proposed analytical formulation of the buckling resistance is based on the so-called Marchant-Rankine's-Murzewski approach (M-R-M approach). The model proposed is of a 2D type and is a simplification of the 3D one that has recently been presented by the authors. The parameters of equivalent stress-strain model of the postwelding steel are calibrated in two stages of the best fit approximation procedure and with use of numerical results of the finite element simulation of the buckling resistance. In the first stage, the postyielding inelastic tangent stiffness parameter ξE,eff is evaluated with fixed value of the first yield parameter ψeff= ψcom. A target of the second stage is to assign the best fit value of the first yield parameter ψeff and the imperfection factor n that allows for accounting the effect of geometric imperfections.

Post-buckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents

Thermal post-buckling behavior of a geometrically imperfect/perfect piezo-magnetic nano-scale beams made of two-phase composites is analyzed in the present paper based on nonlocal elasticity theory. For the first time, the material properties of the nanobeam are considered as functions of piezoelectric phase percentage. All previous investigations on piezo-magnetic nanobeams neglect the effect of geometrical imperfection which is very important since the nanobeams are not always ideal or perfect. The post-buckling problem of such nanobeams is solved by introducing an analytical approach to derive buckling temperatures. The present solution is simple and easily understandable. For both perfect and imperfect smart nanobeams, it will be indicated that post-buckling temperature is dependent on the piezoelectric phase percentage, magnetic potential, electric voltage, imperfection amplitude and nonlocal effects.

Improved knockdown factors for composite cylindrical shells with delamination and geometric imperfections

For cylindrical shell structures under axial compression, it is crucial to provide high-fidelity knockdown factors (KDFs) in preliminary design for aerospace and civil structures. In this paper, numerical studies of buckling response for composite cylindrical shell with geometric imperfections and embedded delamination imperfections are performed to predict the lower-bound buckling loads. Results indicate that composite shells with single dimple-shape geometric imperfection exhibit similar lower bound trend and buckling behavior as those with embedded delamination imperfection. It is found that the lower-bound buckling loads are much less conservative than the corresponding design recommendation from NASA SP-8007. And the effect of geometric imperfections can envelope that of delamination imperfections. Therefore, the worst multiple perturbation load approach (WMPLA) is performed to find the worst combination of dimple-shape geometric imperfections to predict the lower-bound buckling load, and the efficient global optimization (EGO) is employed to improve the computational efficiency of WMPLA. It is demonstrated that the improved WMPLA can provide an improved KDF by examples in open literature. Based on the improved KDFs, it is possible to increase the load-bearing efficiency of composite structures in practical engineering.

Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers.

In order to investigate the effects of geometric imperfections on the static and dynamic behavior of capacitive micomachined ultrasonic transducers (CMUTs), the governing equations of motion of a circular microplate with initial defection have been derived using the von Kármán plate theory while taking into account the mechanical and electrostatic nonlinearities. The partial differential equations are discretized using the differential quadrature method (DQM) and the resulting coupled nonlinear ordinary differential equations (ODEs) are solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). It is shown that the initial deflection has an impact on the static behavior of the CMUT by increasing its pull-in voltage up to 45%. Moreover, the dynamic behavior is affected by the initial deflection, enabling an increase in the resonance frequencies and the bistability domain and leading to a change of the frequency response from softening to hardening. This model allows MEMS designers to predict the nonlinear behavior of imperfect CMUT and tune its bifurcation topology in order to enhance its performances in terms of bandwidth and generated acoustic power while driving the microplate up to 80% beyond its critical amplitude.

Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes

In this paper, a scale-dependent coupled nonlinear continuum-based model is developed for the mechanical behaviour of imperfect nanoscale tubes incorporating both the effect of the stress nonlocality and strain gradient effects. The scale effects on the nonlinear mechanics are taken into consideration employing a modified elasticity theory on the basis of a refined combination of Eringen's elasticity and the strain gradient theory. According to the Euler–Bernoulli theory of beams, the nonlocal strain gradient theory (NSGT) and Hamilton's principle, the potential energy, kinetic energy and the work performed by harmonic loads are formulated, and then the coupled scale-dependent equations of the imperfect nanotube are derived. Finally, Galerkin's scheme, as a discretisation technique, and the continuation method, as a solution procedure for ordinary differential equations, are used. The effects of geometrical imperfections in conjunction with other nanosystem parameters such as the nonlocal coefficient as well as the strain gradient coefficient on the coupled large-amplitude mechanical behaviour are explored and discussed.

Lateral compression response of overlapping jet-grout columns with geometric imperfections in radius and position

Spatial variability in the radius of a jet-grout column is commonly encountered in practice. Although various prediction models for the column radius are available, they have been generally used to predict a nominal radius. The radius variation within a column has been seldom considered. In this study, the intracolumn radius variation was simulated as a lognormal stochastic process. This was done based on the existing prediction models where the column radius can be correlated with the undrained shear strength of in situ soils. A slab consisting of overlapping jet-grout columns was considered. The slab serves as an earth-retaining stabilizing structure in a deep excavation. The effects of radius variation on the mass performance of the slab were examined with the finite-element method. In addition, the positioning errors in jet-grout columns were also investigated. Owing to the random nature of the radius variation, Monte-Carlo simulations were performed to estimate the statistical characteristics of the mass performance of the slab. A strength reduction factor was introduced and tabulated to account for the effects of geometric imperfections in the column radius and column position. With the strength reduction factor, practitioners could quantitatively evaluate the effects of these geometric imperfections in design considerations. Practical recommendations on the column length and column spacing were also proposed.

Searching for imperfection insensitive externally pressurized near-spherical thin shells

This paper studies the buckling behavior and imperfection sensitivity of geodesic and stellated shells subject to external pressure. It is shown that these structures can completely eliminate the severe imperfection sensitivity of spherical shells and can achieve buckling pressure and mass efficiency higher than the perfect sphere. Key results of this paper are as follows. First, a shell with the shape of an icosahedron can carry external pressure significantly higher than a spherical shell, when the effects of geometric imperfections are considered. Second, stellated shells are generally insensitive to imperfections. For pyramids with height-to-radius ratios greater than 35% the buckling pressure is greater than for a perfect sphere. The specific ratio 45% gives the highest buckling pressure, 28% higher than the perfect sphere. Third, stellated icosahedra with concave pyramids have higher mass efficiency than the perfect sphere. Fourth, in terms of volume efficiency, geodesic shells are comparable to spherical shells with a knockdown factor of 0.2 and convex stellated shells are comparable to spherical shells with a knockdown factor of 0.65.

Buckling behavior of a thin-walled cylinder shell with the cutout imperfections

ABSTRACTIn this work, the effects of geometric imperfections on the buckling behavior of thin-walled cylindrical shells under compression were investigated by both experimental and numerical methods. The imperfections were produced by one or two circular cutouts on the shell surface. The configuration of specimens was fabricated by the geometric imperfection parameter α, which was calculated using the circular cutout radius a, thickness t, and cylinder radius R. In the experimental investigation, a three-dimensional (3D) Digital Image Correlation Method, an optical instrument which utilized the full-field and noncontact measurement, was employed to obtain 3D displacement and strains, then the test data were analyzed and compared with the correlation technique that can determine the surface displacements of cylindrical shells. The further numerical simulations showed that parameter a played an important role in the buckling strengths of thin-walled specimens. In addition, the visualization effects of the geometric imperfections on the thin-walled shell structures were also demonstrated by using this optical method.

Effect of local geometrical imperfection on dynamic buckling of cylindrical storage tanks

Steel cylindrical tanks are the most susceptible to damage due to dynamic buckling during earthquakes. The production of cylindrical shell without imperfections is very difficult or sometime even impossible. The most previous research to study the geometrical imperfection in the shell of steel tanks using various methods did not deal with the fluid–structure interaction (FSI) and the dynamic loads. In this paper, the FSI numerical model is used to estimate the effect of local geometrical imperfection with dynamic buckling of fluid-filled tanks. The liquid inside the tank was modeled using specific Ansys’s finite elements and fluid–structure interaction. The calculation includes modal and time history analysis, including material and geometric nonlinearity. Then a typical cylindrical tank is analyzed by the application of three different stability criteria to estimate the critical PGA. The obtained dynamic buckling results of the perfect and imperfect tank are compared. The effect of geometrical imperfection on dynamic buckling is clearly shown. The PGAcr of the imperfect tank models decreases by 09.11%.