Prediction Of Critical Loads Research Articles

Buckling critical load prediction of pultruded fiber-reinforced polymer columns and feature analysis by machine learning

Buckling critical load prediction of pultruded fiber-reinforced polymer columns and feature analysis by machine learning

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.

Parametric study of the quasi-static response of wind turbines in downburst conditions using a numerical model

Many research studies were conducted on wind turbine towers subjected to either seismic loads or synoptic wind loading, such as: hurricanes, typhoons, and tropical cyclones. However, the behavior of wind turbines under localized high-intensity wind events (HIW), such as downbursts, is not well-understood. The localized nature of downbursts makes the prediction of critical loads on wind turbines quite challenging. In the current study, a numerical model is developed and validated to investigate the effect of downburst wind loading on wind turbines. This model incorporates a previously developed Computational Fluid Dynamics (CFD) model for the downburst wind field coupled with a newly developed wind turbine structural model. The numerical model is capable of predicting the effect of downbursts on wind turbines taking into consideration the different downburst parameters such as the jet velocity, the size of the downburst and its location relative to the wind turbine. The model also accounts for the change in the pitch angle of the blades, which is a parameter typically used to control the blades rotation and the power generation. An extensive parametric study is conducted using the developed numerical model to determine the peak moments at the tower base and the roots of the blades considering a large number of downburst configurations and different blade pitch angles. Downburst critical configurations for different pitch angles are obtained and the optimum pitch angle which minimizes the downburst effect on the wind turbine is recommended.

Critical Load Prediction in Notched E/Glass-Epoxy-Laminated Composites Using the Virtual Isotropic Material Concept Combined with the Average Strain Energy Density Criterion.

This paper attempts to validate the application of the Virtual Isotropic Material Concept (VIMC) in combination with the average strain energy density (ASED) criterion to predict the critical load in notched laminated composites. This methodology was applied to E/glass–epoxy-laminated composites containing U-notches. For this purpose, a series of fracture test data recently published in the literature on specimens with different notch tip radii, lay-up configurations, and a number of plies were employed. It was shown that the VIMC–ASED combined approach provided satisfactory predictions of the last-ply failure (LPF) loads (i.e., critical loads).

Mixed mode I/II crack propagation in stainless steel 316L sheets by large plastic deformations: Prediction of critical load by combining LEFM with fictitious material concept

In this research, the load carrying capacity (LCC) of O-notched diagonally loaded square plate (DLSP) samples with pre-existing cracks emanating from the notch edge is investigated theoretically and experimentally under mixed mode I/II loading. The specimens are made of the stainless steel 316L, which is highly ductile and has great strain-hardening. In order to determine the LCC experimentally, several fracture tests are performed on DLSP specimens. Experimental observations reveal that these specimens experience significant plastic deformations at the onset of crack propagation. For theoretical prediction of the experimental LCCs, the Fictitious Material Concept (FMC) is first employed. By utilizing FMC, the stainless steel 316L with highly ductile behavior and great strain-hardening can be replaced with a virtual brittle material having linear elastic behavior. Then, by coupling FMC with two well-known stress based brittle fracture criteria in the field of the linear elastic fracture mechanics (LEFM), the LCCs of the cracked DLSP samples are estimated. In fact, by using FMC, complex and time-consuming elastoplastic failure analysis can be avoided and by performing only linear elastic analysis, the LCC of ductile DLSP specimens can be estimated. It is shown that combination of FMC with the maximum tangential stress (MTS) and the generalized MTS (GMTS) criteria is quite successful in predicting the crack growth instance in ductile DLSP specimens.

An expeditious algebraic formulation to the buckling critical load of risers under dynamic compression

Dynamic compression of risers can play an important role in the structural stability of submerged pipes in catenary-like configuration. In this paper, the analytical formulation for the buckling critical load, developed in the early 2000's, is revisited and extended to cover a wider range of practical cases. A purely algebraic expression for the critical load is provided, eliminating the original formulation requirement related to solving transcendental equations, for both free and anchored risers. The analytic formulations and respective algebraic approximations are compared with numerical simulations, presenting a fairly good agreement. A discussion on the differences and similarities of each formulation ends this paper, highlighting their range of validity. Also, from the comparison, the analytical formulation developed in this work was more suitable for precise and fast determination of the critical buckling load for both riser types, rigid and flexible, and for most typical operating conditions. The proposed algebraic expressions were highly accurate and may substitute the previous analytical formulations for critical load prediction.

Mechanical performance of parallel bamboo strand lumber columns under axial compression: Experimental and numerical investigation

This paper presents an investigation on the mechanical performance of parallel bamboo strand lumber (PBSL) columns under axial compression. Experimental test and numerical analysis were performed for 40 PBSL columns with various slenderness ratios. Failure modes, ultimate capacity and load-strain response are reported and evaluated. Compressive failure is the typical failure mode of columns with small slenderness ratios, however, buckling failure is commonly observed for longer columns. Elastic eigenvalue analysis is found effective to predict critical buckling load of long columns, as buckling occurs within elastic range. However inelastic behavior has significant effect on critical load when the buckling stress exceeds proportional limit of the material. As a result, inelastic approaches provide more accurate prediction of critical load for columns with a slenderness ratio lower than the elastic threshold (λy). The presented experimental results and numerical analysis validated the feasibility of the elastic/inelastic buckling analysis approaches on determination of ultimate capacity of axial loaded PBSL columns.

Improved nonlinear rotational constitutive law for predicting critical loads in elastomeric isolation bearings

Abstract Predicting critical loads in elastomeric isolation bearings has important implications for the design of isolation systems. The key mechanism for predicting the critical loads is to precisely predict the nonlinear rotational properties of the bearings. However, most of the existing rotational constitutive laws of elastomeric bearings are divided into linear stage and nonlinear stage. The predicted critical loads from these piecewise models lead to inaccurate results compared to experimental observations. In this paper, the basic assumptions of previous researches are extended considering the nonlinear properties of bonded rubber layer. On the basis, an improved nonlinear rotational constitutive law is proposed. The improved model can provide a continuous prediction of critical loads throughout the horizontal displacements. The calculated critical loads are confirmed by comparison with existing test data.

An Analysis of Mode-I Fracture in Carbon-Epoxy Laminate for the Prediction of Critical Loads and Crack Lengths

An Analysis of Mode-I Fracture in Carbon-Epoxy Laminate for the Prediction of Critical Loads and Crack Lengths

Fracture Loads Prediction on Notched Short Glass Fibre Reinforced Polyamide 6 Using the Strain Energy Density

This paper provides an energetic approach useful for the prediction of critical loads on U-notched components without an ideally linear elastic behaviour. The methodology has been applied to 100 fracture specimens of short glass fibre reinforced polyamide 6 (SGFR-PA6), combining four different fibre contents (5, 10, 30 and 50 wt %) and five different notch radii (0.00, 0.25, 0.50, 1.00 and 2.00 mm). The proposal combines the application of the strain energy density criterion with the use of the whole absorbed energy in the tensile test (elastic-plastic area under the stress-strain curve). With all of this, the fracture loads have been well estimated in this type of material.

Upheaval buckling of pipelines due to internal pressure: A geometrically nonlinear finite element analysis

This work presents an analysis of upheaval buckling of pipelines triggered by internal pressure. It discusses the existing relationship between internal pressure and equivalent compressive axial force in the buckling context. The main focus is on the relative influence of prop imperfections and soil friction coefficients in critical load prediction and post-buckling configuration. To perform the analyses, numerical models are developed using geometrically-exact finite element of beams, undergoing large displacements and finite rotations. Contact between the pipeline and the soil is also included in the models. As a result, the work shows the equivalence of applying the internal pressure as a distributed load dependent on pipe curvature and as a follower compressive axial force, both in terms of critical load and post-buckling configuration. Varying prop imperfections and soil friction coefficients, it is concluded that the first parameter has more influence in critical load prediction than the last one. The same occurs in terms of post-buckling configuration: for the same increase of internal pressure from critical load, the imperfections have more influence in the post-buckling displacements than the friction between the pipeline and the soil.

Mode jumping analysis of thin film secondary wrinkling

In this paper, a mathematic expression is presented to describe the mode jumping and the equilibrium path reversal characteristics of thin film secondary wrinkling based on the non-linear bifurcation buckling theory. With the usage of variable transformation and the introduction of dimensionless parameters, the non-linear Von-Karman equilibrium equation considering the two-direction loading characteristics, is transformed into a non-linear boundary value problem with zero trivial solution. Based on the bifurcation theory, the eigenvalue problem is addressed through the linearization of non-linear boundary value problem. An approach to critical load prediction of thin film secondary wrinkling is proposed by introducing a critical aspect ratio parameter, since the mechanism of thin film secondary wrinkling is double eigenvalues splitting. Furthermore, this paper presents an analysis in detail on the critical load of the rectangular thin film secondary wrinkling under shear, indicating that the critical load is linearly proportional to the initial stretching displacement, while its relationship with the size of the free edge is nonlinear. The validity of this critical load prediction approach is verified via the digital image correlation experiment. The results provide strong supports for the controlling and tuning of the wrinkles for high precision pre-tensioned thin film structures.

Prediction of Critical Load and Wear Rate of Coatings by Fuzzy Theory

This paper proposes a new method of rule-based fuzzy modelling to predict the critical loads and wear rates of some typical ceramic coating systems. Coating hardness, thickness and friction coefficient were used as the input variables. Experimental results from a number of research laboratories confirmed the feasibility of the fuzzy approach. The proposed method showed its unique advantage to deal with complexity associated with the wear of surface coatings.

Comparison between experimental and boundary element predictions of plate buckling behaviour

Plate buckling is an important design factor in consideration of the endurance and integrity of a variety of structures. Exact analytical formulations for the prediction of critical loads and modes exist only for a restricted set of idealized loading and boundary conditions. More practical conditions and post-critical behaviour have no exact formulation and resort must be made to numerical and experimental techniques. Tests on rectangular plates have made a significant contribution to the assessment of the effect of various design parameters on practical buckling behaviour. The paper reviews some of these aspects of plate buckling brought to light by experimental investigations and presents some data which are subsequently simulated by applying a new, quite general in scope, boundary element solution of the analytical problem. The analysis procedure includes a BEM formulation for the determination of the membrane, elastic, pre-buckling state of stress and it can identify the critical loads as well as the incrementally determined non-linear deflexion initiated by imperfections. The excellent agreement noted in the comparison of the numerical and experimental predictions validates the effectiveness and versatility of the proposed new numerical approach and points to the direction of its further development.

Strengthening of wide-flange columns under load

The present work deals with formulation of theoretical and analytical methods leading to the development of column strength curves. The formulations were developed for both elastic and inelastic behaviour. Two types of reinforcement have been developed for strengthening the W-shape columns under load. Since the column strength curves are based in part on the magnitude and distribution of residual stresses, it is extremely important to consider the new pattern of residual stresses due to welding process. Also, the welding sequence will affect the magnitude and distribution of residual stresses. Theoretical formulations leading to a closed-form solution for the prediction of critical load were developed for two types of strengthening using the superposition of original residual, new welding, and initial loading stresses. A nonlinear finite element analysis based on the large deformation theory of stability was used to predict the strengthened column critical load. It takes into consideration the effect of cooling residual stresses and new welding residual stresses. The formulations were incorporated with gradual penetration of yielding, the spreading of inelastic zones along the member length, the presence of residual stresses, and strain hardening of the material. Experiments were carried out to determine the actual capacity of strengthened columns. Seven specimens were tested using two and four strengthening plates. The welding stresses were measured through a series of experiments, and it was found that the parabolic distribution is a very close approximation to the actual new welding stress distribution. Key words: reinforcement of steel columns, welding stresses, welding sequence, strengthening of existing structures, buckling, steel plating, finite element.

Mode I Delamination of a Three-Dimensional Fabric Composite

Finite element analysis was conducted on the double cantilever beam speci men (DCB) of carbon-epoxy (T300/3501-6) orthogonal interlocked fabric composites. The Mode I strain energy release rate, GI, was evaluated to investigate the influence of through-the-thickness (z-axis) fibers on crack driving force as a function of crack length. The finite element analysis of the DCB specimens showed good agreement with ex perimental results for both compliance and strain energy release rate. The presence of z- axis fibers sharply reduced the strain energy release rate in comparison to the traditional two dimensional (2-D) laminated material. A parametric study revealed that increasing the z-axis fiber stiffness reduces GI. Progressive debonding of the z-axis reinforcement was also modelled. The Mode I strain energy release rate increased as the fiber debonded but was significantly less than the 2-D laminated material in all cases investigated. A model for the prediction of critical load is proposed for Mode I interlaminar fracture of 3-D orthogonal interlocked fabric composites. Fundamental inputs to the model are the z-axis fiber properties, fiber architecture, fiber volume fraction and the Mode I critical strain energy release rate for the 2-D laminate.

Static collapse: A survey of methods and modes of behavior

The phenomenon of static collapse, henceforth called ‘buckling’, is first illustrated by the behavior of a fairly thick cylindrical shell, which under axial compression deforms at first axisymmetrically and later nonaxisymmetrically. Thus, static buckling encompasses two modes of behavior, nonlinear collapse at the maximum point in a load versus deflection curve and bifurcation buckling. Accurate prediction of critical loads corresponding to either mode in the plastic range of material behavior requires a simultaneous accounting for moderately large deflections and nonlinear, irreversible, path-dependent material. A survey is given of plastic buckling, which spans three areas: asymptotic analysis of postbifurcation behavior of perfect and imperfect simple structures, general nonlinear analysis of arbitrary structures, and nonlinear analysis for collapse at a maximum load and bifurcation buckling of shells of revolution. In the survey of general nonlinear structural analysis, some emphasis is given to strategies for solving the governing nonlinear equations incrementally. Numerous examples, generated primarily with the STAGS computer program, which was developed by Almroth and his colleagues, reveal many complex modes of buckling behavior.

Criteria for brittle fracture in biaxial tension

The criteria of maximum tangential stress, maximum tangential principal stress, maximum tangential strain and strain energy density are applied to the problems of slit and elliptical cracks under remote uniform biaxial tension. The predicted direction of crack extension and the critical load are compared with experimental results reported by other investigators. The unstable crack paths are determined. The four criteria differ in the case of unequal tension; the strain energy density criterion is the least satisfactory. The criteria of maximum tangential strain and strain energy density can be modified to give a good prediction of critical load.

Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field Part I: Slit and elliptical cracks under uniaxial tensile loading

Predictions for the angle of crack extension, critical load and unstable crack paths based on the criteria of maximum tangential stress (MTS), maximum tangential strain (MTSN) and strain energy density (SED) for angled slit and elliptical cracks under uniaxial tensile loading are compared. The tangential stress associated with the MTS criterion need not be a principal stress and a new approach to this criterion is suggested. A criterion based on maximum tangential principal stress (MTPS) is proposed. Predictions by these two criteria are compared. Some difficulties associated with the application of the SED criterion are indicated. A new basis, which permits a unification of all the criteria in respect of prediction of critical load, is suggested. Some of the results have been compared with data available in the literature.

Plastic Buckling of Various Shells

The phenomenon of plastic buckling is first illustrated by the behavior of a fairly thick cylindrical shell, which under axial compression deforms at first axisymmetrically and later nonaxisymmetrically. Plastic buckling encompasses two modes of behavior, nonlinear collapse at the maximum point in a load versus deflection curve and bifurcation buckling. Accurate prediction of critical loads corresponding to either mode in the plastic range requires a simultaneous accounting for moderately large deflections and nonlinear, irreversible, path-dependent material behavior. A thumbnail survey is given of plastic buckling which spans three areas: asymptotic analysis of postbifurcation behavior of perfect and imperfect simple structures, general nonlinear analysis of arbitrary structures, and nonlinear analysis for collapse and bifurcation buckling of shells and bodies of revolution. Comparisons between test and theory are presented for elastic-plastic buckling of axially compressed unstiffened and ring-stiffened cylindrical shells, internally pressurized torispherical and ellipsoidal pressure vessel heads, and pipes under combined external pressure and bending. The effect on buckling of fabrication processes such as cold forming and welding is discussed for the case of ring-stiffened cylindrical shells. Two examples are given of rather complex shell structures in which considerations of plastic buckling affect the design.