Uniform Compressive Load Research Articles

Explicit local buckling analysis of stiffened composite plates accounting for periodic boundary conditions and stiffener–plate interaction

Abstract The present contribution is devoted to the closed-form analysis of orthotropic plates under uniaxial uniform compressive load. The plates under consideration are stiffened by open-profile stiffeners in the longitudinal direction which represents a structural situation that is typical, e.g. for many aircraft parts such as tailplanes, wing covers or, at least in an approximate sense, fuselage sections. The analysis method explicitly accounts for periodicity properties of the given structural situation as well as for stiffener–plate interaction and is based on adequate displacement shapes for both the plate as well as the stiffeners in the form of simple polynomials and trigonometric functions. While the plates and the stiffener webs are treated as shear-rigid Kirchhoff-type plates, the stiffener flanges are modeled as Bernoulli-type beam elements in order to allow for a feasible solution of the problem. Using a Ritz-type approach, explicit expressions for the buckling loads are achieved which allow for a straightforward, efficient and yet reliable buckling analysis of stiffened composite panels. The excellent accuracy of the derived analysis method is established through comparison with the results by other authors and with results generated from the exact transcendental elasticity solution that is derived from the governing partial differential equations and the underlying boundary conditions. The characteristic buckling behaviour of stiffened composite plates is discussed for several representative plate-stiffener configurations.

Buckling analysis of thin-walled sections under general loading conditions

This paper presents an investigation of the buckling behaviour of thin-walled sections subjected to general loading conditions. The semi-analytical finite strip method is used. The existing results are only for sections subjected to a uniform loading, namely: uniform compression, uniform bending and uniform distributed loads, which are applied at the shear centre. For a general loading condition, we proposed the realizing linear analysis first to give longitudinal stresses. The stiffness matrix is provided in the standard manner. Each strip is divided into cells and longitudinal stresses are recorded in these cells. The integrations are performed on each cell domain and the sum of them provides the geometric matrix of the strip.

Effects of suppression of bone turnover on cortical and trabecular load sharing in the canine vertebral body

The relative biomechanical effects of antiresorptive treatment on cortical thickness vs. trabecular bone microarchitecture in the spine are not well understood. To address this, T-10 vertebral bodies were analyzed from skeletally mature female beagle dogs that had been treated with oral saline ( n=8 control) or a high dose of oral risedronate (0.5 mg/kg/day, n=9 RIS-suppressed) for 1 year. Two linearly elastic finite element models (36-μm voxel size) were generated for each vertebral body—a whole-vertebra model and a trabecular-compartment model—and subjected to uniform compressive loading. Tissue-level material properties were kept constant to isolate the effects of changes in microstructure alone. Suppression of bone turnover resulted in increased stiffness of the whole vertebra (20.9%, p=0.02) and the trabecular compartment (26.0%, p=0.01), while the computed stiffness of the cortical shell (difference between whole-vertebra and trabecular-compartment stiffnesses, 11.7%, p=0.15) was statistically unaltered. Regression analyses indicated subtle but significant changes in the relative structural roles of the cortical shell and the trabecular compartment. Despite higher average cortical shell thickness in RIS-suppressed vertebrae (23.1%, p=0.002), the maximum load taken by the shell for a given value of shell mass fraction was lower ( p=0.005) for the RIS-suppressed group. Taken together, our results suggest that—in this canine model—the overall changes in the compressive stiffness of the vertebral body due to suppression of bone turnover were attributable more to the changes in the trabecular compartment than in the cortical shell. Such biomechanical studies provide an unique insight into higher-scale effects such as the biomechanical responses of the whole vertebra.

Evaluation of residual stress in pre-stressed concrete material by digital image processing photoelastic coating and hole drilling method

A digital discrete image processing photoelastic coating and hole drilling combined system was developed to determine the magnitude of the residual stress in a pre-stressed concrete specimen subjected to a uniform uniaxial compression load. In the digital image processing fringe analysis, the optical data contained in the reflection photoelastic isochromatics were converted into values of residual stress. The evaluation was conducted through the measurement of the in-plane stress field generated by the introduction of the small hole. The stress field was determined from the calculation of the photostress distribution by means of digital discrete image processing method. The magnitude of the applied stress was calculated and compared with the initial applied stress value in the concrete specimen.

Elastic stability of plates with circular and rectangular holes subjected to axial compression and bending moment

In this paper linear buckling analyses of square and rectangular plates with circular and rectangular holes in various positions subjected to axial compression and bending moment are developed. The aim is to give some practical indications on the best position of the circular hole and the best position and orientation of rectangular holes in steel plates, when axial compression and bending moment act together. Two different orientations are considered for rectangular holes: holes with major dimension parallel to the vertical plate axis (RS holes) and major dimension parallel to horizontal plate axis (RL holes). The effect of bending moment on the stability of the plate is studied and some differences with respect to the uniform compression load case are shown. Some design suggestions on the best orientation of rectangular for stability purposes are given. The influence of dimension and position of perforations on linear buckling behaviour and, in particular, on buckling coefficient of the plate is observed. Some practical design formulations for the calculation of the buckling coefficient, taking into account (a) dimensions and shape (square and rectangular) of the plate, (b) dimensions and shape (circular and rectangular) of the hole, (c) position of the hole (centre in the “maximum” and in the “nodal” point), (d) orientation (RS and RL) of the rectangular hole, and (e) load configuration (uniform compression, combinations of axial compression and bending and pure bending) are finally proposed.

Linear buckling analysis of perforated plates subjected to localised symmetrical load

Holes are often unavoidable in webs of steel beams and in plates, due to inspection, maintenance and also aesthetic purposes. In these situations, the presence of holes may cause redistribution of plane stresses in plates with a significant reduction of stability. In this paper, linear buckling analyses of perforated plates subjected to localised symmetrical load, with circular and rectangular holes, are developed. The results show some relevant differences between the behaviour of the plate subjected to localised symmetrical load with respect to that of uniform compressive load, already known in literature, with a significant increase in the elastic critical load value. The buckling coefficient of square and rectangular perforated panels under symmetrical uniform compression assumes the same value of corresponding whole panels, and it strongly increases for localised symmetrical load, reducing its increment on the basis of the diameter of the hole. Lastly, some indications are given on the best orientation of rectangular holes when localised load are applied showing differences with the uniform compression load case. Holes with the longest edge parallel to the transverse direction of the panel subjected to uniform compression loads are preferable for stability purposes. According to present results obtained for localised loads, holes with the longest edge along the longitudinal direction are preferable.

Development of an in vitro three dimensional loading-measurement system for long bone fixation under multiple loading conditions: a technical description

The purpose of this investigation was to design and verify the capabilities of an in vitro loading-measurement system that mimics in vivo unconstrained three dimensional (3D) relative motion between long bone ends, applies uniform load components over the entire length of a test specimen, and measures 3D relative motion between test segment ends to directly determine test segment construct stiffness free of errors due to potting-fixture-test machine finite stiffness.Intact equine cadaveric radius bones, which were subsequently osteotomized/ostectomized and instrumented with bone plates were subjected to non-destructive axial, torsion, and 4-point bending loads through fixtures designed to allow unconstrained components of non-load associated 3D relative motion between radius ends. 3D relative motion between ends of a 50 mm long test segment was measured by an infrared optical tracking system to directly determine its stiffness. Each specimen was then loaded to ultimate failure in either torsion or bending. Cortical bone cross-section diameters and published bone biomechanical properties were substituted into classical mechanics equations to predict the intact test segment theoretical stiffness for comparison and thus loading-measurement system verification.Intact measured stiffness values were the same order of magnitude as theoretically predicted. The primary component of relative motion between ends of the test segment corresponded to that of the applied load with the other 3D components being evident and consistent in relative magnitude and direction for unconstrained loading of an unsymmetrical double plate oblique fracture configuration. Bone failure configurations were reproducible and consistent with theoretically predicted.The 3D loading-measurement system designed: a) mimics unconstrained relative 3D motion between radius ends that occurs in clinical situations, b) applies uniform compression, torsion, and 4-point bending loads over the entire length of the test specimen, c) measures interfragmentary 3D relative motion between test segment ends to directly determine stiffness thus being void of potting-fixture-test machine stiffness error, and d) has the resolution to detect differences in the 3D motion and stiffness of intact as well osteotomized-instrumented and ostectomized-instrumented equine radii.

The buckling of functionally graded truncated conical shells under dynamic axial loading

The dynamic buckling of truncated conical shells made of functionally graded materials (FGMs) subject to a uniform axial compressive load, which is a linear function of time, has been studied. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the dynamic stability and compatibility equations of functionally graded truncated conical shells are obtained first. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equation with variable coefficient and critical parameters obtained using the Runge–Kutta method. The results show that the critical parameters are affected by the configurations of the constituent materials, compositional profile variations, loading speed variations and the variation of the shell geometry. Comparing the results of this study with those in the literature validates the present analysis.

Elastic Bending Stress Analysis of Fracture Line Generation for Case (Square Tube) of Corrugeted Fiberboard Box Shape under Uniform Compression Loading (On Panel Height/Width=0.8-2)

An elastic bending deformation analysis of fracture line generation for anisotropic side plates [width L=60-120mm, height h= (0.8-2) L and longitudinal elastic coefficients Ex=2.94×103N/mm2 and Ey=1.24×103N/mm2 in width and height directions and Poisson's ratio νxy=0.10 for width direction strain effect to height direction strain] in the case (square tube panel) of the corrugated fiberboard box shape (CFCBS) under uniform compression loading py0 was considered. Deflection W of side plates distributes symmetrically to center lines of width and height directions and becomes the distribution pattern of the convex-concave shape on outer surfaces of side plates. And rate h'*/L (h'* : maximum distance between upper or lower surface and fracture line) becomes nearly constant in range h/L>0.8 and fracture lines for side plates become curves of sine square root in similar figures, and independently of the change of h. Their fracture lines are denoted by the position which loading stress is equal to compression strength per unit area. And the shape of side plates made by fracture lines is similar to the barrack shape. Total load for fracture line generation is nearly constant.

Buckling Interaction in Regular Arrays of Rigidly Supported Composite Laminated Plates with Orthogrid, Isogrid, and Anisogrid Planform

The initial buckling strength of composite plate arrays with novel planform configurations are evaluated for combinations of uniform in-plane compression and shear loading and are presented in the form of dimensionless buckling interaction curves, for direct comparison with isotropic panels of equal mass. Results illustrate the buckling strength sensitivity with respect to changes in the stacking sequence of symmetric, specially orthotropic angle-ply composite laminates including the consideration of both cross-symmetric and non-symmetric

Stiffness and critical buckling load of perforated sheeting

This paper deals with selected foundations of the design of perforated trapezoidal sheeting. Based on numerical analysis, graphs on effective stiffness values for perforated sheeting with different arrays of holes are provided. As an outlook on further research, the calculation of the buckling coefficient for a perforated plate under uniform in-plane compression loading and for an infinitely long perforated plate under shear loading is presented.

A Study on the Structural Stress Analysis of the Steel and the GFRP Laminated Composite Cylindrical Shell with a Stiffened Circular Cutout

The strain distribution around the unstiffened and stiffened circular cutout of the isotropic stainless steel (ANSI type 304) and the GFRP laminated composite cylindrical shells subjected to axial compression are studied. The experimental results are obtained and compared with numerical analysis. In experiment, the strain is measured around the circular cutout by strain measuring system under the axial uniform compression loading. The numerical analysis is performed by the commercial finite element code ANSYS. The strain concentration factor (SCF) is defined to investigate the strain concentration around the circular cutout. The SCF of the stainless steel cylindrical shell with a stiffened cutout is decreased 39% in experiment and 50 % in numerical analysis. The SCF of GFRP laminated composite cylindrical shell is decreased 22% in experiment and 31 % in numerical analysis.

Elastic Stress Analysis on Corrugated Fiberboard Container of a Box Shape under Uniform Compressive Loading in Upper and Lower Edges (On Isotropic Side Plates)

上下辺の幅方向の変位零であるとして，一様圧縮荷重を受ける段ボール箱型容器（幅350mm，高さ300mm，板厚5．44mm，縦弾性係数291N／mm2，ポアソン比0．10）の側板の弾性曲げ変形表示を妥当な応力関数の組合を用いて導出することを試みた。この表示によって，諸曲げ応力を求め，それらの特性を議論した。幅方向の曲げ垂直応力の絶対値最大値（σbxmax＝－0．0652N／mm2）は側板辺中央に，高さ方向の曲げ垂直応力の最大値（σbymax＝0．262N／mm2），たわみ（＝3．36mm）の絶対値の最大値，曲げ主応力の最大値（σbymax＝0．262N／mm2）は側辺中央にあり，曲げせん断応力（τbxymax＝±0．162N／mm2）および曲げ主せん断応力（＝±0．163N／mm2）の絶対値の最大値は板4隅にある。諸曲げ応力（σxmax，σymax，τxymax）と板の諸応力との比はσbxmax／σxmax＝6．6，σbymax／σymax＝2．6，τbxymax／τxymax＝33．5であり，この値の大きさは薄く，広い側板の形状によって生じる。

The buckling of rectangular plates with opening using a polynomial method

In this paper an energy method is presented for the linear buckling analysis of first order shear deformable plates. The displacement fields are defined in terms of the shape functions, which correspond to a set of predefined points and are composed of significantly high order polynomials. The locations of these points are found by mapping the geometry using the naturalized coordinates and bilinear shape functions. In order to evaluate the method, fully clamped and simply supported rectangular plates subjected to uniform uniaxial compressive loading on two opposite edges of the plate are investigated thoroughly and the results are compared with the exact solution given in the monograph of Timoshenko and Gere (1961). The method is extended to the analysis of perforated plates, wherein the negative stiffness computed over the opening area from in-plane and out-of-plane deformation modes is superimposed to the stiffness of the full plate. Numerical results are then favorably compared with those obtained by finite element methods. Other cases such as; rectangular plates with eccentrically located openings of different shapes are studied and reported in this paper with regards to the effect of aspect ratio, hole size, and hole position on the buckling. For a square plate with a large circular opening at the center, diameter being 80 percent of the length, the present method yields buckling coefficient 12.5 percent higher than the one from the FEM.

Buckling of long compression-loaded anisotropic plates restrained against inplane lateral and shear deformations

An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to uniform axial compression loads and elastically restrained against inplane expansion, contraction, and shear deformation is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates (coupling between bending and twisting) that are subjected to combined mechanical loads and is based on nondimensional parameters. In addition, nondimensional loading parameters are derived that account for the effects of the elastic inplane deformation restraints, membrane orthotropy, and membrane anisotropy on the induced prebuckling stress state. The loading parameters are used to determine buckling coefficients that include the effects of flexural orthotropy and flexural anisotropy. Many results are presented, for some selected laminates, that are intended to facilitate a structural designer’s transition to the use of the generic buckling-design curves that are presented and discussed in the paper. Several buckling response curves are presented that provide physical insight into the behavior for combined loads, in addition to providing useful design data. An example is presented that demonstrates the use of the generic design curves, which are applicable to a wide range of laminate constructions. The analysis approach and generic results indicate the effects and characteristics of laminate orthotropy and anisotropy in a very general and unifying manner.

Elastic Bending Stress Analysis for Case of Corrugated Fiberboard Box Shape (Square Tubular) under Uniform Compressive Loading (On Anisotropic Side Plates)

Formulations of elastic deflection and bending stresses for anisotropic side plates (width 350, height h=300 and thickness 5.44mm, and longitudinal coefficients E x =291 and E y =153 N/mm2 in width and height directions and Poison's ratio νxy=0.10 for width direction strain to height direction strain) in the case of the corrugated fiberboard box shape (CFCBS) under uniform compression py0 were expressed using the constrain of four edges, and behaviors of deflection iv and bending stresses for its box were discussed by these formulations. w and bending normal stresses σbx and σby in width and height directions of side plates distribute symmetrically to center lines in width and height directions, and shear stress τbxy distributes antisymmetrically to their center lines. Maximum wm of|w| is at side edge centers in the side plate, and maximum σbxm of σbx is at side edge centers and maximum σbym of |σby| is at positions of L/32 from the plate center in the width direction. And maximum τbxym of |τxby| is at corners of the side plate. Ratios w (aniso) /w (iso), σbx (aniso) /σbx (iso), σby (aniso) /σby (iso) and τbxy (aniso) /τbxy (iso) for the anisotropic plate to the isotropic plate (longitudinal coefficient E =E x and Poison's ratio ν=νxy) are about 2, 2, 1 and 4/3 respectively.

On the Buckling Analysis of Plates Reinforced with Stiff Ribs

This paper deals with analytical buckling analysis of the rectangular orthotropic simply supported plates reinforced with longitudinal stiff ribs. It was considered that the ribs with rectangular and circular cross-sections were parallel and equivalent to each other. It was further assumed that the ribs were rigidly fastened to the plate and that their cross sections were perpendicular to the undeformed middle surface of the plate. These reinforced plates were subjected to the uniaxial uniform distributed compressive loads. In the study, the effect of the numbers and the cross-sections of the ribs on the buckling load were investigated. The results are striking in that how the ribs effect the isotropic plates with low strength.

Effect of residual stresses in a filament wound laminated conical shell

This paper examines the effect of residual fabrication stresses on the crushing behaviour, energy absorption, failure mechanism and failure mode of a filament wound laminated conical composite shell. The static crushing behaviour of the conical composite shell under uniform axial compressive load is investigated experimentally. The cone vertex angles were 0°, 6°, 12° and 18°. The numerical result shows that residual stresses developed have been concentrated at the small ends of cones. Experimental results obtained from this investigation show that the initial failure was dominated by interfacial and shear failure, while the delamination and eventually fibre fracture were dominated by the failure mechanism after the initial failure. It is also found that the static crushing behaviour of the conical shell is highly sensitive to the change in cone vertex angle, which strongly dominates the residual fabrication stress development. It can be deduced that as the axial residual stress increases, the initial failure load decreases.

On the Use of a Regular Yield Surface for the Analysis of Unreinforced Masonry Walls

A complete methodology for the non-linear macroscopic analysis of unreinforced masonry (URM) shear walls under biaxial stress state is presented, using the finite element method. The methodology focuses on the definition / specification of a general anisotropic (orthotropic) failure surface of masonry under biaxial stress, using a cubic tensor polynomial, as well as on the numerical solution of this non-linear problem. The characteristics of the polynomial used, ensure the closed shape of the failure surface which is expressed in a unique mathematical form for all possible combinations of plane stress, making it easier to include it into existing software for the analysis of masonry structures. The validity of the method, using the derived failure surface, is demonstrated by comparing the results from the study of the non-linear behaviour of URM wall panels, under uniform compressive and shear loading, against results derived by other investigators.

Load transfer mechanisms in cylindrical interbody cage constructs.

A finite-element model was created to study parametrically the load transfer characteristics of a lower lumbar motion segment implanted with dual anteroposterior cylindrical interbody cages. To describe the frontal plane bone-implant interface stresses acting on a generic cylindrical interbody cage, to evaluate the effect of implant material properties on these stresses, and to determine the associated load transfer mechanisms. From a biomechanical perspective, the long-term success of an interbody cage fusion depends on effective load transfer. The cage must stress the graft sufficiently to promote fusion, while keeping bone-implant interface stresses in a range that will prevent implant subsidence or loosening. At this writing, no published study has described interface stresses or load transfer mechanisms for these devices. A planar finite-element model was used to simulate uniform compression loading of the implanted segment. Material properties of the interbody cage were varied to simulate cortical bone, titanium, and stainless steel implants. Normal and shear interface stresses were output along the length of the interface. Magnitudes of both the normal and shear interface stresses were substantially higher at the medial and lateral sides of the interface than in the center. Interface stresses were largely independent of implant material. Cylindrical interbody implants have inherent limitations, including stress concentrations at the bone-implant interface and possible stress shielding of the graft. The results from the current study suggest that implants made of cortical bone have substantially the same load transfer characteristics as metal devices of similar geometry.