Buckling Electrothermal NEMS Actuators: Analytic Design for Very Slender Beams

Analytic approximations are presented for the response of buckling-mode electrothermal actuators with very slender beams with a width-to-length ratio of W/L≤0.001 of the type found in nanoelectromechanical systems (NEMS). The results are found as closed-form solutions to the Euler beam bending theory rather than by an iterative numerical solution or a time-consuming finite element analysis. Expressions for transverse deflections and stiffness are presented for actuators with the common raised cosine and chevron pre-buckled shapes. The approximations are valid when the effects of bending dominate over those of axial compression. A few higher-order approximations are also presented for less slender beams with 0.001≤W/L≤0.01.

Design of cylindrical steel liquid tanks with stepped walls using One-foot method

Cylindrical steel tanks are used in most countries to store bulk volumes of both solid and liquid products such as water, oil, gasoline and grain. Such steel tanks are prone to buckling when subjected to external pressure either due to vacuum or due to wind. These types of shell structures are generally controlled by elastic buckling failure because of the thin wall thickness. Cylindrical shells are commonly constructed with stepwise variable wall thickness due to economic reasons. The thickness of the tank shell wall is designed to increase from top to bottom because the stress resultants on the tank wall gradually increase towards the base of the tank. For open-top tanks, a primary stiffening ring is required at or near the top to maintain roundness under all loads. Stress resultants in a primary stiffening ring were previously identified by the Author for uniform wall thick tanks. In this new study, the applicability of this hand calculation method in stepped wall tanks has been investigated. Pursuant to this goal, a specified tank shell was designed considering One-foot method. Then, the stepped wall tank was transformed into an equivalent 1-course tank for hand calculation. Using the previously developed hand calculation method by Author, a test for the in-plane bending moment in the ring was conducted to achieve an acceptable value for stepped wall tanks. The analysis results show that the previously proposed method for uniform wall thick tanks may also be used for stepped wall tanks considering an equivalent thickness. On the other hand, using Linear Buckling Analysis (LBA), the buckling mode was obtained for two different stepped wall tanks in the study.

Global Buckling Investigation of the Flanged Cruciform H-shapes Columns (FCHCs)

In China, increasing the application ratio of hot-rolled H-shapes has become a severe problem that the government, academia, and engineering circles must vigorously address. Research on reasonable hot-rolled H-shapes built-up columns is one of the primary methods. After reviewing the various combination columns in the existing research, the paper proposes the new flanged cruciform H-shapes columns (FCHCs) made of three hot-rolled H-shapes. Using comprehensive imperfections given by the design standard, GB50017-2017, the paper analyzes the global buckling of FCHCs subjected to the axial compression load. The global buckling factor obtained is compared with the current national design code. Comparative analysis of seventy-two specimens of Q345 and Q460 steel found that the global buckling mode of FCHCs was flexural bending buckling around the axis of symmetry, and global torsional buckling and local buckling did not occur. Furthermore, the corresponding column curves in current design codes overestimate the dimensionless buckling strength of the novel FCHCs. Therefore, designers need to drop a class to select the global buckling factor within a specific range. Finally, new column global buckling curves are proposed based on a non-linear fitting of the numerical results according to the current national design codes.

Composite plate analysis made in an unsymmetric configuartion

The work presents a thin-walled plate element with the central rectangular cut-out which can be use as an elastic or load-bearing element. Plates were made of carbon epoxy laminate and subjected to uniform compression. Plates were simply supported on shorter edges, and loaded axial load. The study included analysis of the critical and weakly post-critical behavior using experimental and numerical methods. Numerical analysis was performed with using linear analysis of eigenvalue problem to determination critical loads. The second step connected nonlinear analysis of structure with initiated geometrically imperfection corresponding to the flexural-torsional buckling mode of the plate. To the numerical calculations the commercial ABAQUS program was used.

Buckling Pattern Transition Of Periodic Porous Elastomers Induced By Proportional Loading Conditions

This paper focuses on the buckling instabilities of periodic porous elastomers under combined multiaxial loading. A numerical model based on the periodic boundary condition (PBC) for the 2D representative volume element (RVE) is proposed, in which two proportional loading parameters are employed to control the complex stressing state applied to the RVE model. A homogenization-based orthogonal transformation matrix is established by satisfying the equality of the total work rate to realize a proportional multiaxial loading on the RVE. First, the transition behavior of buckling patterns of periodic porous structures is revealed through instability analysis for the RVE consisting of [Formula: see text] primitive cells with circular holes subjected to different proportional loading conditions. Simulation results show that the first-order buckling mode of RVE may change suddenly from a uniaxial shearing buckling pattern to a biaxial rotating buckling pattern at a critical loading proportion. Then the influences of the number of primitive cells in the enlarged RVE on the buckling behavior are discussed. When the number of primitive cells in any enlarging direction is odd, the points of buckling pattern transition of the enlarged RVEs vary significantly with the number of cells in RVE. When the number of primitive cells is even in both enlarging directions, there is no apparent difference for the critical buckling stresses of the enlarged RVEs.

CLASSIFICATION OF BUCKLING MODES IN STIFFENED FUNCTIONALLY GRADED COMPOSITE TUBES SUBJECT TO BENDING

Bamboo poles, and other one-dimensional thin-walled structures are usually loaded under compression, which may also be subject to bending arising from eccentric loading. Many of these structures contain diaphragms or circumferential stiffeners to prevent cross-sectional distortions and so enhance overall load-carrying response. Such hierarchical structures can compartmentalize buckling to local regions in addition to withstanding global buckling phenomena. Predicting the buckling mode shapes of such structures for a range of geometric parameters is challenging due to the interaction of these global and local modes. Abaqus finite element software is used to model thousands of circular hollow tubes with random geometric parameters such that the ratios of radius to periodic length range from 1/3-1/7, the ratio of wall thickness to radius varies from 1/4-1/10. The material used in this study is a type of bamboo, where the Young’s and shear moduli are point-wise orthotropic and gradually increase in magnitude in the radial direction. Under eccentric loads with varying eccentricity, the structures can buckle into a global mode or local modes within an internode, i.e. periodic unit. Moreover, the local modes may contain only one wave or multiple waves in the circumferential direction. As expected, numerical results show that the global mode is more likely to occur in small and thick tubes, whereas the local modes are observed in larger tubes with a smaller number of circumferential waves present in thicker walls. Also, greater eccentricity pushes the local mode domains towards smaller tubes. An efficient classification method is developed herein to identify the domains of each mode shape in terms of radius, wall thickness and eccentricity. Based on linear discriminant analysis, explicit boundary surfaces for the three domains are defined for the obtained data, which can help designers in predicting the mode shapes of tubular structures under axial bending.

SCALING METHODOLOGY FOR BUCKLING OF COMPOSITE CONICAL SHELLS IN AXIAL COMPRESSIONConical shells are commonly used as structural components for launch vehicles. The axial compression experienced during launch is one of the sizing load cases, because it can lead to loss of structural stability. Because experimentally testing these full-scale structures is cumbersome and expensive, it is expedient to understand how reduced-scale shells can be designed such that their buckling behavior is representative of the full-scale shell behavior. An analytical, sequential scaling methodology is developed based on the nondimensional governing equations for composite conical shells with a symmetric, balanced layup and negligible flexural anisotropy. Linear and nonlinear finite element analyses characterizing the buckling behavior of the different size shells yielded comparable results in terms of buckling load, meridional displacement, and buckling mode. The inclusion of geometric imperfections affects the prediction accuracy, but not to the extent that the methodology is no longer valid.

Conical shells are commonly used as structural components for launch vehicles. The axial compression experienced during launch is one of the sizing load cases, because it can lead to loss of structural stability. Because experimentally testing these full-scale structures is cumbersome and expensive, it is expedient to understand how reduced-scale shells can be designed such that their buckling behavior is representative of the full-scale shell behavior. An analytical, sequential scaling methodology is developed based on the nondimensional governing equations for composite conical shells with a symmetric, balanced layup and negligible flexural anisotropy. Linear and nonlinear finite element analyses characterizing the buckling behavior of the different size shells yielded comparable results in terms of buckling load, meridional displacement, and buckling mode. The inclusion of geometric imperfections affects the prediction accuracy, but not to the extent that the methodology is no longer valid.

Stiffness compensation through matching buckling loads in a compliant four-bar mechanism

In this paper a novel alternative method of stiffness compensation in buckled mechanisms is investigated. This method involves the use of critical load matching, i.e. matching the first two buckling loads of a mechanism. An analytical simply supported four-bar linkage model consisting of three rigid links and four torsion springs in the joints is proposed for the analysis of this method. It is found that the first two buckling loads are exactly equal when the two outer springs are three times stiffer than the two inner springs. The force-deflection characteristic of this linkage architecture showed statically balanced behavior in both symmetric and asymmetric actuation. Using modal analysis, it was shown that the sum of the decomposed strain energy per buckling mode is constant throughout the motion range for this architecture. An equivalent lumped-compliant four-bar mechanism is designed; finite element and experimental analysis showed near zero actuation forces, verifying that critical load matching may be used to achieve significant stiffness compensation in buckled mechanisms.