Stability of tapered cantilever columns subjected to follower forces

Accurate estimates of critical loads of tapered cantilever columns with fixed or spring hinged ends subjected to follower forces are obtained in this paper. A Galerkin finite element method is used to solve the governing differential equation with variable coefficients. The effect of the stiffness of the spring hinge on the critical load is also studied.     

Dynamic stability of cantilever columns resting on an elastic foundation

Instability boundaries for cantilever columns resting on an elastic foundation are determined using finite element method for various foundation modulii. The study reveals that dynamic stability boundaries for such columns can be represented in terms of three separate dynamic stability curves corresponding to low foundation moduli, high foundation moduli and the transition regions of foundation moduli.     

Probabilistic free vibration analysis of beams subjected to axial loads

A stochastic finite-element-based algorithm for the probabilistic free vibration analysis of beams subjected to axial forces is proposed in this paper through combination of the advantages of the response surface method, finite element method and Monte Carlo simulation. Uncertainties in the structural parameters can be taken into account in this algorithm. Three response surface models are proposed. Model I: star experiment design using a quadratic polynomial without cross-terms; Model II: minimum experiment design using a quadratic polynomial with cross-terms; Model III: composite experiment design using a quadratic polynomial with cross-terms.A separate set of finite element data is generated to verify the models. The results show that the Model II is the most promising one in view of its accuracy and efficiency. Probabilistic free vibration analysis of a simply supported beam is performed to investigate the effects of various parameters on the statistical moments of the frequency response of beams. It is found that the geometric properties of beams have significant effects on the variation of frequency response.     

Parametric instability of spinning pretwisted beams subjected to sinusoidal compressive axial loads

The equations of motion of a spinning pretwisted beam under pulsating compressive axial loads are formulated using Euler beam theory and the assumed mode method. Unstable regions of flutter instability are found to exist for beams with non-zero pretwist angles, within the stable critical speed zones. The narrower regions of flutter instability separate the stable critical speed zones into smaller stable sub-regions. The compressive axial force is assumed to consist of a steady state value and a time-dependent portion. The multiple scale method is used to determine the regions of instability due to the resulting parametric excitations. As the spin speed varies within the stable sub-regions, consistent shifts and widening of unstable regions due to axial load perturbation are observed. Widths of the unstable regions are found to decrease with decreasing pretwist angle and compressive axial force as well as increasing aspect ratio towards unity.     

Initially stressed vibrations of a cantilever beam subjected to an intermediate concentrated axial load

A finite element formulation including the effect of shear and rotatory inertia is used to obtain the fundamental frequency of a cantilever beam subjected to an intermediate concentrated axial load. Results in terms of buckling and fundamental frequency parameters as a function of critical load at various intermediate positions are presented in tables for various slenderness ratios of beams.     

Finite element analysis of spiral strands with different shapes subjected to axial loads

In this paper a new mathematical geometric model of spiral one or two-layered oval wire strands are proposed and an accurate computational two-layered oval strand 3D solid model, which is used for a finite element analysis, is presented. The three dimensional curve geometry of wires axes in the individual layers of the oval strand consists of straight linear and helical segments. The present geometric model fully considers the spatial configuration of individual wires in the right and left hand lay strand. Derived geometric equations were used for the generation of accurate 3D geometric and computational models for different types of strands. This study develops 3D finite element models of two-layer spiral round, triangular and oval strands subjected to axial loads using ABAQUS/Explicit software. Accurate modelling and understanding of their mechanical behaviour is complicated due to the complex contact interactions and conditions that exist between individual spirally wound wires. Comparisons of predicted responses for the strands with different shapes and constructions are presented. Resultant stress and/or deformation behaviours are discussed.     

Analysis of shallow spherical and paraboloidal cantilever shells under symmetrically distributed loads

A mathematical stress and deformation analysis of thin shallow spherical and paraboloidal cantilever shells is presented. This paper describes a method of solution of Reissner's differential equations for the generally distributed loads, and then shows the determination of the particular solutions corresponding to rotationally symmetrical distributed loads. Computer results generated in the form of nondimensional curves for cantilever shells supported continuously around the apex by a rigid ring provide stresses and displacements in the most general form, allowing the engineer to perform an automatic stress analysis and to obtain an optimized design in a minimum length of time.     

The large deformation,post-buckling and catastrophic stability of slender cantilever columns

Several solutions, analytical and numerical, exist for the cases of nonlinear bending of beams and post-buckling of columns. However, the solution for the general case of an arbitrarily inclined load does not seem to exist. In this paper, the governing equation of equilibrium for a cantilever of variable cross section under an arbitrarily inclined load is formulated, by using the axial and transverse displacement quantities. The solution is obtained by means of a simple numerical iterative procedure. The results for the post-buckling and non-linear bending of the structure under concentrated tip load, uniformily distributed load and linearly varying load are presented, and compared with the available results, wherever possible. Further, a type of catastrophic behaviour in post-buckling region is observed and studied using the same numerical scheme. The method is general and can be used for any load variation and for any tapered beam-column.     

Stability of columns subjected to a uniformly distributed load with one end elastically restrained to move axially

The stability behaviour of columns, subjected to a uniformly distributed axial load and with one end elastically restrained to move axially, is studied in this paper. The elastic axial restraint is represented by means of an axial spring. The finite element formulation, including prebuckling load analysis and stability analysis, is briefly described. Numerical results in terms of stability parameter for various values of axial spring stiffness parameter for four types of boundary conditions are obtained. Stability mode shapes for three specific values of axial spring stiffness parameter are given.     

Dynamic stiffness matrix of an axisymmetric shell and response to harmonic distributed loads

This paper describes a procedure for taking into account distributed loads in the dynamic stiffness matrix formulation, also known as the continuous element method. In that formulation, concentrated or linearly distributed loads are taken into account by considering the necessary number of elements in such a way that these loads are applied on element boundaries. As for distributed loads such as pressure and surface forces, they were not provided for in the formulation. The validation is achieved by comparison of accuracy and computational time of harmonic response calculations performed by the continuous element model and a finite element model.     

Post-buckling analysis of spring-hinged cantilever columns

The post-buckling behaviour of spring-hinged cantilever columns has been investigated in this paper. The governing nonlinear differential equation with variable coefficients has been solved using Galerkin finite element method. Three loading conditions, namely, a concentrated tip load, a uniformly distributed load and a linearly varying load, acting on the column are considered in the present analysis. Very accurate estimates of the axial load parameters have been presented for different end slopes and for different spring constants.     

Post-buckling analysis of tapered cantilever columns

The post-buckling behaviour of tapered cantilever columns is investigated in this paper. The governing nonlinear differential equation with variable coefficients is solved using the Galerkin finite element method. Three loading conditions on the column are considered in the analysis - a concentrated tip load, a uniformly distributed load and a linearly varying load. Very accurate estimates of the axial load parameters are presented for various end slopes and for different taper parameters.     

Computer-aided analysis of reinforced concrete columns subjected to axial compression and bending. Part II: T-shaped sections

This paper presents the writer's experience in investigating numerically the strength behaviour of short T-shaped reinforced concrete (RC) columns in order to provide design aids for structural engineers. Computer programs were developed for the analytical study of T-shaped RC column sections subjected to uniaxial/biaxial bending with axial compression. The interaction curves for L-shaped members, in Part I [Mallikarjuna and P. Mahadevappa, Comput. Struct. 44, 1121–1138 (1992)], and for T-shaped sections, in the present paper, were derived to provide advice for design information. This paper deals with the definitions and materials that are used in the limit state design of reinforced concrete structures. The programs presented here are written to operate in a conversational mode so that the analyst can respond to messages from the computer.     

Dynamic stability of a stiff-edged cylindrical shell subjected to a follower force

In this paper, the dynamic stability of a completely free cylindrical shell under a follower force is analyzed. Both edges of the shell are assumed to have rings to increase the rigidity of the structure. Hamilton's principle is used to derive the equations of motion, and the finite element method is applied to investigate the dynamic stability of the shell. Numerical analysis is performed for each circumferential wave number by using the orthogonality of the vibration modes of the shell. The kinetic or static analysis is carried out according to whether the circumferential wave number is equal to one or not. Numerical results show that the stiffening ring stabilizes the circumferential higher modes. On the other hand, it is found that the ring may destabilize the beam-like mode.     

Optimal design of clamped columns for stability under combined axial compression and torsion

In this paper the problem of the optimal design of columns under combined compression and torsion is investigated. A cross-sectional area varying along the axis of the column which leads to the maximal critical loading is sought. The varying cross-section is approximated either by a function with free parameters or is determined using Pontriagin’s maximum principle.     

Dynamic pull-in of thermal cantilever nanoswitches subjected to dispersion and axial forces using nonlocal elasticity theory

Microsystem Technologies - Precise analysis of nanoelectromechanical systems has an outstanding contribution in performance improvement of such systems. In this research, the dynamic...     

Influence of an elastic end support on the stability of a nonuniform cantilever subjected to dissipative and nonconservative forces

The influence of an elastic end support on the stability of a damped, linearly tapered cantilever of rectangular cross section subjected to a follower-end-load is studied. The equation of motion is formulated within the Euler-Bernoulli theory for the case of a Kelvin model viscoelastic beam. The effect of external damping is also included in the partial differential equation of motion. The associated adjoint boundary value problem is derived and appropriate adjoint variational principle is introduced. This variational principle is used as the basis for determining approximately the values of the critical load of the system as it depends upon the taper parameters and the stiffness of the elastic end support. It is found that for a given damped, tapered beam the introduction of an elastic support may destabilize the system in certain eases. Furthermore, the critical value of the stiffness of elastic support at which the instability mechanism changes from flutter to divergence or vice versa is decreased as taper increases. For a given support, an increase in taper also decreases the value of the critical load of the system. These reducing effects are more pronounced with increase in thickness taper. The familiar destabilization phenomenon due to small internal damping is observed from the numerical results, but sufficiently large internal damping may have a stabilizing or destabilizing effect depending on the stiffness of the elastic support.     

Stability of columns subjected to an intermediate concentrated load

In column stability studies where columns are subjected to intermediate concentrated loads, effects of shear deformation will be predominant even though the columns are slender when the loaded length of the column is appreciably small compared with its overall length. This aspect is studied in detail in this paper and realistic estimates for the stability parameters of columns subjected to intermediate concentrated loads are presented.     

Elastic buckling of perforated plates subjected to concentrated loads

Results are presented for concentrated loading applied to perforated plates of different aspect ratios. Two different in-plane restraint conditions and four edge conditions have been analysed. The results have been obtained by the application of the conjugate load/displacement method of elastic stability analysis, and show how simple modifications to plate geometry, particularly with respect to perforation aspect ratio and support conditions, can effect major changes to the elastic critical load.