Finite Element Buckling Analysis Research Articles

Buckling analysis of PMMA hemispherical pressure shells with thickness variation

The buckling behaviour of polymethyl methacrylate (PMMA) hemispherical pressure shells under uniform external pressure was investigated experimentally and numerically. Six PMMA hemispherical pressure shells were prepared via the free blow-forming process. The geometry and wall thickness of each hemispherical shell were measured. The collapse loads and final failure modes of all shells were obtained via a hydrostatic pressure device. In addition, through optical 3D scanning, a numerical model of the hemispherical shell that reflects the actual geometric imperfection was established and used in the finite element buckling analysis. The numerical results were in agreement with the test results. These findings provide a reference for evaluating the buckling load of PMMA hemispherical shells prepared via the free blow-forming process.

Size-dependent finite element buckling analysis of porous cylindrical micro-shells reinforced by graphene platelets

This study introduces a spatial shear deformable rectangular element formulation to investigate the size-dependent buckling behavior of porous graphene platelets (GPL) reinforced micro-shells within the framework of the modified couple stress theory (MCST) for the first time in the worldwide term. The rectangular element, characterized by 4 nodes with 19 degrees of freedom each and possessing weak continuity of order C 1 , incorporates a length scale parameter enabling size-dependent analyses of shells. The research considers three distinct functions for the distribution of porosity combined with three different patterns of the GPL distribution (called by patterns A to C) along the micro-shell thickness. The elastic modulus of the nanocomposite in the absence of porosity is obtained using the Halpin-Tsai micromechanics model. Subsequently, the study meticulously validates the modeling accuracy and then investigates variations in the critical buckling load with respect to porosity distribution functions, distribution patterns of GPL, porosity coefficient, weight percentage of GPL, geometric parameters of the cylinder, and the length-scale parameter. The results reveal that the combination of the GPL pattern A with the first symmetric type porosity distribution yields the highest critical buckling loads. On the contrary, if the pattern B is combined with the second symmetric type of porosity distribution, the lowest critical buckling load will be observed. Given the accuracy of the results obtained and the versatility of the finite element method (FEM) in handling complex geometries together with diverse boundary conditions, the developed element holds promise for analyzing shells of various shapes under different boundary conditions.

Elastic Lateral‐Torsional Buckling of Girders with Corrugated Web: Equivalent Section Properties Approach

AbstractOne of the benefits of using corrugated web girders is the increase of lateral‐torsional buckling resistance. Different approaches have been presented to obtain the value of the critical moment as a function of the cross‐section geometry. Previous research works consider that the increase in buckling resistance must be accredited to a higher warping constant. The paper presents a systematic finite element numerical analysis of girders with different corrugated web shapes. Bending with respect to the weak axis shows that corrugated web implies higher moment of inertia. Torsion analysis results clearly demonstrate that the increase of torsion resistance is mainly due to higher torsional constant. The paper compares the elastic critical moment values obtained by using finite element elastic buckling analysis with the values provided by theoretical expressions introducing equivalent section properties. Results show that the equivalent section properties approach provides values very close to those obtained using finite elements. Finally, the paper presents closed form expressions to directly compute approximate equivalent section properties of any girder with corrugated web, which compare very satisfactory with those values obtained with finite element buckling analysis.

A novel seismic energy dissipation device: Laboratory tests, mathematical modeling, and numerical analysis

Seismic energy dissipation devices are used in buildings to dissipate seismic energy in the event of an earthquake. These devices use steel and its yielding properties to dissipate the input seismic energy and protect the building’s structure from damage and failure. There are many types of seismic energy dissipation devices, but all share the same goal of dissipating seismic energy. As part of an ongoing research program, a novel steel seismic energy dissipation device has been proposed. The device is made of a curved diaphragm plate made of mild steel. The diaphragm plate is welded to flanges and transverse stiffeners and can be connected to beam–column joints with a number of bolts. The damper and its geometric variants have been designed and tested in the lab under quasi-static cyclic loading conditions. In the present study, we briefly discuss the experimental program and its main outcomes; however, the main objectives will be mathematical modeling and numerical simulations. The proposed dampers are found to exhibit a stable nonlinear hysteretic behavior with small and large load–deflection loops. This behavior is an indicator of the damper’s capabilities in dissipating significant amounts of input energies with varying intensities. Mathematical modeling of the proposed damper was performed using the Bouc–Wen–Baber–Noori (BWBN) model of hysteresis to simulate the degradation of the device after repetitive loading cycles. The identification of the BWBN model parameters is discussed in detail. Nonlinear finite element buckling analysis was found to be in good agreement with test results of the best performing variant. Interesting results about the shear stress distribution at different buckling stages are presented and discussed in detail.

Magnetorheological Fluid Filled Spring for Variable Stiffness and Damping: Current and Potential Performance

Magnetorheological (MR) fluid is a smart material utilized for semi-active damping devices thanks to its ability to become viscoelastic solid under a magnetic field and provide variable damping. While most of these devices primarily utilize the fluid’s drastic increase in viscosity, its variable stiffness is rarely utilized. A MR fluid filled spring is a novel device with variable stiffness and damping and is the subject of the present study. First, the derived analytical model and the device’s controllable stiffness capability were experimentally validated by performing tensile tests with a fabricated hollow polymer spring filled with MRF-132DG. The analytical model was proved to describe the MR fluid static effect of increased spring stiffness accurately. Secondly, dynamic testing demonstrated the device’s controllable damping and capability to shift natural frequencies. In addition, the testing unveiled an enhanced dynamic performance of the spring due to the cumulative effect of MR fluid activation and specifically aligned uniform magnetic field. Finally, the hollow spring design was optimized through analytical and non-linear finite element buckling analysis to maximize MR fluid stiffness effect. The resulting critical parameters of the optimized design were used to estimate the effects of hollow spring material and operating conditions on the variable stiffness of the device.

Elastic Buckling Strength of Hollow Structural Section Steel Beam-Columns under Compression and Bending

This paper describes a methodology to evaluate the global buckling strength of Hollow Structural Section (HSS) steel columns. The methodology is based on the energy method by applying a new displacement function, which is able to describe the buckling modes for various loading conditions defined by end moments and axial force. In this paper, a unique trigonometric series is used as the buckling displacement function. With such displacement function, a closed-form strength formula can be obtained based on the principle of least potential energy. A finite element buckling analysis is also performed for comparison to clarify the accuracy of the evaluation formula.

Prediction of Nominal Compressive Strength in Steel Piles Subject to Corrosion Losses: A Finite Element Approach

This paper presents a method for predicting the nominal compressive strength of steel I-shaped piles subject to cross-sectional losses caused by corrosion. The method requires a finite element linear buckling analysis of the corroded cross-section. Results from the finite element buckling analysis may be integrated into design capacity equations contained in the 15th edition of the American Institute of Steel Construction Steel Construction Manual. Non-linear post-buckling analyses were used to verify the accuracy of the proposed method. Three cross-sectional geometries (W14x82, W14x90, and W14x120) were analyzed at varying degrees of cross-sectional loss. Results show close agreement between the non-linear finite element analyses and the proposed method of calculating nominal compressive strength.

Free Vibration and Buckling Analysis of Parabolic Frame Structures

Numerous engineering structures take place in many fields such as construction, automotive, naval industry, aerospace, etc. Parabolic frame structures have a significant role in those industries. There are many gaps in terms of the literature studies about these structures. In this paper, free vibration and buckling behavior of parabolic frame structures by using the finite element method are investigated. The structure is modeled by considering a frame element that has three degrees of freedom and neglects the displacement in y-axis. In addition, two-bay parabolic frame structure with different radius of curvature is investigated. The numerical results are compared with the CAD model of the structure by using SolidWorks for various cases. It is concluded that the results are in very good agreement with those results that are obtained from SolidWorks. It is also understood that for the different radius of curvatures the approach that is used for finite element buckling analysis in perpendicular distributed loading case does not change.

Finite element buckling analysis of double-layered graphene nanoribbons

In this paper, the molecular structural mechanics method is applied to assess the critical buckling stress of double-layered graphene nanoribbons (DLGNRs) for different types of chirality, stacking modes and aspect ratios. In the developed atomistic model, the DLGNRs are considered as space-frame structures, in which the interlayer van der Waals (vdW) interactions and the in-plane covalent bonds are modeled as truss and beam elements, respectively. The beam sectional properties are obtained by establishing a conjunction between the structural and molecular mechanics. The Lennard-Jones potential is used to derive the elastic properties of the truss rod elements. The finite element method is employed for an eigenvalue-based buckling analysis. The results show that the critical buckling stress of the DLGNRs increases with increasing the mode shape number and decreases with increasing the aspect ratio for both the inphase and the antiphase modes for different types of chirality and stacking modes. Also, it is found that for the inphase modes, the critical buckling stress reaches its maximum value for the configuration with AA stacking mode and armchair chirality for all the aspect ratios. In the antiphase modes, the configuration with the highest stability is dependent on the aspect ratio. For the aspect ratios below 10, the configuration with AB stacking mode and armchair chirality has the highest stability; however, on the other hand, by increasing the aspect ratio above 10, the configuration with AB stacking mode and zigzag chirality represents the highest stability.

An analytical solution of distortional buckling resistance of cold-formed steel channel-section beams with web openings

Circular holes can be commonly found in the web of cold-formed steel beams to accommodate services such as electric wires and pipelines. The presence of holes will reduce the critical buckling stress of the beams. Hancock proposed solution for determining the distortional critical stress of channel section beams, but limited to the sections without holes. This paper presents an analytical study on the distortional buckling of cold-formed steel channel-section beams with circular holes in the web. Hancock's solution has been modified to derive a simple formulation for approximating the elastic critical stress and moment of distortional buckling of the channel-section beams with circular holes in the web, which are compared with those from the finite element buckling analysis using ANSYS. Finally, the influence of multiple holes on the distortional buckling behaviour and corresponding elastic buckling stress of beams in bending is discussed.

Study of thermal buckling behavior of plain woven C/SiC composite plate using digital image correlation technique and finite element simulation

In this study, the thermal buckling behavior of plain woven C/SiC composite plate is investigated by a noncontact measurement based on the three-dimensional digital image correlation (DIC) technique and finite element analysis. The plain woven C/SiC composite plate is fixed by a water-cooling steel frame and one-side heated by quartz lamp array heating apparatus. The buckling temperature and the first buckling mode shape of the C/SiC composite plate are determined from the temperature-displacement curves and full-field deformation that are obtained from the DIC-based experiment. A nonlinear finite element buckling analysis with initial imperfection is performed using the ANSYS software. In order to improve the accuracy of the numerical simulation, a clamping frame model is further proposed for simulating the real clamping boundary in experiment. The results of the finite element simulation and DIC-based measurement coincide well regarding the temperature-displacement curve tendency and critical buckling temperature. Finally, a parametric study is performed using the presented numerical model to investigate the thermal buckling behavior of plain woven C/SiC composite plates with various dimension sizes.

超双対数を用いた 2-mode 漸近展開法と有限要素座屈解析への応用

超双対数を用いた 2-mode 漸近展開法と有限要素座屈解析への応用

Elastic Stability Behavior of Self-Anchored Suspension Bridges by the Deflection Theory

To investigate the elastic buckling behavior of self-anchored suspension bridges subjected to proportionally increasing dead loads, a new stability procedure is proposed based on the deflection theory. For this purpose, a finite element buckling analysis is performed using the initial state solution based on the unstrained length method (ULM) (Ref. 1 ). The finite element solutions are compared with those by the deflection theory. It is shown that both the main girder and tower of the self-anchored suspension bridge are under compression, but their fundamental buckling modes are tower-dominant. Importantly, it is observed that local buckling within the main girder supported by hangers occurs without any geometric change of the main cable, in the higher buckling modes of the self-anchored suspension bridge.

Non-associative [formula omitted] plasticity model for finite element buckling analysis of shells in the inelastic range

The development and numerical implementation of a special-purpose constitutive model is described for investigating the structural stability of cylindrical metal shells under axial compression and bending, which buckle in the inelastic range. The model employs von Mises yield surface (J2 plasticity) and the rate form of J2 deformation theory, leading to a non-associated flow rule. Special emphasis is given on plastic flow continuity. The numerical implementation is conducted through both the classical Euler-backward and Euler-forward substitution numerical schemes, where stress and strain tensors are described in curvilinear coordinates, with the extra constraint of zero normal stress through the shell thickness. The numerical results will be compared with available experimental data. The model is implemented within an in-house finite element technique for the nonlinear analysis of relatively thick cylindrical metal shells that uses a “tube-element” discretization, and it is employed for the solution of some benchmark problems.

Buckling analysis of unitized curvilinearly stiffened composite panels

Innovative manufacturing technology has led to the fabrication of complex shape and multi-functional structures by using the concept of integrated and bonded unitized structural components. To study the stability behavior of such structural designs, this paper presents an efficient finite element buckling analysis of unitized stiffened composite panel stiffened by arbitrarily shaped stiffeners. A first-order shear-deformation theory is employed for both the panel and the stiffeners. Displacement compatibility conditions are imposed at the panel-stiffeners interfaces. To obviate remeshing when the stiffener shape changes, the stiffeners’ geometry and displacement are expressed in terms of those of the panel middle surface through compatibility conditions that make use of the interpolation polynomials employed in the finite element method. To accommodate any shaped stiffeners, a generalized geometry parametrization tool is developed to parameterize the shape of the stiffeners including the stiffener placement and the stiffener geometric curvature. Convergence and validation studies using the present method for the buckling analysis of stiffened isotropic and composite panels are conducted to illustrate the accuracy of the present method. Parametric studies show that the stiffener placement, the stiffener geometric curvature, the stiffener depth ratio (height-to-width ratio) and laminates fiber ply orientation influence both the plate bucking load and the correspond buckling mode shape. The tailoriability of the stiffeners shape and the laminates fiber ply orientation provides an enhanced design space in the structural design for improving the structural stability.

Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory

Graphene-polymer nano-composites are one of the most applicable engineering nanostructures with superior mechanical properties. In the present study, a finite element (FE) approach based on the size dependent nonlocal elasticity theory is developed for buckling analysis of nano-scaled multi-layered graphene sheets (MLGSs) embedded in polymer matrix. The van der Waals (vdW) interactions between the graphene layers and graphene-polymer are simulated as a set of linear springs using the Lennard-Jones potential model. The governing stability equations for nonlocal classical orthotropic plates together with the weighted residual formulation are employed to explicitly obtain stiffness and buckling matrices for a multi-layered super element of MLGS. The accuracy of the current finite element analysis (FEA) is approved through a comparison with molecular dynamics (MD) and analytical solutions available in the literature. Effects of nonlocal parameter, dimensions, vdW interactions, elastic foundation, mode numbers and boundary conditions on critical in-plane loads are investigated for different types of MLGS. It is found that buckling loads of MLGS are generally of two types namely In-Phase (INPH) and Out-of-Phase (OPH) loads. The INPH loads are independent of interlayer vdW interactions while the OPH loads depend on vdW interactions. It is seen that the decreasing effect of nonlocal parameter on the OPH buckling loads dwindles as the interlayer vdW interactions become stronger. Also, it is found that the small scale and polymer substrate have noticeable effects on the buckling loads of embedded MLGS.

Buckling Analysis of Composite Lattice Cylindrical Shells with Ribs Defects

In this paper, the buckling behavior of a composite lattice cylindrical shell is studied and effects of rib defects on the distribution of stress field and buckling response of the shell is investigated. A three dimensional finite element buckling analysis of the lattice shell is carried out using ANSYS suit of program. Geometrical data and material properties of the shell are obtained from the specimens made by filament winding method. Effects of various parameters including the geometrical ratios, defects of ribs on buckling response of the shell are studied. Buckling loads of composite lattice cylindrical shells under axial and shear forces have been obtained experimentally and results are compared with finite element results.

Finite element buckling analysis of laminated composite sandwich panels with transversely flexible core carrying attached elastic strip

In this article, a three-dimensional finite element model is proposed to study the effect of distributed attached mass with thickness and stiffness on the buckling instability of sandwich panels with transversely flexible cores. Unlike the previous works in the literature which have made use of unified displacement theories, the present model uses different types of finite elements to model the core and the face sheets. It utilizes shell elements for the face sheets and three-dimensional solid elements for the core which enables the model to account for the transverse flexibility of the structure. The motions of the face sheets and the core as well as the attached mass are related through defining constraint equations between the nodes of their respective finite elements based on the concept of master and slave nodes which is incorporated into the finite element analysis program ANSYS through a user-defined subroutine. The validated finite element model is then used to study the effects of size, thickness, material property, aspect ratio, and the position of the attached mass on the buckling load of a sandwich panel under different combinations of boundary conditions. The results presented in this study have hitherto not been reported in the literature.

The Overall Stability Calculation Method for Sway Frame

There are three levels in stability calculating for sway frame. The first level is the traditional effective length method. The second level is the effective length method considering interaction of columns in one story and the third level is the effective length method considering inter-story interaction. The traditional effective length method may lead to unsafe design. Using the concept of equivalent negative stiffness, story stiffness to negative stiffness ratio factor and story support factor were proposed. Through the story stiffness to negative stiffness ratio factor, the weak-story and the inter-story support relationship can be found. Then, a formula for calculating the elastic stability capacity of sway frame is proposed, by which the inter-column interaction and inter-story interaction can be considered, and the finite element buckling analysis for stability capacity can be avoided. Through the stability capacity, the column effective length can be calculated. The results show that this simple calculation method has good precision and accuracy, can be used for engineering design and theoretical calculations.

Research on Buckling Analysis of Pressure Vessel Based on Finite Element Analysis and Support Vector Machine

The failure mode of structural instability failure caused by inner stress is unexpected collapse and has more dangerous than the intensity failure. While finite element buckling analysis, an efficient numerical method, can be used to research the stability of pressure vessel for various critical loads. In this study, the geometrical stiffness matrix is formed and several special working conditions are considered in finite element analysis process. Numerical examples are presented to verify the proposed design of the pressure vessel with shell framework because it is actually the critical step in the thin-walled shell configuration that tend to happen structural failure. The 3D model of pressure vessel was established and the buckling load calculations under the actual operating conditions have been carried out to obtain the modal deformation condition and the safety factor. The FEM analysis results performed by using ANSYS software showed that the structure has a smaller deformation and a higher structural stability, which indicated that the vessel design can meet the working condition requirements.