In-plane Uniaxial Compression Research Articles

The in-plane non-linear compression of regular honeycombs

A theoretical analysis is made of the in-plane uniaxial compression of regular honeycombs made from a range of materials. Both the elastic and elastic-plastic responses are considered, as a function of the honeycomb density, for strains until the faces touch. The stress–strain relationship and lateral expansion are predicted for loading in the symmetry axis directions, for deformation modes with and without vertex rotation. For an elastic honeycomb, compressed parallel to one set of faces, a buckling mode with vertex rotation gives the lower stress, for strains exceeding 10% in honeycombs with single thickness vertical faces, and 15% strain for double-thickness faces. If the material yields, or other forms of non-linearity occur, there can be strain softening, which leads to strain localisation. Deformation mechanisms are linked to the material response and the honeycomb density, and are compared with experiments on polymeric honeycombs.

Experimental Results for Bending and Buckling of Rectangular Orthotropic Fiber-Reinforced Plastic Plate Structures

Solid unstiffened, sandwich, and hat-stiffened rectangular orthotropic fiber-reinforced plastic (FRP) plates were tested in uniaxial in-plane compression and out-of-plane uniform pressure. The two short edges of all plates were clamped, whereas the two long edges of the unstiffened and sandwich plates were simply supported and the same edges of the hat-stiffened plate were left free. Unstiffened plates reached global buckling at about 688 kN (155 klb); however, the plates did not collapse up to the machine load limit of 1334 kN (300 klb). Sandwich plates never reached the overall elastic buckling load; they collapsed in local buckling by face sheet delamination and core shear failure at loads of about 939 kN (211 klb). Hat-stiffened plates exhibited local buckling of the outer unsupported flanges at a load of about 356 kN (80 klb). All hat-stiffened plates collapsed under uniaxial compression due to a combination of face sheet to stiffener delamination followed by hat-stiffener local buckling at loads of about 939 kN (211 klb). The stresses and deflections due to out-of-plane uniform pressure were compared between the unstiffened, sandwich, and hat-stiffened plates from pressures of 6.895 kPa (1 psi) to 34 kPa (5 psi). With the plates under uniaxial compression and out-of-plane uniform pressure simultaneously, there was a general decrease in buckling and collapse with an increase in out-of-plane uniform pressure.

Mobility anisotropy of two-dimensional hole gases in (001)GaAs/Al0.5Ga0.5As heterostructures and the influence of uniaxial compression

Transport properties of 2D hole gases in (001)GaAs/Al0.5Ga0.5As heterostructures in the [1 = 10] and [110] directions have been investigated. In-plane uniaxial compression up to 5 kbar was applied in one or the other of the two directions, and measurements were performed in the temperature range 1.4 - 60 K and in a magnetic field up to 6 T. Without uniaxial compression the mobility is largest in the [1 = 10] direction, the [1 = 10]:[110] mobilities ratio attaining its largest values at low temperatures and high carrier densities. Interface roughness scattering together with acoustic phonon scattering is suggested to be the underlying phenomenon. Under uniaxial compression the electrical resistance decreases in the direction parallel to the compression, and it increases in the direction perpendicular to the compression. This behaviour is found to be in qualitative agreement with recent band structure calculations.

Stress Induced Anisotropy of Fermi Surface in p-GaAs/AlGaAs Quantum Wells

The valence band structures of single and double p-GaAs/Al0.5Ga0.5As heterostructures under in-plane uniaxial compression have been calculated. Hole subbands are split in the single heterostructure and there is no splitting in the double one. The energy spectrum and Fermi surface were found to become strongly anisotropic under applied uniaxial compression. The electrical resistance decreases in the direction parallel to the compression and increases in the perpendicular direction.

Viscoelastic analysis of creep response for uniaxially-compressed laminates with initial deflection including the effect of physical aging

The viscoelastic behavior of simply-supported, cross-ply and angle-ply laminated plates with a physical aging phenomenon is examined. The laminates considered are under uniaxial inplane compression and have various amplitudes of initial imperfection. The analysis is based on a geometrically nonlinear viscoelastic formulation. The effective time theory is employed to construct the stress-strain relations. By assuming every component of relaxation moduli in each lamina has the same aging shift rate, the analysis is conducted on the effective time scale. The stress function is obtained by solving the compatibility equation by the use of the Laplace transform and a numerical integration scheme. Deflection is calculated from the moment equation by the Galerkin method in conjunction with the numerical integration. Numerical results for deflection history and edge shortening for the glass-reinforced vinyl ester laminates are presented. The effects of the physical aging, the pre-loading aging time, the amplitude of imperfection, the magnitude of loading, and the coupling relaxation moduli on the creep responses are illustrated in the numerical examples. Solutions based on the quasi-elastic approach are also presented for comparison.

Stability and failure of symmetrically laminated plates

This paper describes a numerical and experimental study on the stability and failure behaviour of rectangular symmetric laminated composite plates. The plates are simply supported along the unloaded edges and clamped along the loaded ends, and they are subjected to uniaxial in-plane compression. The finite element method was employed for the theoretical study. The study examines the effect of the plate\'s stacking sequence and aspect ratio on the stability and failure response of rectangular symmetric laminated carbon fibre reinforced plastics composite plates. The study also includes the effect of the unloaded edge support conditions on the postbuckling response and failure of the plates, Extensive experimental investigation were also carried out to supplement the finite element study. A comprehensive comparison between theory and experimental data are presented and discussed in this contribution.

建設材料 ２次元モデルにおけるアコースティック・エミッション波形解析

Acoustic emission (AE) is a phenomenon caused by the propagation of elastic wave generated from micro cracks as sources. A procedure named as SiGMA (simplified Green's function for moment tensor analysis) to identify the crack kinematics from AE waveforms has been developed recently. By this procedure, the crack location, crack orientation and crack type can be determined. To apply the SiGMA procedure for AE source inversion in two-dimensional (2D) models, the SiGMA-2D procedure is proposed in this paper. The in-plane uniaxial compression tests of poly-methyl-metacrylate plates having an internal through-thickness slit are carried out for the experimental verification of SiGMA-2D solutions. These results confirm the applicability of the SiGMA-2D procedure for elucidating the crack mechanism. Crack identification by using SiGMA-2D is also performed in the mixed-mode fracturing of concrete and mortar plates, and the fracture process is investigated.

Large Deflections of Orthotropic Plates in Compression

Rectangular specially orthotropic plates subjected to uniaxial in-plane compression are analyzed into the large deflection regime, using the computer program ELDAROP. All four edges are simply supported against out-of-plane movement, and opposite pairs of edges are maintained straight and parallel. Some plates analyzed are initially flat. Others have a geometrical imperfection shaped as a single half-sine wave in both directions. Particular attention is given to the effects on plate behavior of the modular ratio Ex/Ey, and the geometrical imperfection amplitude ΔO/t. For flat plates, the initial postbuckled stiffness depends entirely on the membrane rigidities and the aspect ratio a/b. However, on further loading, the bending rigidities then have a significant effect, provided the membrane behavior is not close to being isotropic.

Large deflection analysis of orthotropic plates—adaptation of Coan's method

The problem considered is the elastic large deflection analysis of thin, rectangular, specially orthotropic plates with two axes of symmetry. Coan's method for allowing the prescription, for isotropic plates, of the in-plane tensile or compressive loading along two opposite edges, is adapted to deal with orthotropic plates. This analysis has been incorporated into an existing computer program (ELDAROP), and the results agree well with previous work on isotropic plates. Results are given for the post-buckling of square orthotropic plates under uniaxial in-plane compression. These confirm that if the unloaded edges are maintained straight, the post-buckled stiffness increases, and this effect decreases as the modular ratio increases.

The dynamic behaviour of postbuckled composite plates under acoustic excitation

The Rayleigh-Ritz method was used to find the postbuckling static displacement pattern of a composite plate (CFRP) under uniaxial in-plane compression of uniform edge-shortening. The resonance frequencies and mode shapes at various postbuckled states are then evaluated by eigenvalue analysis of the dynamical matrix equation consisting of up-dated tangential stiffness matrix at corresponding static configuration. The theoretical results are compared with experimental results obtained in 16-layered CFRP laminate of aspect ratio 1·5. The resonance frequencies and mode shapes obtained are used to interpret the multimodal and nonlinear strain responses to high level of acoustic excitation. The dominance of second-mode contribution and softening-spring behaviour are found in the strain response of postbuckled plates.

An evaluation of the elastic-plastic analyses of steel plates loaded by uniaxial in-plane compression

The review considers recent finite-element, finite difference, dynamic relaxation, and energy methods for the analysis of plates, accounting for welding residual stresses and initial out-of-flatness. The principles of each method, and the approximations made, are described. Load-shortening curves for 16 representative cases are compared, and the differences are identified and their likely causes described. Changes to the shape of the residual stress pattern, the use of simplified full-section yield criteria, and failure to account for residual out-of-balance loads at the end of an increment are found to be the major causes of differences. The strengths obtained from these detailed solutions are also compared with approximate solutions based on large-deflection, elastic analysis.

Collapse behaviour of aluminium plates

Theoretical predictions of the collapse behaviour of thin rectangular aluminium plates are presented and discussed. The plates are simply supported around all four edges, and are subjected to uniaxial in-plane compression. The method of analysis developed by the author is described elsewhere. The material behaviour of aluminium is characterised by the Ramberg-Osgood stress-strain formula. Two methods of using this formula are discussed—one based on the usual percentage proof stress, and the other on the stress at which the plastic strain is a stated proportion of the elastic strain. It is shown why the latter method is more suited to the normalisation of results for collapse analyses. The results presented here give an indication of the effects on plate strength of plate slenderness, initial out-of-flatness, and n, the “knee” factor of the material stress-strain curve.

Dynamic behaviour of isotropic plates under combined acoustic excitation and static in-plane compression

A study is described which was carried out to investigate the dynamic response of an aircraft-type aluminium alloy plate, with fully clamped boundaries, subjected to combined acoustic excitation and uniaxial in-plane compression. Experiments were conducted in an acoustic tunnel with sound pressure levels up to 150 dB. The non-linear characteristics of the plate have been examined under sinusoidal and broad band random excitation and a study made of the statistical and spectral properties of the response. Theoretical and experimental estimates of the plate natural frequencies and mode shapes are described.

Elasto-plastic analysis of orthogonally stiffened plates with initial imperfections under uniaxial compression

In general, the stiffened plates consisting of steel plate elements are unavoidably accompanied by initial imperfections such as residual stresses and initial deflections, which have considerable effects on their ultimate strength. Therefore, it is needed for designing them to develop more rational method taking the ultimate strength influenced by initial imperfections into account rather than the conventional design method being on the basis of the linear elastic buckling theory. From this point of view, this study aims to evaluate rigorously the ultimate strength of orthogonally stiffened plate with initial imperfections under uniaxial in-plane compression. The elasto-plastic finite element method is applied to attain this purpose. By a happy combination of modal analytical technique and conventional finite element method, much reduction of the degree of freedom can be expected to be realized herewith. Some numerical calculations are performed by means of this rigorous method to examine the exactness of the analysis. Moreover, the numerical results are compared with the experimental ones.