The in-plane shear failure of transversely stiffened thin plates

This paper examines the response of stiffened plates with plain flat outstands when subjected to in-plane shear loading in the form of applied in-plane shear displacement. The buckling and post-buckling failure capabilities of thin plates subjected to in-plane shear, can, of course, be improved through the introduction of stiffening elements whose flexural and torsional rigidities can contribute significantly towards a more stabilised structural system. This paper details appropriate suitable finite element modelling strategies and procedures to enable the determination of the post-buckled failure response of the stiffened shear panels and to highlight the significant influence of the stiffeners. The modelling procedures are able to describe the complete loading history of the stiffened panel structures from the onset of initial buckling through the elastic post-buckling phase of behaviour involving the considerable interaction between plate and stiffener and then through initial material yielding and yield propagation to ultimate conditions and elasto-plastic unloading.     

The buckling characteristics of some integrally formed bead stiffened composite panels

Composite panel stability can easily be improved by using vertical male beads. In this paper, new methods of stabilizing techniques used for the panels, webs and ribs of composite structures are studied. A parametric study is performed to assess the effects of important design considerations such as, bead length, number of beads, bead radius, bead depth and bead spacing on the initial buckling load of the panels. The results show that, there is an optimum bead spacing for each panel containing more than one bead which can be estimated using a simple equation. Integration of vertical beads with a length of less than 0.5 times the panel's length has no significant effect on the buckling load. There are no significant changes on the buckling loads of the beaded panels with bead depths greater than 0.6 times the bead radius. In this investigation, the instability of the nose and main ribs of a light airplane wing structure made of woven E-glass material and stiffened by P.V.C foam core and vertical male beads are also studied using experimental methods. The experimental results show that we can easily improve the buckling capability of the panels and webs by using vertical male beads instead of sandwiched construction. It is estimated that this would cause a weight reduction of about 50% and a manufacturing time reduction of about 50%.     

Buckling and dynamic instability analysis of stiffened shell panels

The static and dynamic instability characteristics of stiffened shell panels subjected to uniform in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effect of various parameters like shell geometry, stiffening scheme, static and dynamic load factors, stiffener size and position, and boundary conditions are considered in buckling and dynamic instability analysis of stiffened panels subjected to uniform in-plane harmonic loads along the boundaries.     

Ultimate shear strength of intact and cracked stiffened panels

The present paper focuses on the ultimate shear strength analysis of intact and cracked stiffened panels. Several potential parameters influencing the ultimate shear strength of intact panels are discussed, including the patterns and amplitudes of initial deflection, the slenderness and aspect ratios of the plates, and the boundary conditions defined by the torsional stiffness of support members. An empirical formula for the ultimate shear strength of intact stiffened panels is proposed based on parametric nonlinear finite element analyses in ANSYS. Furthermore, the ultimate shear strength characteristics of cracked stiffened panels are investigated in LS-DYNA with the implicit method. Three types of cracks are considered, namely vertical crack, horizontal crack and angular crack. A simplified method is put forward to calculate the equivalent crack length. And the formula for the ultimate shear strength of cracked stiffened panels is derived on the basis of the formula for intact stiffened panels.     

Buckling and post-buckling strength of shear panels degraded by near border cracks

There have been many reports on fatigue cracks induced on slender webs breathing under repeated loading. Cracks may also initiate due to welding, corrosion, or mishandling. Edge cracks are generally formed adjacent to the flange, stiffeners or any kind of boundary members. It is also generally accepted that cracks degrade the load bearing capacity of thin panels. The aim of this paper is to investigate the buckling and the post-buckling behaviour of shear panels that have edge cracks. Cracks are presumed to be either parallel or normal to the boundaries. The influence of various geometrical and mechanical characteristics of cracks and panels, (such as the length and the position of cracks, boundary conditions, the aspect ratio and slenderness of panels, and Poisson’s ratio and Young’s modulus of materials) is determined by means of linear and nonlinear finite element analysis. It is shown that a substantial degradation can be anticipated if a crack forms in the area at which tension field occurs.     

The computational post-buckling analysis of fuselage stiffened panels loaded in shear

Fuselage panels are commonly fabricated as skin-stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post-buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the Finite Element method and employing non-linear material and geometric analysis procedures it is possible to model the post-buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Previous work has demonstrated that using a commercial implicit code, the Finite Element method can be used successfully to model the post-buckling behaviour of flat riveted panels subjected to uniform axial compression. This paper expands the compression modelling procedures to flat riveted panels subjected to uniform shear loading, investigating element, mesh, idealisation and material modelling selection, with results validated against mechanical tests. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform shear loading, highlighting subtle but important differences between shear and compression modelling requirements.     

Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method

Differential quadrature element method (DQEM) for buckling analysis of stiffened circular cylindrical panels subjected to axial uniform compressive stresses is presented for the first time. The methodology and procedures are worked out in detail. The circular cylindrical panel and the stiffeners are treated separately. Governing differential equations are derived based on the equilibrium of the panel and the stiffener, and on compatibility conditions along the interface of panel elements and stiffeners. Torsional stiffness of the stiffener is ignored. Circular cylindrical panels with a stringer stiffener or a chordwise stiffener are analyzed by the DQEM, and the results are compared with previously published data to verify the established methodology and procedures. Some new results are presented for the circular cylindrical panels with two orthogonal stiffeners.     

A numerical and experimental investigation on composite stiffened panels into post-buckling

The structural behaviour of composite stiffened flat panels under axial compression is here investigated up to collapse. The panel configuration is designed to buckle once the limit load is reached and to work in post-buckling until the ultimate load. The design phase is based on the use of four different kinds of finite element analyses: eigenvalue, non-linear static with modified Riks’ method and both implicit and explicit dynamic analyses. Once the final configuration is identified, two specimens are manufactured. The initial geometrical imperfections are measured and analyzed, then axial compression tests are performed until collapse. As foreseen by the numerical analyses, experimental results prove the ability of the panels designed to work in the post-buckling field until collapse which takes place due to the failure of the stiffener blades. Finally, the measured initial imperfections are included in the model significantly increasing the numerical–experimental correlation.     

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.     

Buckling design of stiffened sheet-based inner core based on bifurcation analysis

In the structural design of the sandwich plate, the inner core plays a key role to have its maximum performance. A shaped pyramidal truss core is proposed in order to increase the strength and productivity of the sandwich core. In this paper, the design guidelines of the shaped pyramidal truss core, which is enhanced by forming a cross-section of an arc shape at the strut of the inner core, is described. The inner core is composed of a stiffened section and a transient section with a varying cross-section. The critical load for bifurcation in compressive instability is calculated using an analytical and FEM simulation. The analytical equation for the critical load of the shaped column is derived using the energy method. The various buckling modes (global, distortional, local) occur due to these effects. Therefore, complications induced by such effects must be taken into account in the design. Parametric studies for the stiffened core are conducted. The effect of geometric parameters is investigated for optimal design of the inner core and their influence have been discussed.     

An analytical study on post-buckling behaviour of imperfect sandwich panels subjected to uniform thermal stresses

The governing equations for determining thermal buckling of imperfect sandwich plates are developed using the large deflection theory and considering first shear deformation principles. The equations are then solved via an analytical method comprising infinite summation of trigonometric series and defining in-plane and out-of-plane displacement. After verification of the proposed method and convergence studies, the effects of parameters like plate aspect ratio, material properties and layer setting angles on buckling stress and the post-buckling path are studied. Numerical results show that the number of trigonometric terms does not affect the buckling thermal stress or the post-buckling path of sandwich plates having face layer setting angles less than 15°. Results also show that the buckling stress and post-buckling path for complementary layer setting angles are similar and that the rate of variation of bifurcation points for different face layer setting angles of sandwich panels strongly depend on material properties, especially on the face and core stiffness. Furthermore, for aspect ratios greater than five, buckling thermal stress remains about constant.     

Buckling measurement and numerical analysis of M-type ribs stiffened composite panel

A combination of methods of strategy which combines optical measurements and numerical calculations was developed to study the buckling behavior and failure modes of composite panel with M-type stiffeners under compression. Utilizing the non-contact optical means for non-destructive testing, the full-field buckling deflections/evolution and compressive failure of the panel surface were systematically collected for mechanical analysis. Based on continuum mechanics modeling, the buckling and post-buckling behaviors of the composite panel were predicted and compared with the buckling shapes that are obtained from experiments. The numerical simulation methods and experimental test technique in the work provides a useful tool to study the compressive buckling behaviors of composite panel with M-type stiffeners.     

Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory

The third-order shear deformation theory of Reddy and collocation with radial basis functions is used to predict the buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse strains through the thickness of the plate. It is shown that the collocation method with radial basis functions produces highly accurate critical buckling loads and modes.     

Shear resistance of longitudinally stiffened panels—Part 1: Tests and numerical analysis of imperfections

This paper deals with the results of four full-scale tests, numerical simulation of tests and initial geometric imperfection analysis for longitudinally stiffened panels in shear. The tests examine the influence of varying position and bending stiffness of one trapezoidal longitudinal stiffener on the panel shear resistance and its buckling behaviour. The stiffeners were designed such as to obtain both global and local buckling shapes. Numerical simulations (FEA), based on the test girder geometry, the measured initial geometric imperfections and elastic-plastic material characteristic from the tensile tests, demonstrate a very good agreement with the tests. The initial geometric imperfection study on different verified numerical models shows a limited sensitivity of the panel shear capacity to any kind of imperfection shape variation with amplitude at the allowable fabrication tolerances. Finally, the paper offers some ideas for modelling geometric imperfections with regard to the design or research demands.     

Experimental investigation of composite shear walls under shear loadings

One of the efficient methods for improving the seismic behaviour of high-rise buildings is using Composite Steel Plate Shear Wall (CSPSW). In this paper, extensive experimental studies of one and three-story CSPSWs with the scale of 1:3 and 1:4, together with stress equations of each element are reported. The experimental results indicate that this system has reliable behaviour if the columns have high bending stiffness. Also bolts spacing to plate thickness ratio has direct relationship with system ductility. However, plate yield load has an inverse relationship with this ratio. In this system, plate stiffening requirement is obtained with minimum reinforcement for reinforced concrete, though for damage prevention high strength concrete is preferred. Also, the results show a good agreement for the recommended values of (b/t) by an AISC code for preventing plate buckling.     

Parametrical study of masonry walls subjected to in-plane loading through numerical modeling

This paper deals with the numerical assessment of the influence of parameters such as pre-compression level, aspect ratio, vertical and horizontal reinforcement ratios and boundary conditions on the lateral strength of masonry walls under in-plane loading. The numerical study is performed through the software DIANA^® based on the Finite Element Method. The validation of the numerical model is carried out from a database of available experimental results on masonry walls tested under cyclic lateral loading. Numerical results revealed that boundary conditions play a central role on the lateral behavior of masonry walls under in-plane loading and determine the influence of level of pre-compression as well as the reinforcement ratio on the wall strength. The lateral capacity of walls decreases with the increase of aspect ratio and with the decrease of pre-compression. Vertical steel bars appear to have almost no influence in the shear strength of masonry walls and horizontal reinforcement only increases the lateral strength of masonry walls if the shear response of the walls is determinant for failure, which is directly related to the boundary conditions.     

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.     

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.     

A semi-analytical model for global buckling and postbuckling analysis of stiffened panels

A computational model for global buckling and postbuckling analysis of stiffened panels is derived. The loads considered are biaxial in-plane compression or tension, shear, and lateral pressure. Deflections are assumed in the form of trigonometric function series, and the principle of stationary potential energy is used for deriving the equilibrium equations. Lateral pressure is accounted for by taking the deflection as a combination of a clamped and a simply supported deflection mode. The global buckling model is based on Marguerre’s nonlinear plate theory, by deriving a set of anisotropic stiffness coefficients to account for the plate stiffening. Local buckling is treated in a separate local model developed previously. The anisotropic stiffness coefficients used in the global model are derived from the local analysis. Together, the two models provide a tool for buckling assessment of stiffened panels. Implemented in the computer code PULS, developed at Det Norske Veritas, local and global stresses are combined in an incremental procedure. Ultimate limit state estimates for design are obtained by calculating the stresses at certain critical points, and using the onset of yielding due to membrane stress as the limiting criterion.     

A semi-analytical method for the elastic–plastic large deflection analysis of stiffened panels under combined biaxial compression/tension, biaxial in-plane bending, edge shear, and lateral pressure loads

In the earlier publications [Paik JK, Thayamballi AK, Lee SK, Kang SJ. A semi-analytical method for the elastic-plastic large deflection analysis of welded steel or aluminium plating under combined in-plane and lateral pressure loads. Thin-Walled Struct 2001;39;125–52; Paik JK, Thayamballi AK. Ultimate limit state design of steel-plated structures. Chichester: Wiley; January 2003], the author presented a semi-analytical method for the elastic–plastic large deflection analysis of unstiffened plates under biaxial loads, edge shear, biaxial in-plane bending and out-of-plane (lateral) pressure loads until the ultimate strength is reached. In the present paper, a similar method is applied to stiffened panels subjected to the same type of loading. The effect of initial imperfections in the form of initial deflection and welding residual stresses is accounted for in the calculations. The validity of the developed method is demonstrated by comparing with existing theoretical and numerical results where relevant. The present theory can be useful for ultimate strength analysis of plates and stiffened panels made of steel or aluminium alloys.