Critical Load Coefficient Research Articles

Effects of composite material layering on the buckling mode of a cylindrical shell

Introduction. At present, composite materials are widely used in building structures and their components. The relevance of the work is determined by the buckling study of a shell structure made of a carbon fiber reinforced polymer. Despite the available experience in creating geometric models of finite element grids and studying the buckling of shell structures, the task of analyzing the mechanical behavior of shell layers remains insufficiently investigated. Therefore, research into the effects caused by polymer layering variations on a buckling mode appears to be urgent for regulating the layering process at various angle combinations due to a lack of sufficient data.Aim. The study was aimed at identifying a layering pattern, under which maximum and minimum critical forces operate.Materials and methods. The object of the study involves a cylindrical shell with a radius of 300 mm, a height of 600 mm, and a wall thickness of 1.56 mm made of eight variously-oriented carbon fiber layers impregnated with epoxy resin. The design modeling was performed using the finite element method. The cylindrical shell walls were modeled in terms of Laminate type flat elements, taking into account the composite layers. At the lower end, the cylinder was rigidly fixed and 100 kN axial compressive force was applied to the upper end of the cylinder. Using a software package, the variants of buckling modes were obtained for further analysis.Results. The data, describing the buckling of a cylindrical shell, including the critical load coefficient at the first buckling mode were obtained by the finite element method. In addition, the dependence of a critical force on layering patterns was determined. Depending on the critical force value and the buckling mode, the most and least favorable patterns of layering in a package of a composite material were selected.Conclusions. The orientation of layers in a composite material package affects the buckling mode and the value of critical force. An optimal selection of the layer orientation increases the critical force value by 2.25 times based on the information about the conditions of structural loading and fastening.

Service Limits for Metal Oxide Varistors Having Cylindrical Symmetry as Function of the Ambient Temperature

This article presents an original experimental method applied to assess the stability limits of a given Metal Oxide Varistor (MOV), with cylindrical symmetry (cylinder or disk shape), as a direct relation between the ambient temperature and the service rated voltage, in the permanent operational regime. As the crossing current of a certain varistor is heavily influenced by its physical temperature, we must find an empirical relationship between these two parameters for a symmetrical configuration. Each ambient temperature can increase the temperature reference and any higher voltage will also produce an increased current, causing a uncontrolled runaway heating process, in an avalanche model. We tried to eliminate any references to technical dimensions or device values, focusing on material parameters. In the case of a symmetric MOV, we will consider the load coefficient, which is the ratio between the service DC voltage and the nominal DC opening voltage. By using experimental measurements and a simple mathematical model, we will establish the relation between the critical load coefficient and the ambient temperature in the case of symmetrical MOVs. This procedure could be applied to the design of more performant and safe surge arrester devices using existing MOVs, for all voltage levels and symmetrical configurations.

Initial prestress design and optimization of cable-stiffened latticed shells

The cable-stiffened latticed shell is a hybrid structure composed of a single-layer latticed shell and a cable-strut system. Only after the initial prestress is applied can the rigid and flexible components work together, so this paper proposes a new initial prestress design and optimization method of cable-stiffened latticed shells. Firstly, based on the equilibrium matrix theory and static analysis, independent self-internal force modes of the hybrid structure are obtained accurately. The force finding analysis is carried out by a linear combination of these self-internal force modes, ensuring the initial cable forces in computational models are the same as the design values. Then the design values of the initial forces in a cable-stiffened latticed shell are optimized, taking the combination coefficients of the self-internal force modes as the optimization variables. And the maximum bending moment of the key members and the critical load coefficient when the emergence of slacking cables are considered as optimization objectives. Then, a hybrid multi-objective optimization algorithm is proposed based on the interior point method and NGSA-II algorithm. The optimization example shows that the initial prestress optimization has a significant effect on the stability of the structure. The maximum bending moment can be reduced by 18%, and the ultimate bearing capacity can be increased by 47%, which verifies the correctness and applicability of the proposed design and optimization method.

Energy method-based stability calculation of stiffened panels

ABSTRACTThis study aims to investigate the stability of stiffened panels, which is important for marine structures. A series of finite-element (FE) calculation models of 4-side simply supported stiffened panels under uniaxial compression load with different stiffener count and stiffener section-cross area are established by energy method. The variation rules of buckling strength of stiffened panel with longitudinal number and longitudinal cross-section area are analysed. The results show that critical load coefficient (CLC) is much sensitive to longitudinal cross-section area; it increases with the growth of longitudinal cross-section area and the amplitude of increment increases gradually. CLC almost increases with the growth of longitudinal number. CLC of stiffened panel is not only related to the number of longitudinal but also to the longitudinal position. The closer the location of longitudinal to the buckling half-wave crest, the better the buckling strength of the stiffened panel will be.

A Study on Effective Length of Slender Column with Elastic Restraints

Abstract The bottom slender columns are widely used in modern high rise buildings because of the existence of floor with opening, and the effective length will deeply affect bearing capacity of the column. This paper presents a new methodology for calculate the effective length of the bottom slender columns based on the equivalent model. The elastic restraints of beams are considered as lateral support spring, and the effective length of the column is determined through buckling analysis of the column fixed at bottom and elastic supported at top. A case study of high rise building with 20 m bottom slender column was conducted as follows: A horizontal force was applied on the floor supporting of the slender column top, and the lateral displacement of the column could be calculated through whole structure analysis in design procedure, therefore, the spring stiffness can be figured out through the applied horizontal force divided by the displacement. Then, eigenvalue buckling analysis was conducted on the column by using software ANSYS. The buckling mode shape were checked and the lowest buckling mode was solved, the buckling critical load could be obtained by multiplying the critical load coefficient by compression stress of the member. Finally, the effective length factor could be determined by comparing the bearing capacity of the bottom slender column with bearing capacity of that column with hinge joint at both ends. The results indicate that the effective length factor of the bottom slender column based on the proposed method is 21% larger than that in the design code. The weakness in bearing capacity of the bottom slender column should be considered during design.

Study for Dynamic Stability Behavior of I-Section Cantilever Beam under Axis Compressive Load

By mean of the energy functional variational principle and considering shear lag effect of flange, the dynamic governing differential equation for the I-section cantilever beam in the action of compressive loadPat the member end is obtained. The equation is solved by the separation variable method. According to the weigh residual method, the relation between natural frequency coefficient and critical load coefficient as well as the flutter critical load coefficient are made, the influence of shear lag effect on natural frequency coefficient and critical load coefficient is discussed.

Buckling Reliability Analysis for the Cylindrical Shell with Initial Defects

in this paper, the asymptotic expression of the buckling critical load coefficient of the thin cylindrical shell with local axial symmetry initial defects under the axial loads is deduced by used the Karman-Donnel Equation. The buckling safety margin equation of the cylindrical shell with initial defects is constructed. Furthermore, the buckling reliability index is solved by used AFOSM (Advanced First-Order Second Moment) method. In the end, a numerical example is given to analyze the influence of the band width and amplitude of local axial symmetry initial defects on the structural buckling reliability index.

Optimization Design and Buckling Analysis of ZLP500L Type Suspended Platform

To take ZLP500L type suspended platform for research object, establishes parametric finite element model with ANSYS, and analyze static performance of its structure. Define the platform section parameters as the design variables, and structure in dangerous working conditions of stress and displacement as state variables, makes optimization design of platform with first-order method, so obtain lightweight high degree of section parameters which reducing 26.16% total quality of platform. Meanwhile makes buckling analysis of optimized platform to obtain smallest the critical load coefficient is 171.56, and then verifies the platform structure stability, provides theory basis to ZLP500L type suspended platform design and alteration.

Integrity Stable Reliability Analysis of Stochastic Structure System under Multiple Stochastic Loads

Generally, a safe margin equation is established by critical load coefficient and external load coefficient of the system in structural integrity stable reliability analysis, and then the reliability index of structural integrity stability is educed. Critical load coefficient is always obtained on condition that structure is acted on by one load. Actually, besides one load acting on the structure, their distribution is not always the same. In addition, because of the stochastic characteristic of structure system itself (e.g., cross-section of element, length, modulus of elasticity etc. are random variables), it is difficult for structural integrity stable reliability analysis. According to the theory of structure system stability and basal concept of reliability, the safe margins of structure system under different distribution loads are presented in this paper. The expression of safe margin sensitivity is given by stochastic finite element method because the safe margin is the expression of implicit function. Furthermore, the reliability indexes of the safe margin under different condition are educed by the advanced first order second moment method (AFOSM). By comparison and analysis, the structural integrity stable reliability index is ultimately obtained.

Initial Compressive Buckling of Clamped Plates Resting on Tensionless Elastic or Rigid Foundations

The unilateral contact buckling problem of thin plates resting on tensionless foundations is investigated. Three different plate models are considered. For a plate of limited length on a tensionless elastic foundation, the plate is first simplified to a one-dimensional mechanical model by assuming a buckling mode in terms of transverse coordinates, after which a new method is employed to determine the initially unknown boundaries of the areas in contact. Based on the continuity condition on the borderline between contact and noncontact regions, the buckling mode displacements of the whole plate may be expressed through the critical load coefficient and the first half-wavelength, reducing the buckling problem to two nonlinear algebraic equations with two unknowns. This procedure has been named the transfer function method. For a very long plate with a symmetric buckling mode, an infinite plate model with two half-waves is presented. For a plate on a rigid foundation, a single half-wave buckling model is shown to be appropriate. Comparison of limiting cases with exact solutions and with ABAQUS results showed good agreement. Finally, the influences of aspect ratio and foundation stiffness are presented.