Tension buckling and parametric instability characteristics of doubly curved panels with circular cutout subjected to nonuniform tensile edge loading

This paper deals with the study of tensile buckling, vibration, and parametric instability behaviour of doubly curved panels with central circular cutout subjected to uniaxial in-plane partially distributed tensile edge loadings using finite element method. First order shear deformation theory is used to model the curved panels, to consider the effects of the transverse shear deformation and rotary inertia. The vibration analysis for this problem shows that for certain parameters of the tensile loading, the frequencies of the panel initially rise with the load, but begin to decrease with increasing tension, showing the onset of tension buckling. The parametric instability behaviour under tensile periodic edge loading with different load parameters shows that instability regions are influenced by the cutout size, load width and its location.     

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.     

Dynamic buckling of thin isotropic plates subjected to in-plane impact

The dynamic stability behaviour of imperfect simply supported plates subjected to in-plane pulse loading is investigated. For the calculation of dynamic buckling loads a stress failure criterion is applied. The large-deflection plate equations are solved by a Galerkin method by using Navier's double Fourier series. In this paper the dynamic load factor (DLF) is redefined and plots that are useful for the design of plate structures are presented. Parametric studies are performed in which the influences of the pulse duration, shock function, imperfection, geometric dimensions and limit stress of the material are discussed. Comparison between the dynamic buckling loads, which are obtained by the commonly used criterion of Budiansky and Hutchinson [Proceedings of the 11th International Congress of Applied Mechanics (1964) 636], and the dynamic elastic limit loads, which are computed by the stress failure criterion, shows that the latter criterion is more useful for the design of lightweight structures.     

Natural frequencies of plates with square holes when subjected to in-plane uniaxial, biaxial or shear loading

The finite element method is used to determine the natural frequencies of flat square plates containing eccentrically located square holes. The plates are subjected to in-plane uniaxial, biaxial or uniformly distributed shear along the four outer edges. These edges are either simply supported or clamped.

In order to evaluate the stiffness and mass matrices, the non-conforming rectangular displacement element is used to model the out-of-plane behaviour of the plate. The in-plane stress distribution within the plate, required in the analysis, is determined by using a rectangular finite element having the only essential degrees of freedom at each of the four corner nodes. The element displacement functions are based on assumed strains and satisfy the exact requirements of strain free rigid-body modes of displacements.

The variation of the natural frequency with the size and location of the hole is first investigated in the absence of any in-plane stresses. This analysis is then repeated for a series of values of the applied in-plane stresses. When uniform shear is applied, tension and compression zones are produced in the plate and hence the effect of locating the hole in each of the regions is also investigated. The values of the applied in-plane stresses ranged up to the point that would cause the plates to buckle. In this way a comprehensive set of results can be obtained.     

Vibration of cross-ply laminated composite plates subjected to initial in-plane stresses

Natural frequencies, modal displacements and stresses of cross-ply laminated composite plates subjected to initial in-plane stresses are analyzed by taking into account the effects of higher-order deformations and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for rectangular laminates is derived through Hamilton’s principle. Several sets of truncated approximate theories can be derived to solve the eigenvalue problems of a simply supported laminated plate. After examining the convergence properties of the lowest natural frequency, only the numerical results for M=5, which are considered to be sufficient with respect to the accuracy of solutions, are presented. Numerical results are compared with those of the published existing three-dimensional theory and FEM solutions. The modal displacement and stress distributions in the thickness direction are plotted in figures. The buckling stresses can be obtained in terms of the natural frequencies of the laminates without initial in-plane stresses.     

Differential quadrature buckling analyses of rectangular plates subjected to non-uniform distributed in-plane loadings

The new version of differential quadrature method (DQM), proposed by the senior author recently, is used to obtain buckling loads of thin rectangular plates under non-uniform distributed in-plane loadings for the first time. Two steps are involved: (1) solve a problem in plane-stress elasticity to obtain the in-plane stress distributions and (2) solve the buckling problem under the loads obtained in step (1). The methodology and procedures are worked out in detail and buckling problems with loadings of non-uniform distributions are studied. Numerical studies are performed and the DQ results are compared well with analytical solutions and finite element results. This fact indicates that the DQ method can be employed for obtaining buckling loads of plates with other combinations of boundary conditions subjected to non-uniform distributed loadings.     

Simple and combination resonances of rectangular plates subjected to non-uniform edge loading with damping

The effects of damping on the behaviour of simple and combination resonances of simply-supported rectangular plates subjected to non-uniform in-plane periodic loading are studied. Finite element formulation is applied to obtain the equilibrium equation for the plate. The relations for the boundaries of parametric instability regions are obtained by using the method of multiple scales. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. For nearly uniform loading, the combination resonance zones are very small in width and may disappear in the presence of slight damping. The effects of damping show that there is a finite critical value of the dynamic load factor for each zone below which the plate cannot become dynamically unstable. It is also shown that the effects of damping on the combination resonances may be destabilizing under certain conditions.     

Elastic/plastic buckling of a composite flat plate subjected to uniform edge compression

A theoretical approach, based on the plastic theory, has been developed for studying the elastic/plastic buckling behavior of a simply supported rectangular anisotropic plate subjected to edge compression. The said approach was employed to determine the critical buckling stresses of three different types of fiber reinforced composite plates, namely, carbon epoxy, glass epoxy and boron aluminum plates. Since the proposed approach is for a preliminary prediction of critical buckling loads of composite plates, the results obtained are deemed acceptable compared with those obtained by other authors experimentally.     

Scaling laws for buckling of polar orthotropic annular plates subjected to compressive and torsional loading

This paper derives the similitude invariants and scaling laws for buckling of polar orthotropic annular plates subjected to radial compressive load and torsional load. The similitude transformation is applied to the governing differential equation directly resulting in a scaling law for buckling load of annular plates and the similarity conditions between a model and a prototype. The scaling law is verified by a series of numerical tests using the solutions from the Ritz method as the theoretical solutions. For complete similitude cases, the buckling loads obtained from the scaling laws are identical to those of the theoretical solution. Since the derived scaling law is independent of the boundary conditions, it is valid for any pairs of model and prototype on the condition that they have identical boundary condition. Therefore, buckling behaviors of the prototype with complicated boundary conditions, of which a theoretical solution is not available, can be predicted from the experimental result on the model. Partial similitude model or scaling law for a pair of model and prototype without complete similarity is also investigated. The partial similarity model is not recommended for polar orthotropic materials, however it demonstrated good estimations for isotropic materials.     

Vibration and buckling of plates with mixed boundary conditions

This paper deals with the vibration or buckling of thin plates with either mixed boundary conditions or discontinuous boundary conditions using the spline element method.

To demonstrate the accuracy of the method, several examples are solved, and results are compared with those obtained by other numerical methods. The effects of partial rotational constraints and angles of skew on frequencies and buckling loads of isotropic skew plates are also investigated.     

Square hollow section (SHS) T-joints with concrete-filled chords subjected to in-plane fatigue loading in the brace

In recent years, there has been an increased use of concrete-filled composite tubular joints in bridge construction. The reliability of these joints under fatigue therefore need to be investigated to avoid any catastrophic failures. In this paper, hollow section T-joints made up of square hollow section (SHS) chords and braces are investigated. The chords of the SHS–SHS T-joints were concrete-filled thereby forming welded composite tubular T-joints. The SHS–SHS T-joints with concrete-filled chords were strain gauged and tested under static loading to determine stress concentration factors (SCFs) at hot spot locations, where cracks are likely to propagate. Fatigue tests of the welded composite joints were also carried out under cyclic in-plane bending in the brace to obtain stress range vs. number of cycles (S–N) data. The maximum stress concentration factor (SCF) at hot spot locations in a welded composite tubular T-joint was found to be generally lower than the maximum SCF in an empty (or called unfilled) hollow section SHS–SHS T-joint. Fatigue failure in welded composite tubular T-joints occurred through the initiation and propagation of cracks at weld toes in either the chord or brace member, with the majority of tests exhibiting the first visual crack at weld toes in the chord. The welded composite tubular T-joints were found to have better fatigue strength compared to the empty hollow section SHS–SHS T-joints. Design rules are recommended for the SHS–SHS T-joints with concrete-filled chords through analysis of fatigue test data using the hot spot stress method.     

Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading

Buckling failure is a common occurrence in thin plates under compression loading, in particular when there are some imperfections such as openings and cracks. This form of failure can often precede strength failure. In this paper, experimental and numerical studies on the critical buckling load of cracked plates subjected to axial compression is carried out. For this purpose, the rectangular plates made by 1200A aluminum alloy with central inclined crack are considered. The effects of crack length and orientation, thickness of plates and plate aspect ratio are investigated experimentally and numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading such as partial edge acting forces and supports. Finally, the results of experiments are compared with the results of numerical methods.     

Nonlinear dynamic stability of composite plates with piezoelectric layers subjected to periodic in-plane load

Nonlinear dynamic stability characteristics of composite plates subjected to periodic in-plane load are investigated via the finite element method with dynamic response analysis. Piezoelectric actuator layers are embedded at the top and bottom of the laminated composite plate. The theoretical formulation is based on the modified first order shear deformation theory (MFSDT) incorporating the von Kármán type nonlinear strains. The structural system is considered to be undamped. The nonlinear governing equations obtained are solved using the Newmark's direct integration method coupled with the direct iteration method. The boundaries of dynamic instability regions are obtained using Bolotin's approach. Effects of in-plane forcing frequency and applied voltage on the characteristic features of dynamic stability behaviour are investigated using both linear and nonlinear dynamic response analyses.     

Elastic and elasto-plastic buckling of thin-walled columns subjected to uniform compression

The problem of local stability loss in the elasto-plastic range of a thin-walled column, loaded by uniform compressive stresses, is examined on the basis of the J₂ deformation theory and the J₂ incremental theory of plasticity. The problem is solved in two different ways. Several types of closed and open cross-sections are considered. The results of numerical calculations are presented in graphical form, showing the relationship between the critical stress and the slenderness ratio for the column section. All possible buckling modes in the elastic range and local buckling in the elasto-plastic range are demonstrated in the case of a column of channel form cross-section.     

Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading

Buckling failure is a common occurrence in thin plates under compression loading, in particular when there are some imperfections such as openings and cracks. This form of failure can often precede strength failure. In this paper, experimental and numerical studies on the critical buckling load of cracked plates subjected to axial compression is carried out. For this purpose, the rectangular plates made by 1200A aluminum alloy with central inclined crack are considered. The effects of crack length and orientation, thickness of plates and plate aspect ratio are investigated experimentally and numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading such as partial edge acting forces and supports. Finally, the results of experiments are compared with the results of numerical methods.     

Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings, etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (Lc/Rc∼1, Rc/t=117, 175, 280) cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination of dents do not have much effect on static buckling strength of thin cylindrical shells, whereas in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically. It is also found that the reduction in buckling strength of thin cylindrical shell with a dent of same size and orientation increases with increase in shell thickness.     

Response of stiffened and unstiffened plates subjected to blast loading

This paper describes the results of dynamic analyses carried out on both stiffened and unstiffened panels using both simplified and advanced analytical techniques. For unstiffened panels with inplane restraint along their edges, the dynamic response of an imperfect panel was predicted using a large displacement elastic analysis based on Lagrange's equation, with the panel being treated as a shallow shell. For stiffened panels, the finite element (FE) technique was used to establish the validity of using the simplified technique to predict the inter-stiffener panel displacements for a simply supported panel. A parametric study has been carried out to analyse the effects of in-plane boundary conditions, local stiffener buckling and initial imperfections on the overall response. The significant effect of boundary conditions is demonstrated by including the actual boundary conditions of a test frame in the finite element modelling of a large-scale stiffened floorplate panel used in an experimental test series.     

Collapse load analysis of square and rectangular tubes subjected to transverse in-plane loading

Experiments to determine the collapse load of aluminum and mild steel tubes, of square and rectangular cross-sections, between parallel rigid platens were carried out in an Instron machine. A two stage analysis for the collapse of these tubes was carried out by considering the out-of-straightness of arms, corner radius, friction between the platens and the specimen and stability of the vertical arms. Results thus obtained compare well with experiments.     

Global buckling and the interaction of initial imperfections of columns subjected to conservative loading

This paper deals with the problem of global instability of slender systems with imperfections. The inaccuracies in the systems are modelled assuming an initial curvature and the introduction of the eccentricity of an external load. Systems loaded by Euler’s load or by a force directed towards the positive pole are considered. The problem is formulated on the basis of an energetic method. Analysis of the global imperfections is carried out. The results of analytical, numerical and experimental research concerning the mutual relations between the introduced imperfections and their influence on the system behaviour are presented.