Buckling Load Parameter Research Articles

A Simple Formula for Evaluating the Fundamental Frequency Parameter of Initially Stressed Uniform Beams on Elastic Foundation

A simple design formula is derived here to evaluate the fundamental frequency parameter of initially stressed (subjected to axial concentrated load at the ends) uniform beams resting on elastic foundation. Even though the basis for derivation of the formula is based on the finite element method, the applicability of the formula is general and can be used effectively, once the buckling load parameter, stress free frequency parameter and the applied concentrated load parameter are known, to obtain the fundamental frequency parameter of the stressed beam. The assumption involved in deriving the formula is that the mode shapes of buckling, stress free vibration and stressed vibration are the same. The effectiveness of the formula is demonstrated through numerical examples.

ASYMMETRIC VIBRATIONS AND ELASTIC STABILITY OF POLAR ORTHOTROPIC CIRCULAR PLATES OF LINEARLY VARYING PROFILE

Asymmetric vibration of polar orthotropic circular plates of linearly varying thickness subjected to hydrostatic in-plane force are discussed on the basis of classical plate theory. An approximate solution of the problem has been obtained by the Ritz method, which employs functions based upon the static deflection of polar orthotropic plates. This method has a faster rate of convergence as compared to the polynomial co-ordinate functions. Frequency parameters of the plate with elastically restrained edge conditions are presented for the three modes of vibrations for various values of taper parameter, rigidity ratio, flexibility parameter and buckling load parameter. The critical buckling loads for elastically restrained edge conditions have been obtained. A comparison of results with those available in the literature shows an excellent agreement.

Optimization of multilaminated structures using higher-order deformation models

A refined shear deformation theory assuming a non-linear variation for the displacement field is used to develop discrete models for the sensitivity analysis and optimization of thick and thin multilayered angle ply composite plate structures. The structural and sensitivity analysis formulation is developed for a family of C 0 Lagrangian elements, with eleven, nine and seven degrees of freedom per node using a single layer formulation. The design sensitivities of structural response for static, free vibrations and buckling situations for objective and/or constraint functions with respect to ply angles and ply thicknesses are developed. These different objectives and/or constraints can be generalized displacements at specified nodes, Hoffman's stress failure criterion, elastic strain energy, natural frequencies of chosen vibration modes, buckling load parameter or the volume of structural material. The design sensitivities are evaluated either analytically or semi-analytically. The accuracy and relative performance of the proposed discrete models are compared and discussed among the developed elements and with alternative models. A few illustrative test designs are discussed to show the applicability of the proposed models.

Buckling sensitivity analysis and optimal design of thin laminated structures

This paper presents a discrete model for the buckling sensitivity analysis of thin multi-layered angle-ply composite structures. The model is based on a simple and efficient plate-shell element with 18 d.f. using the discrete Kirchhoff theory for the bending effects. Angle-ply design variables and vectorial distances from the middle surface to the upper surface of each layer, indirectly the thickness of each layer, are considered as design variables. The objective of the design is the maximization of the constrained or unconstrained buckling load parameter. The optimization process can be carried out using a two-level approach. The design sensitivities are evaluated analytically, quasi-analytically and by global finite difference. The efficiency and accuracy of the model developed is discussed with reference to several applications.

Thermal buckling of circular plates with localized axisymmetric damages

Thermal buckling analysis of circular plates with localized axisymmetric damages has been carried out using the finite element method. The damages are characterized as degradation in material properties locally. Thermal buckling load parameters are evaluated for both simply supported and clamped circular plates with varying locations, magnitudes and lengths of damage. Numerical results are presented for different cases, and trends in variations of load parameters are discussed.

The effect of localized axisymmetric damages on the buckling of circular plates

Local material damages, characterized as degradation of material properties, are considered in evaluating the buckling behaviour of circular plates. Employing the finite element method, buckling load parameters for simply supported and clamped circular plates are obtained for different locations, lengths and extents of the axisymmetric damage. The results are expected to be useful as design data.

A model for the optimum design of thin laminated plate-shell structures for static, dynamic and buckling behaviour

This paper presents a discrete model for the sensitivity analysis and optimization of thin, multi-layered, angle-ply composite structures. The model is based on a plate-shell element with 18 degrees of freedom, using the discrete Kirchhoff theory for the bending effects. Angle-ply design variables and vectorial distances from the middle surface to the upper surface of each layer (indirectly, the thickness) are considered as design variables. Different objectives and constraints can be used as a specified displacement or the structure elastic strain energy or the volume of structural material or a chosen natural frequency or buckling load parameter. The design sensitivities are evaluated analytically. The efficiency and accuracy of the model developed is discussed with reference to several applications.

Axisymmetric free vibrations of internally compressed moderately thick annular plates

Buckling load and frequency parameters evaluated through the finite element method for moderately thick annular plates uniformly compressed at the inner edge are provided in this paper. This exhaustive set of numerical results covers annular plates of various radii and thickness ratios with different combinations of boundary conditions at the inner and outer edges of the plates. The frequency parameters are evaluated with various percentages of the corresponding buckling load parameter values applied as internal loads. A brief description of the finite element formulation and discussion of the numerical results are included.

Parametric instability of Timoshenko beams resting on an elastic foundation

The parametric instability behavior of a Timoshenko beam resting on an elastic foundation of the Winkler type is studied by the finite element technique. The effect of the elastic foundation on the natural frequencies, the static buckling loads and the regions of dynamic instability of the Timoshenko beams with different end conditions is investigated. The natural frequency and buckling load parameters for a Bernoulli-Euler beam, which is a special case of the present model, indicate excellent agreement with the available results. The dynamic instability diagrams for both beams are presented for different values of the elastic foundation constant. As the elastic foundation constant increases, the regions of dynamic instability are shifted away from the static buckling axis and the sizes of these regions are slightly decreased. Due to the effects of rotatory inertia and transverse shear deformation, the regions of dynamic instability are shifted closer to each other and the sizes of these regions are increased.

Post-buckling behaviour of moderately thick cylindrically orthotropic annular plates

A finite element formulation including the effects of shear deformation and cylindrically orthotropic material properties is described for studying the post-buckling behaviour of annular plates. Numerical results for the buckling load parameter and ratios of nonlinear load parameter to buckling load parameter for various values of orthotropic properties, thicknesses and radii ratios of the plates are presented.

Dynamic stability of short cantilever columns subjected to distributed axial loads

Dynamic stability of short cantilever columns subjected to two types of distributed loads are investigated by using a finite element formulation. Buckling load parameters and frequency parameters bounding the instability regions are presented for various slenderness ratios.

A mixed finite element method for the elastoplastic plate bending and buckling

We propose and test a mixed finite element method for the elastoplastic plate problem. We approximate the plane displacement with a P 1 ∩ C 0 finite element. The deflection and the curvature tensor, considered as independent degrees of freedom, are approximated with a P 1 ∩ C 0 triangular finite element. This proves insufficient for some triangulations (those not generated by three families of parallel lines) and particularly for the computation of the buckling load parameter value. The use of a P 2 ∩ C 0 finite element gives satisfactory results for the bending problem, as well as that of stability and of buckling.

Post-buckling of cylindrically orthotropic circular plates on elastic foundation with edges elastically restrained against rotation

The post-buckling behaviour of cylindrically orthotropic circular plates is investigated through a finite element formulation, with the plates resting on an elastic foundation and their edges are elastically restrained against rotation. Results are presented in the form of linear buckling load parameters and empirical formulae for radial load ratios for various values of spring stiffness, foundation stiffness and orthotropy parameter.

Elastic Buckling and Flexural Vibration of Annular Plates under Axisymmetric In-plane Forces

The problems of elastic buckling and flexural vibration of annular plates under axisymmetric in-plane forces have been analyzed by the Galerkin method. By adopting natural vibration modes of an annular plate without an in-plane force as admissible functions, these problems have been dealt with under various combinations of boundary conditions at the outer and inner edges. Two cases, one the case with uniform in-plane forces along the inner and/or outer edges and the other with steady state thermal stress caused by the temperature difference between inner and outer edges, have been analyzed as examples of axisymmetric in-plane force distributions. The relation of the buckling load parameter with the hole size and the relation of the natural frequency parameters with the magnitude of the in-plane force have been evaluated. It has been found that there is possibility of buckling even in the case of tensile in-plane force or cooling, when the distributed in-plane stress has compressive components.

Elastic Buckling and Flexural Vibration of Annular Plates under Axisymmetric In-plane Forces

The problems of elastic buckling and flexural vibration of annular plates under axisymmetric in-plane forces have been analyzed by the Galerkin method. By adopting natural vibration modes of an annular plate without an in-plane force as admissible functions, these problems have been dealt with under various combinations of boundary conditions at the outer and inner edges. Two cases, one the case with uniform in-plane forces along the inner and/or outer edges and the other with steady state thermal stress caused by the temperature difference between inner and outer edges, have been analyzed as examples of axisymmetric in-plane force distributions. The relation of the buckling load parameter with the hole size and the relation of the natural frequency parameters with the magnitude of the in-plane force have been evaluated. It has been found that there is possibility of buckling even in the case of tensile in-plane force or cooling, when the distributed in-plane stress has compressive components.