Ultimate capacity of uniaxially compressed perforated plates

An approximate method of predicting the ultimate load carrying capacity and the post-buckling behaviour of perforated plates typically used in engineering structures is presented. The theory is based on a mechanism solution, used in conjunction with an elastic loading path derived from energy methods. Experiments have shown that a good approximation of the loading and unloading paths for simply supported plates containing square and circular openings has been obtained by the suggested theoretical treatment. Curves suitable for the use of designers have been proposed and can be employed to determine the ultimate capacity of approximately square plates containing centrally placed holes.     

Design formula for axially compressed perforated plates

This paper is concerned with post-buckling behaviour and the ultimate load capacity of perforated plates with different boundary conditions and subjected to uniaxial or biaxial compression. Plates were analysed using the finite element method (FEM), and extensive studies were carried out covering parameters such as plate slenderness, opening size, boundary conditions and the nature of loading. A design formula to determine the ultimate load carrying capacity was established based on a best-fit regression analysis using the results from the finite element analyses. The accuracy of the proposed formula was established by comparison with experimental values of ultimate capacity and similar finite element values. Ultimate load values are also presented in the form of charts for various values of plate slenderness and opening size.     

Elastic buckling of perforated plates under shear

Finite element studies aimed at computing the buckling coefficient for plates containing cut-outs and subjected to shear are reported. The cases considered are:

1. 1. Square and rectangular plates with central circular cut-outs.

2. 2. Square plates with centrally placed rectangular cut-outs.

3. 3. Square plates with eccentrically placed circular cut-outs.

4. 4. Square plates with reinforced circular cut-outs.

5. 5. Square plates with reinforced rectangular cut-outs.

Simply supported plates as well as clamped plates have been studied and approximate formulae for the use of designers have been suggested for the practical cases where the hole dimension is generally not greater than half the width of the plate.     

Elastic stability of orthotropic plates

A semi-numerical method is presented for the analysis of orthotropic rectangular plates subjected to uniform, linearly-varying and partial inplane loads. The solution procedure is based on the classical method of separation of variables. The basic functions are chosen as the eigenfunctions for straight prismatic beams in free vibration. The two-dimensional governing partial differential equation is first reduced to an ordinary differential equation. The classical unidirectional finite difference method is then employed to solve the resulting ordinary differential equation. Results are presented for plates with different edge and loading conditions.     

Elastic post-buckling analysis of compressed plates using a two-strip model

This paper shows that a simple two-strip model can be used to describe the post-buckling behaviour of simply supported rectangular plates subjected to uni- and biaxial compression, provided the ratio of the post-buckling to pre-buckling stiffness of the perfectly flat plate is known. The formulas for this two-strip model are derived in two ways: by using a force method, and by using an energy method. The two-strip model is compared to other available solutions in literature and it is shown that the model can be regarded as a modification of the lower bound plate analysis method.     

Elastic stability of bi-axially loaded rectangular plates with a single circular hole

The finite-element method has been employed to determine the elastic buckling stresses of a bi-axially loaded perforated rectangular plate with dimensions a and b in the x- and y-directions, respectively. The considered perforation is a single circular hole whose center is located along the longitudinal axis of the plate. The considered plate has simply supported edges in the out-of-plane direction and is subjected to bi-axial uniformly distributed end loads (compressive load σ_x in the x-direction, and compressive or tensile load σ_y in the y-direction). Parameters considered in the study are the plate's aspect ratio a/b, the stress ratio ξ between the applied stresses in the y- and x-directions (ξ=σ_y/σ_x), the circular hole size d and location e_x.The study shows that, in most of the considered cases, the bigger the hole size d, the lesser the plate stability and the lesser the buckling stresses. It also shows that the plate aspect ratios, a/b, between 0.6 and 1.2 should be avoided for plates with large holes and negative ξ, due to the large reduction in the buckling stresses. The hole location should also be selected to be away from the loaded edge of the plate as much as possible (better to have e_x/b>1.0) to increase the buckling stresses and improve stability. The study demonstrates also that the increase in tension in the y-direction in bi-axially loaded plate with large hole (d/b>0.4) reduces its stability. This is in contrary to the expected increase in the stability due to the increase in tension which can be seen clearly in the cases of solid plates and plates with small holes.     

Experimental tests of stability and load carrying capacity of compressed thin-walled multi-cell columns of triangular cross-section

In the work the results of experimental tests of stability and ultimate load of compressed thin-walled columns of triangular cross-sections are presented. The tests have been conducted in order to prove that by substituting a single-cell cross-section by multi-cell one (at constant value of area) it is possible to exploit the material strength properties more efficiently. The experiments allow for verification of calculation methods proposed earlier and for the analysis of the inevitable imperfections’ influence on the behaviour and load carrying capacity of the tested models.     

Unilateral buckling of point-restrained triangular plates

In this paper the unilateral buckling behavior of point restrained triangular plates is studied. Firstly, the energy functional of a general triangular plate with elastic foundation is calculated. The Rayleigh–Ritz method for investigating the local buckling of unilaterally restrained triangular plates is applied. The displacement functions and restraining medium are modeled as polynomials and tensionless foundation respectively. The results are obtained for different boundary conditions, aspect ratios and various in-plane compressive and shear loadings. Confirming the validity of this investigation, convergence and comparison studies are undertaken. The comparisons show the efficiency and accuracy of the presented method.     

The elastic stability of square perforated plates under combinations of bending, shear and direct load

This paper presents solutions for the elastic stability of plates containing perforations using the conjugate load/displacement method. Interaction curves for a variety of load cases and support conditions are presented. The effect of the size of a central square hole in a square plate on the elastic buckling load is demonstrated and, where possible, results are compared with the work of other authors.     

Strength of perforated plates subjected to in-plane loading

Finite element solutions for the buckling and geometrically nonlinear elasto-plastic collapse of perforated plates are presented. Triangular elements are used to model the plates and the elasto-plastic stress-strain relationships are based on Ilyushin's approximate area yield function assuming full plastification of the entire thickness of the plate for stress states on the yield surface. Solutions are presented for square plates with central square and circular holes subjected to uniaxial compression, biaxial compression and pure shear, and are shown to be in close agreement with existing approximate and semi-empirical solutions which have been verified by test results.     

The stability of eccentrically compressed thin plates with a longitudinal free edge and with stress variation in the longitudinal direction

This paper presents results of the investigation of the stability of eccentrically compressed thin plates with one longitudinal free edge with the participation of loadings generating the variation of stresses in the direction of the length of a plate. A deflection function (5) is proposed to enable modelling of boundary conditions on the second longitudinal edge from a simply supported, through elastically restrained, to a built-in edge. Formulas are derived for work done by external force under loading generating the variation of stress according to a linear function and according to parabola 2°. Tables and plots of buckling coefficient (k) for variously supported and variously loaded plates with a free edge, which are not found in the literature, are determined. The effect of a longitudinal stress variation on the plate buckling modes is analyzed.     

Evaluation of perforated steel plates as connection in glulam-concrete composite structures

This paper shows the results of an experimental investigation carried out on a connection element of glulam and concrete composite structures, through double-sided push-out shear tests. The connection system was composed of perforated steel plates glued with epoxy adhesive. Five specimens were made and tested under shear forces. This innovative connection system showed an average initial slip modulus equivalent to 339.4 kN/mm. In addition, the connection system was evaluated by means of numerical simulations and the software ANSYS was used for this purpose. The numerical simulations demonstrated good agreement with the experimental data, especially in the regime of elastic-linear behavior of materials.     

风管阻尼板的设计与应用

分析了几种阻尼板的阻尼特性,介绍了阻尼板在通风空调系统中的应用,以解决实际工程中各支风管的风量平衡问题,给出了阻尼板调节装置开孔率选用图.     

Buckling of compressed rectangular plates at non-uniformly elevated temperatures

A perturbation analysis of the influence of non-uniformly elevated temperatures upon the critical buckling loads of uniaxially compressed rectangular plates is presented. Within the framework of the uncoupled theory of thermal stresses a temperature dependence of the modulus of elasticity has been taken into consideration. In the special case of a simply supported square plate, the range of practical applicability of the resulting approximate formula has been checked by means of a variational finite-difference method.     

Strengthening of perforated plates under uniaxial compression: Buckling analysis

This paper focuses on the cutout-strengthening of perforated steel plates subjected to uniaxial compressive loads. The square plates considered each has a centrally placed circular hole and four simply supported edges in the out-of-plane direction. Four types of stiffeners named ringed stiffener (RS), flat stiffener (FS), longitudinal stiffener (LS) and transverse stiffener (TS) are mainly discussed. The finite element method (FEM) has been employed to analyse the elastic and elasto-plastic buckling behaviors of strengthened and unstrengthened perforated plates. The results show that the strengthened perforated plates have higher buckling strengths than those of the unstrengthened ones, while the elevations in elastic buckling stress and elasto-plastic ultimate strength are closely related to stiffener types (i.e., RS, FS, LS and TS) as well as plate geometric parameters (i.e., a plate slenderness ratio and a hole diameter ratio). Furthermore, comparisons of strengthening efficiency considering the variations of buckling stress with stiffener weight are carried out, and recommendations on the most efficient cutout-strengthening methods for the uniaxially compressed perforated square plates with centric circular holes are proposed.     

Ultimate strength of perforated steel plates under edge shear loading

The aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under edge shear loading, which is a primary action type arising from cargo weight and water pressure in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges and kept straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the cutout size (diameter) as well as plate dimensions (plate aspect ratio and thickness). By the regression analysis of the FEA results obtained, a closed-form empirical formula for predicting the ultimate shear strength of perforated plates, which can be useful for first-cut strength estimations in reliability analyses or code calibrations, is derived. The accuracy of the ultimate strength formula developed is verified by a comparison with more refined nonlinear FEA results.     

Vibration of general triangular composite plates with elastically restrained edges

Triangular fibre reinforced composite plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration behaviour of anisotropic triangular plates with edges elastically restrained against rotation and translation. The approach developed is based on the Rayleigh–Ritz method and the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. Several examples are solved and some results which correspond to particular cases are compared with existing values in the literature. New results are also presented for single layer composite plates with different fibre orientations and combinations of boundary conditions. For some plates, mode shapes of free vibration are also shown. Selected new transverse vibration mode shapes are presented to illustrate the effects of boundary constraints, aspect ratio and fibre orientation.The method can be applied to a wide range of elastic restraint conditions, any aspect ratio and for higher modes. The effect of the fibre orientation on the natural frequencies for plates with these restraint conditions are also considered.     

Elastic local buckling of perforated webs of steel cellular beam-column elements

In this study, the finite element method is employed to determine the critical in-plane longitudinal load at which elastic local buckling of the web of cellular beam-column elements occurs. To simplify the simulation of the problem, the interaction between the flanges and perforated web is approximated by modelling the web only as a long plate having aspect ratio (L/h_w≥10) with multiple circular perforations. The utilized model incorporates restrained out-of-plane displacements along the four edges of the plate. Analyzed plates are subjected to linearly varying in-plane loads to simulate various combinations of axial and flexural stresses. The effect of different geometrical parameters on the elastic buckling load of perforated web plate is investigated. These geometrical parameters include the plate’s length and width, and the perforations’ diameter and spacing. Comprehensive finite element analyses are conducted to identify the behaviour of wide spectrum of perforated web plates at buckling under various combinations of axial compressive load and bending moment. Outcomes of the study are expected to enhance the understanding of the elastic local buckling of web plates of cellular beam-column elements.     

Non-linear analysis of perforated steel plates subjected to localised symmetrical load

Although the literature contains a number of studies which have been developed to describe the non-linear behaviour of ordinary plates, few works are available on perforated plates, and studies on non-linear behaviour of perforated plates under localised symmetrical load are not studied in depth. The aim of this paper is to provide some insights into the elasto-plastic behaviour of plate girder web panels with circular holes under localised symmetrical load.Numerical analyses of square and rectangular perforated plates with centred and eccentric holes were developed. Results provide new insights into post-critical mechanisms in perforated plates subjected to localised loads when the length of the symmetrical compressive load, hole diameter and steel yield limit vary. An increase in the critical slenderness of the plate (a value at which transition from elastic to plastic collapse occurs) and a corresponding reduction in the elastic critical load occur when the dimensions of the hole increase. A further increase in the critical slenderness occurs when the length of the localised load is reduced. High-performance steel may be subject to buckling with a lower possibility of post-critical mechanisms: a reduction in critical slenderness occurs when the steel grade increases. Lastly, numerical analyses of slender and thick perforated plates were developed and their results compared.     

On the effect of the local overall interaction on the postbuckling of uniformly compressed channels

On the basis of the general theory of elastic stability due to Koiter, postbuckling analysis of simply supported channels under uniform compression is performed. Attention is essentially focused on local/eularian and local/flexural-torsional simultaneous bucklin modes interaction. The column is treated as a plate assemblage. Linearized expressions for the displacement field are employed while assuming strain-displacements relationships that are linear for the curvatures and up to second order terms for the in-plane strains. The total potential energy is hence written up to third order terms in order to investigate asymmetric buckling phenomena. A discrete model is developed through an automatic procedure of algebraic manipulation, and an extensive parametric analysis is performed. After determining the range of geometric parameters which characterize different types of interaction, it is found that in the postbuckling range the local/eulerian interaction is more dangerous than the local/flexural-torsional one, due to the column higher imperfection sensitivity.