Tanchum Weller

Experimental and theoretical studies of columns under axial impact

Abstract The dynamic response of columns loaded by an impulsive axial compression was studied experimentally and theoretically. Approximate criteria for determination of dynamic buckling are discussed and applied. The investigation was carried out on clamped specimens, made of metals and composite materials, loaded impulsively by a striking mass. In the theoretical study Rayleigh-type beam equations are assumed for a geometrically imperfect column of a linear-elastic anisotropic material. A numerical solution, by a finite-difference approach, yields buckling behavior which correlates well with the experimental results. It is shown that initial geometrical imperfection, duration of impulse and effective slenderness have a major influence on the buckling loads whereas the effect of the material is secondary. The major effects are presented in a form that can guide the designer.

Dynamic buckling of beams and plates subjected to axial impact

Abstract Analytical studies with the ADINA computer code were performed to determine the Dynamic Load Amplification Factor (DLF) of metal beams and plates subjected to axial in-plane impact compression loading. The results were compared with experimental ones and those yielded by self developed finite differences programs. The influences of initial geometric imperfections, as well as duration of loading on the DLP were evaluated. As anticipated, the DLFs were usually higher than unity. However, in a few cases, in the presence of certain magnitudes of initial geometric imperfection and for loading durations close to the first natural period in bending, DLFs smaller than unity were observed.

Buckling Behavior of Composite Laminated Stiffened Panels Under Combined Shear-Axial Compression

Experimental results on the behavior of four torsion boxes, each comprising of two stringer stiffened cylindrical graphite-epoxy composite panels that have been subjected to torsion, axial loading and their combinations are reported. The buckling and post buckling behavior of these torsion boxes demonstrated consistent results. Prior to performing the buckling tests, the initial geometric imperfections of the boxes were scanned and recorded. The tests were complemented by finite element calculations, which were performed for each box. These detailed calculations have also assisted in identifying critical regions of the boxes and the boxes were reinforced accordingly to avoid their premature failure. The tests indicated that: the torsion carrying capacity is laminate lay-up dependent; axial compression results were in very good agreement with previous tests performed with single identical panels; and that the boxes have a very high post-buckling carrying capacity.

Influence of predetermined delaminations on buckling and postbuckling behavior of composite sandwich beams

Abstract An investigation was performed to obtain the behavior of composite sandwich beams in the presence of predetermined delaminations, due to disbonding between the faceplate and the less rigid core. An analytical model for predicting buckling and describing the postbuckling behavior of the beam was developed. Griffiths fracture energy release rate model was introduced to predict the stability of the delamination propagation under external loading. Parametric studies over a wide range of damage sizes, and composite facings were carried out to study the effects of these parameters on the overall behavior of the beams, as well as its damage tolerance. The results demonstrate that sandwich construction is very ‘sensitive’ to the presence of predetermined delaminatoins: premature buckling failure occurs at external loads, which are significantly lower than those corresponding to a ‘perfect’ sandwich beam. The limit load is obtained before delamination propagation takes place. In ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load carrying capacity of the beam. It was also shown that the proposed model can be used to study the influences of predetermined delaminations in composite beams.

Buckling of cylindrical panels under axial compression

Abstract This paper investigates the effects of boundary conditions and panel width on the axially compressive buckling behavior of unstiffened, isotropic, circular cylindrical panels. Numerical results are presented for eight different sets of boundary conditions along the straight edges of the panels. For all sets of boundary conditions except one (SSI), the results show that the panel buckling loads monotonically approach the complete cylinder buckling load from above as the panel width is increased. Low buckling loads, sometimes less than half the complete cylinder buckling load, are found for simply supported panels with free in-plane edge displacements (SSI). The SSI buckling loads are below the complete cylinder load even for ‘360° panels’. It is also observed that the prevention of circumferential edge displacement is the most important in-plane boundary condition from the point of view of increasing the buckling load, and that the prevention of edge rotation (i.e. clamping) in the circumferential direction also significantly increases the buckling load. Parametric studies are also performed to determine the effects of variations in panel length and thickness on the buckling loads.

Buckling and postbuckling behavior of delaminated sandwich beams

Abstract An investigation was performed to study the buckling and postbuckling behavior of sandwich beams containing lengthwise and depthwise through-the-width delaminations. An analytical beam model was developed to predict the buckling load of the beam and to describe its postbuckling response for arbitrarily situated delaminations and various combinations of boundary conditions. Griffiths energy release rate model was employed to predict the stability of delamination propagation under external loading and to determine the direction of delamination growth. Parametric studies over a wide range of beam geometries, damage sizes and locations, composite facings and beam boundary conditions were carried out to study their effects on the overall behavior of the sandwich structure, as well as its damage tolerance. The results demonstrated that a sandwich construction is very ‘sensitive’ to the presence of delaminations situated at the core-faceplate interface. Premature buckling failure occurs at external loads which are significantly lower than the buckling load for a ‘perfect’ sandwich beam; in ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load-carrying capacity of the beam; varying either the boundary conditions in a sandwich beam or the lengthwise location of a delamination has a small effect on the postbuckling behavior of the beam. Delaminations located within composite faceplates have less pronounced influence, and as the defect is moved outwards the limit load may reach the buckling load corresponding to that of the ‘perfect’ beam. The proposed model is capable of analyzing the postbuckling behavior of both sandwich and composite laminated beams for arbitrary locations of the delamination, and various combinations of boundary conditions.

Durability of stiffened composite panels under repeated buckling

Abstract An experimental study of the durability under repeated buckling of Graphite/Epoxy stiffened panels subjected to shear and axial compression was carried out. The shear panels were hybrid Wagner beams with composite webs bonded to an aluminum alloy frame, whereas the axial compression specimens were “I” and “J” stiffened cocured composite panels. The test results demonstrate that composite stiffened panels are less fatigue sensitive than comparable metal ones. In the shear panels repeated buckling, even when causing extensive damage, does not reduce the residual strength by more than 20 percent. For the axial compression panels no reduction in residual strength was observed. Safe design of stiffened Graphite/Epoxy panels well beyond their initial buckling is therefore feasible. This can lead to more efficient structures.

Repeated buckling and its influence on the geometrical imperfections of stiffened cylindrical shells under combined loading

Abstract The present experimental study aims at providing better inputs for improvement of the buckling load predictions of stiffened cylindrical shells subjected to combined loading. The work focuses on two main factors which considerably affect the combined buckling load of stiffened shells, namely geometric imperfections and boundary conditions. Six shells with nominal simple supports were tested under various combinations of axial compression and external pressure. The vibration correlation technique is employed to define the real boundary conditions. The geometric imperfections of the integrally stiffened shells are measured in the present experiments in situ and are used as inputs to a multimode analysis which yields the corresponding “knockdown” factor for various combinations of loading. Thus, when employing the repeated buckling procedure for obtaining interaction curves, each point on the curve is adjusted (using the multimode analysis) for the measured “new” surface of the shell and this results in more realistic interaction curves. The geometrical imperfections of the preloaded shells can also serve as an input to the International Imperfection Data Bank for future studies on the correlation between the manufacturing method of the shell and their geometric imperfections.

Buckling of unstiffened conical shells under combined loading

An experimental program was conducted in order to determine the family of interaction curves for the buckling of unstiffened conical shells under combined axial compression, torsion, and external or internal pressure. Careful experimental technique permitted many repeated buckling tests on the same aluminumalloy shell without noticeable damage and yielded reliable interaction curves. Results of combined-loading tests are presented and compared with linear theory. Test results show that the interaction curve for compression-torsion-pressure loading is defined by superposition of compression-pressure, torsion-pressure and compression-torsion behavior.

Global dynamic stability of a shallow arch by poincaré-like simple cell mapping

Abstract Global dynamic stability of a shallow elastic arch subjected to a distributed constant load is studied by Poincare-like simple cell mapping. The present solution of the dynamic model of the arch consists of two modes, one symmetric and one anti-symmetric. The global structure of the domains of attraction of the modes is determined and presented. The dynamic behavior, due to displacement and velocity disturbances imposed on the arch, is considered. Values of “safe” disturbances below which no buckling occurs are obtained.