On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

Combined shear/compression structural testing of asymmetric sandwich structures

Asymmetric sandwich technology can be applied in the design of lightweight, non-pressurized aeronautical structures such as those of helicopters. A test rig of asymmetric sandwich structures subjected to compression/shear loads was designed, validated, and set up. It conforms to the standard certification procedure for composite aeronautical structures set out in the “test pyramid”, a multiscale approach. The static tests until failure showed asymmetric sandwich structures to be extremely resistant, which, in the case of the tested specimen shape, were characterized by the absence of buckling and failure compressive strains up to 10,000 μ strains. Specimens impacted with perforation damage were also tested, enabling the original phenomenon of crack propagation to be observed step-by-step. The results of the completed tests thus enable the concept to be validated, and justify the possibility of creating a much larger machine to overcome the drawbacks linked to the use of small specimens

Postbuckling failure of composite plates with central holes

The postbuckling failure of square composite plates with central holes is analyzed numerically and experimentally. The particular plates studies have stacking sequences of: (+ and - 45/0/90)(sub 2S); (+ and - 45/0(sub 2))(sub 2S); (+ and - 45/0(sub 6))(sub S); and (+ and - 45)(sub 4S). A simple plate geometry, one with a hole diameter to plate width ratio of 0.3 is compared. Failure load, failure mode, and failure location are predicted numerically by using the finite element method. Predictions are compared with experimental results. In numerical failure analysis the interlaminar shear stresses, as well as the inplane stresses are taken into account. An issue addressed in this study is the possible mode shape change of the plate during loading. It is predicted that the first three laminates fail due to excessive stresses in the fiber direction, and more importantly, that the load level is independent of whether the laminate is deformed in a one-half or two-half wave configuration. It is predicted that the fourth laminate fails due to excessive inplane shear stress. Interlaminar shear failure is not predicted for any laminates. For the first two laminates the experimental observations correlated well with the predictions. Experimentally, the third laminate failed along the side support due to interlaminar shear strength S(sub 23). The fourth experimental laminate failed due to inplane shear in the location predicted, however material softening resulted in a different failure load from predictions

A numerical investigation into the plastic buckling paradox for circular cylindrical shells under axial compression

It is widely accepted that for many buckling problems of plates and shells in the plastic range the flow theory of plasticity leads to a significant overestimation of the buckling stress while the deformation theory provides much more accurate predictions and is therefore generally recommended for use in practical applications. The present work aims to contribute to further understanding of the seeming differences between these two theories with particular regards to circular cylindrical shells subjected to axial compression. A clearer understanding of the two theories is established using accurate numerical examples and comparisons with some widely cited accurate physical test results. It is found that, contrary to common perception, by using a geometrically nonlinear finite element formulation with carefully determined and validated constitutive laws very good agreement between numerical and test results can be obtained in the case of the physically more sound flow theory of plasticity. The reasons underlying the apparent buckling paradox found in the literature regarding the application of deformation and flow theories and the different conclusions reached in this work are investigated and discussed in detail. © 2014 Elsevier Ltd

Compression behavior of delaminated composite plates

The response of delaminated composite plates to compressive in-plane loads was investigated. The delaminated region may be either circular or elliptical, and may be located between any two plies of the laminate. For elliptical delaminations, the axes of the ellipse may be arbitrarily oriented with respect to the applied loads. A model was developed that describes the stresses, strains, and deformation of the sublaminate created by the delamination. The mathematical model is based on a two dimensional nonlinear plate theory that includes the effects of transverse shear deformation. The model takes into account thermal and moisture induced strains, transverse pressures acting on the sublaminate, and contact between the sublaminate and plate. The solution technique used is the Ritz method. A computationally efficient computer implementation of the model was developed. The code can be used to predict the nonlinear-load-strain behavior of the sublaminate including the buckling load, postbuckling behavior, and the onset of delamination growth. The accuracy of the code was evaluated by comparing the model results to benchmark analytical solutions. A series of experiments was conducted on Fiberite T300/976 graphite/epoxy laminates bonded to an aluminum honeycomb core forming a sandwich panel. Either circles or ellipses made from Teflon film were embedded in the laminates, simulating the presence of a delamination. Each specimen was loaded in compression and the strain history of the sublaminate was recorded far into the postbuckling regime. The extent of delamination growth was evaluated by C-scan examination of each specimen. The experimental data were compared to code predictions. The code was found to describe the data with reasonable accuracy. A sensitivity study examined the relative importance of various material properties, the delamination dimensions, the contact model, the transverse pressure differential, the critical strain energy release rate, and the relative growth direction on the buckling load, the postbuckling behavior, and the growth load of the sublaminate

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

This paper presents buckling and free vibration analysis of composite plate/shell structures of various shapes, modulus ratios, span-to-thickness ratios, boundary conditions and lay-up sequences via a novel smoothed quadrilateral flat element. The element is developed by incorporating a strain smoothing technique into a flat shell approach. As a result, the evaluation of membrane, bending and geometric stiffness matrices are based on integration along the boundary of smoothing elements, which leads to accurate numerical solutions even with badly-shaped elements. Numerical examples and comparison with other existing solutions show that the present element is efficient, accurate and free of locking

The behavior of bonded doubler splices for composite sandwich panels

The results of an investigation into the behavior of adhesively bonded doubler splices of two composite material sandwich panels are presented. The splices are studied from three approaches: analytical; numerical (finite elements); and experimental. Several parameters that characterize the splice are developed to determine their influence upon joint strength. These parameters are: doubler overlap length; core stiffness; laminate bending stiffness; the size of the gap between the spliced sandwich panels; and room and elevated temperatures. Similarities and contrasts between these splices and the physically similar single and double lap joints are discussed. The results of this investigation suggest several possible approaches to improving the strength of the sandwich splices