Uniaxial In-plane Loading Research Articles

Buckling analysis of rectangular plates with rotationally restrained edges subjected to linearly varying in-plane loading

This study addresses a comprehensive procedure for the buckling behavior of rectangular plates with rotationally restrained edges. They are subjected to uniaxial in-plane load that varies linearly from compression to bending. The load is applied to opposite edges with variable boundary conditions, ranging from simply supported to clamped. The other edges can also be free, guided, or between them. For the first time, the generalized integral transform technique (GITT) is applied to the buckling equation of such a plate. The integral kernel perfectly satisfies the plate boundary conditions and its constituent terms are limited to the approximate range of ±1 which prevents the numerical instability. The transformed equation is a set of linear algebraic equations which establish an eigenvalue problem. The plate buckling coefficient, and corresponding mode shape (contours of the buckled plate, the number of half-waves in each direction, etc.) are presented according to variations of the edge relative stiffness as well as the plate aspect ratio, the loading shape, and Poisson's ratio. The latter parameter has a significant effect on the buckling behavior when at least one of the edges is free, guided, or between them. This portion is developed for auxetic materials (negative Poisson's ratios), and it was concluded that the minimum buckling load mostly occurs as the Poisson's ratio tends to zero.

Effect of the Fibre Orientation Angles on Stress Concentration Around Various Shapes of Hole in Laminated Composite Plate Subject to in - Plane Loading

Abstract The current study employs the finite element method to compare stress concentration pertaining to a graphite / epoxy rectangular laminated composite plate that possess holes in different shapes. The hole enables redistributing in-plane stresses, impacts the stress concentration factor (SCF), and focuses maximum stress near the hole. The ANSYS program has been designed to be employed for parametric studies pertaining to plates that have a hole under uniaxial in-plane load. Analysis was done for angle-ply, four-layered symmetrically laminated rectangular plates that include different stacking sequences ± θ.

Experimental and FEM study on the in-plane and out-plane loaded reversible dual-material bio-inspired lattice structures with improved energy absorption performance

In the current study, bio-inspired lattice structures are derived from the architecture of the Euplectella aspergillum (sea sponge). All the lattice structures are fabricated using the fused filament fabrication (FFF) process. The fabricated structures are subjected to quasi-static uni-axial compressive in-plane and out-plane loading conditions. The results shows that energy absorption performance of lattice structures also depends on the structure's stiffness. When used in lattice structures, soft material like thermoplastic polyurethane (TPU) has good energy absorbing performance. However, the stiffness of soft materials is not good enough to increase energy absorption. Here an attempt has been made to increase the energy absorption capacity of lattice structures by using a combination of hard (PLA) and soft phase (TPU) material in the fabrication of structures. Overall, the mechanical properties and deformation behavior in the experimental and finite element studies are quite similar. Structures under in-plane loading conditions showed a shorter linear elastic region and longer plateau region, whereas the structures subjected to out-plane loading conditions showed longer nonlinear elastic regions and a shorter plateau region. Overall, the structures loaded in the in-plane condition have a more stable response, whereas those loaded in the out-plane loading conditions have higher mean plateau stress, higher energy absorption and better efficiency. In both in-plane and out-plane loaded structures, dual-material fabricated structures showed higher efficiency; in-plane structures showed the highest experimental efficiency of 0.453 whereas out-plane structures showed the highest efficiency of 0.470. Combination of dual-material showed improved performance without compromising the reversibility of the energy absorbers. Hence this study opens a field for the design and fabrication of better energy absorbers.

Performance evaluation of the energy dissipating hysteretic infill wall frame considering opening under in-plane and out-of-plane loading

An energy dissipating hysteretic infill wall system comprising slotted concrete blocks interlinked with energy dissipating link elements is conceptualized and developed. A comprehensive experimental and numerical study is conducted on the energy dissipating hysteretic infill system to prove its efficacy and efficiency over the conventional brick infill system. The energy dissipating hysteretic infills act as passive energy dissipating system with an improvement over the conventional infills such as the arrest of the diagonal compressive strut formation, a stable post-yield behavior for the infilled frame, and a better failure mechanism. The performance of the energy dissipating hysteretic infilled frames is evaluated under uni-axial in-plane loading, out-of-plane loading, and also simultaneous bi-axial loading, considering the effect of opening. The observed behavior is ascribed to the energy dissipation mechanism, which is a combination of the yielding of the energy dissipating link elements and the friction between the blocks. A numerical modeling of the energy dissipating hysteretic infill is developed in OpenSees by calibrating the YamamotoBiaxialHDR element and singleFPBearing element with the experimental test data of the energy dissipating hysteretic infill wall system.

Inspection of U-shaped steel dampers based on residual plastic deformation

Hysteretic dampers are widely applied as earthquake-induced energy dissipation devices in the design practice of seismic isolated structures. Therefore, an indispensable condition of urban function recovery determines whether the dampers can be used immediately after an earthquake. The deformation behavior of U-shaped steel dampers under uniaxial (in-plane) loading was the focus of investigation in this study. In this regard, two sets of loading tests on full-scale specimens were conducted: (i) cyclic loading tests with constant deformation amplitude, and (ii) cyclic loading tests with complicated loading histories. Image analysis was used to reproduce the deformation behavior of the dampers in loading tests. According to the obtained results in the tests with constant deformation amplitude, a numerical model that can describe the relation between residual plastic deformation and cumulative damage was adopted. Important findings were provided by the experimental results of the cyclic loading tests with complicated loading histories. Additionally, an evaluation method for the residual plastic deformation–cumulative damage of U-shaped steel dampers that are loaded with in-plan excitations was proposed.

Development of In-plane Biaxial Compression Test Method for Thin Sheet and Investigation of SD Effect under Biaxial Stress Condition

The accuracy of the finite element simulation (FE simulation) of press forming has improved as a result of sophisticated material modelling using data of the various experiments such as uniaxial compression, biaxial tension, and in-plane cyclic loading tests. However, the biaxial compression test of sheet material has never been reported lowing to the difficulty in buckling suppression, and differences between material behavior under biaxial tension and that under biaxial compression have not yet been discussed. In this paper, the biaxial compression test of sheet material using special tools to suppress buckling and a specimen shape that leads to uniform deformation in the measurement area is proposed mainly on the basis of FE simulation. The special tool has a urethane plate where the tool come into contact with the measurement area of the specimen to prevent damage of the strain gauges. Absolute values of compressive stresses during plastic work measured by the biaxial compression test were larger than tensile stresses during the same plastic work measured by the biaxial tension test. Similar results observed in uniaxial tension and compression tests are known as the strength differential (SD) effect.

The effect of buckling and post-buckling behavior of laminated composite plates with rotationally restrained and Pasternak foundation on stacking sequence optimization

This paper presents a stacking sequence optimization for maximizing the buckling load of rotationally restrained laminated composite rectangular plates with different boundary conditions resting on an elastic Pasternak foundation subjected to uniaxial and biaxial in-plane static loads. The Mindlin Plate Theory (MPT), which considers the first-order shear deformation effect, is used to extract the characteristic equations of the plates under in-plane loading, including plate-foundation interaction. The buckling problem of the laminated plates is analyzed by the Rayleigh–Ritz method. The aim of optimization is to maximize the buckling load and post-buckling load capacity by using the Genetic Algorithm (GA) method, and the design variable is the ply orientation. The results showed that the optimal orientation, θ, of the laminated square plate under biaxial in-plane loading with various conditions is 〖45〗^∘ approximately. The existence of a foundation, clamped boundary conditions, and high aspect ratio lead to increase the optimal orientation.

Elastic Buckling Analysis of Uniaxially Compressed CCCC Stiffened Isotropic Plates

This paper reports a research study that investigated buckling of stiffened rectangular isotropic plates elastically restrained along all the edges (CCCC) under uniaxial in-plane load, using the work principle approach. The stiffeners were assumed to be rigidly connected to the plate. Analyses for critical buckling of stiffened plates were carried out by varying parameters, such as the number of stiffeners, stiffness properties and aspect ratios. The study involved a theoretical derivation of a peculiar shape function by applying the boundary conditions of the plate on Taylor Maclaurin’s displacement function and substituted on buckling equation derived to obtain buckling solutions. The present solutions were validated using a trigonometric function in the energy method from previous works. Coefficients, <i>K</i>, were compared for various numbers of stiffeners and the maximum percentage difference obtained within the range of aspect ratios of <i>1.0</i> to <i>2.0</i> is shown in Figs 2 - 7. A number of numerical examples were presented to demonstrate the accuracy and convergence of the current solutions.

Static and dynamic analyses of graphene-reinforced aluminium-based composite plate in thermal environment

The enhanced thermo-mechanical static and dynamic behaviors are investigated for the functionally graded graphene nanoplatelet reinforced aluminium-based (GRA) composite plate. The partial differential governing equations of motion for the static and dynamic analyses of the GRA composite plate are obtained based on the first-order shear deformation plate theory, von Karman nonlinear geometric relationship and Hamilton's principle. Numerical simulations are finished through using the differential quadrature (DQ) method and direct iterative process. Three different distribution patterns of the graphene nanoplatelets (GPLs) are considered, including the uniform distribution pattern, U pattern, and functionally graded (FG) patterns of X and O patterns. For the static analyses, the thermal buckling and post-buckling behaviors of the GRA composite plate subjected to the uniaxial or biaxial in-plane loads are discussed with varying the boundary conditions. For the dynamic behaviors, the thermal linear and nonlinear vibrations of the GRA composite plate are analyzed in details. The numerical results demonstrate that there are remarkable distinctions among the thermo-mechanical behaviors of the GRA composite plates with three different GPL distribution patterns. The present investigations are significant to the optimal design and practical applications of the GRA composite plate, especially in the thermal environment.

A lumped parameter model for strip-shaped dielectric elastomer membrane transducers with arbitrary aspect ratio

Dielectric elastomer (DE) membrane transducers allow to achieve large strain, low energy consumption, low-noise, and highly compact mechatronic devices. To optimize the design of membrane DEs via numerically efficient software tools, as well as to develop accurate control and self-sensing algorithms, a lumped parameter model is required. In the case of rectangular DE strips clamped at both ends and subject to a uniaxial in-plane load, the resulting necking and inhomogeneous deformation turn out to be challenging to be described via standard lumped models, thus making it necessary to rely on numerically involved finite element (FE) tools. In this paper, we present a novel modeling framework that permits to accurately describe clamped DE membranes with generic aspect ratio in a control-oriented fashion. The model is grounded on an anisotropic free-energy function, which maps the inhomogeneities due to clamping within the constitutive membrane behavior. In this way, a lumped description of the DE can be obtained in terms of average stress and stretch quantities. After presenting the model, an extensive validation is performed by means of comparative studies with FE simulations as well as experimental results. It is observed how the proposed model permits to accurately describe the electro-mechanical response of clamped DE membranes for a wide range of aspect ratios, including nearly-uniaxial, nearly-pure shear, as well as intermediate configurations.

Sequential damage study induced in fiber reinforced composites by shear and tensile stress using a newly developed Arcan fixture

This work presents the application of both uniaxial and bi-axial in-plane loads to unidirectional carbon fiber reinforced polymer laminates using a newly developed Arcan fixture, which is a reliable experimental set-up to obtain a uniform shear stress field in a butterfly specimen. The set-up can be used for both damage model validation and parameters identification at various fiber orientations while using the same specimens. A sequential damage study was completed to highlight the influence of diffused damage induced in pure shear on the fiber direction tensile behavior of the laminate. This was accomplished by applying load on the specimens in two steps: (i) the pure shear step and then unloading at approximately 70% of the shear failure strength, (ii) in the tensile step until final failure. A clear drop in the tensile behavior of the laminate was observed by the diffused damage induced in the first loading step of pure shear. The experimental study is also supplemented with numerical simulations using a nonlinear elasto-plastic coupled damage constitutive law by employing Puck’s failure theory for mesodamage activation. In addition to the damage pattern, the non-linear mechanical behavior in shear is predicted and found in good correspondence with the experimental results.

Development of Matched Interface and Boundary Method for Buckling Analysis of Plates with Various Interfaces

Buckling problems of plates with interfaces caused by step changes in thickness, internal line supports and line hinges under uni-axial and bi-axial in-plane compressive loads are solved by using the matched interface and boundary (MIB) method. In view of buckling problems of plates, new MIB algorithms and their interpolation formulations are developed to deal with various interfaces. A number of examples are taken to examine the accuracy and convergence of the present algorithms. Numerical results are compared with the existing solutions to validate the applicability of these algorithms to the title problems. Numerical analysis shows that on the whole, MIB and its interpolation formulation are equivalent, and they are highly accurate and efficient approaches for buckling analysis of plates with various interfaces.

Macro scale material characterisation in support of meso scale modelling of masonry under uniaxial in-plane loading

The amount of detailed experimental data on the mechanical properties of brick masonry in the literature is limited regarding the orthotropic strength and fracture energy. A combined experimental/numerical methodology is proposed for the derivation of the macro scale properties of masonry. The experimental aspect deals with the mechanical characterisation of the individual materials, small masonry samples and masonry wallettes, including the relation of couplet to wallette strength. The numerical aspect is the calculation of the macroscopic properties of the masonry through discrete cracking calculations in two orthogonal directions. The numerical analysis results are compared with the experimental stress-strain results and Digital Image Correlation analysis. The Young's modulus and compressive fracture energy for the masonry composite are derived. The results are analysed in view of the resulting anisotropy of masonry and the obtained failure modes.

Macro scale material characterisation in support of meso scale modelling of masonry under uniaxial in-plane loading

The amount of detailed experimental data on the mechanical properties of brick masonry in the literature is limited regarding the orthotropic strength and fracture energy. A combined experimental/numerical methodology is proposed for the derivation of the macro scale properties of masonry. The experimental aspect deals with the mechanical characterisation of the individual materials, small masonry samples and masonry wallettes, including the relation of couplet to wallette strength. The numerical aspect is the calculation of the macroscopic properties of the masonry through discrete cracking calculations in two orthogonal directions. The numerical analysis results are compared with the experimental stress-strain results and Digital Image Correlation analysis. The Young's modulus and compressive fracture energy for the masonry composite are derived. The results are analysed in view of the resulting anisotropy of masonry and the obtained failure modes.

Electro-mechanical characterization of three-dimensionally conductive graphite/epoxy composites under tensile and shear loading

Abstract An experimental study was performed to compare the electro-mechanical response of three-dimensionally conductive woven carbon fiber/epoxy laminated composites under quasi-static uniaxial tensile and in-plane shear loading conditions. Three-dimensional (3D) electrical network was generated in these composites by embedding carbon nanotubes (CNTs) of 0.025 wt% in the epoxy and reinforcing short carbon fibers (150 μm and 350 μm long) with a fiber density of 1000 fibers/mm2 between the laminates using electro-flocking process. CNTs are effectively dispersed in the epoxy matrix using a combination of ultrasonication and shear mixing techniques. A compression molding fabrication technique was employed to fabricate composite materials. For all composite types, in general, the in-situ electrical response showed a trend of initial decrease in resistance and later increase in resistance for tensile loading. However, no noticeable increase in electrical resistance was observed until failure of the composite under shear loading conditions. Both CNTs and short carbon fibers made new contacts with neighboring carbon fiber laminates for entire duration of shear loading even though the composite was undergoing progressive failure.

Differential quadrature method (DQM) for studying initial imperfection effects and pre- and post-buckling vibration of plates

The effects of initial geometric imperfection and pre- and post-buckling deformations on vibration of isotropic rectangular plates under uniaxial compressive in-plane load have been studied. The differential equations of plate motions, using the Mindlin theory and Von-Karman stress-strain relations for large deformations, were extracted. The solution of nonlinear differential equations was assumed as the summation of dynamic and static solutions. Due to a large static plate deflection as compared with its vibration amplitude, the differential equations were solved in two steps. First, the static equations were solved using the differential quadrature method and the arc-length strategy. Next, considering small vibration amplitude about the deformed shape and eliminating nonlinear terms, the natural frequencies were extracted using the differential quadrature method. The results for different initial geometric imperfection and different boundary conditions reflect the impact of the mentioned factors on the natural frequencies of plates.

Effect of dynamic evolution of misfit dislocation pattern on dislocation nucleation and shear sliding at semi-coherent bimetal interfaces

Misfit dislocation pattern is generally accepted to play a critical role on the interface mediated deformation mechanism such as dislocation nucleation and shear sliding in various flat interfaces, however, a specific mechanical loading may dynamically modify its distribution and character before the appearance of distinct plastic flow out of interfaces. Taking bimetal semi-coherent interfaces with high symmetrically distributed misfit dislocations as an illustration, we reveal for the first time that the dynamic evolution of misfit dislocation patterns in interface appears for some specific interface types and loading schemes, and eventually governs the preferred sites of dislocation nucleation and the shear sliding mechanism. In contrary to the nearly unchanged feature of misfit dislocations under biaxial in-plane tension, the initial patterns around nodes of misfit dislocations are found to be distorted and spread anisotropically within interface during uniaxial in-plane loading, which in turn governs the non-Schmid phenomena of dislocation nucleation. A similar dependence of shear sliding mechanism on the anisotropic feature of core spreading of misfit dislocations in interface is also observed, depending on the characteristic of misfit dislocation patterns. Further investigations suggest that the dynamic evolution of misfit dislocation patterns may differ substantially for different types of interfaces, and consequently contribute to different mechanisms of dislocation nucleation and shear sliding. These results suggest a necessity to investigate the dynamic evolution of misfit dislocation patterns to get a more realistic understanding on the interface dominated plasticity.

SIMULATION OF FRICTIONAL DISSIPATION UNDER BIAXIAL TANGENTIAL LOADING WITH THE METHOD OF DIMENSIONALITY REDUCTION

The paper is concerned with the contact between the elastic bodies subjected to a constant normal load and a varying tangential loading in two directions of the contact plane. For uni-axial in-plane loading, the Cattaneo-Mindlin superposition principle can be applied even if the normal load is not constant but varies as well. However, this is generally not the case if the contact is periodically loaded in two perpendicular in-plane directions. The applicability of the Cattaneo-Mindlin superposition principle guarantees the applicability of the method of dimensionality reduction (MDR) which in the case of a uni-axial in-plane loading has the same accuracy as the Cattaneo-Mindlin theory. In the present paper we investigate whether it is possible to generalize the procedure used in the MDR for bi-axial in-plane loading. By comparison of the MDR-results with a complete three-dimensional numeric solution, we arrive at the conclusion that the exact mapping is not possible. However, the inaccuracy of the MDR solution is on the same order of magnitude as the inaccuracy of the Cattaneo-Mindlin theory itself. This means that the MDR can be also used as a good approximation for bi-axial in-plane loading.

An original single variable shear deformation theory for buckling analysis of thick isotropic plates

This work proposes an original single variable shear deformation theory to study the buckling analysis of thick isotropic plates subjected to uniaxial and biaxial in-plane loads. This theory is built upon the classical plate theory (CPT) including the exponential function in terms of thickness coordinate to represent shear deformation effect and it involves only one governing differential equation. Efficacy of the present theory is confirmed through illustrative numerical examples. The obtained results are compared with those of other higher-order shear deformation plate theory results.

Progressive failure prediction of a landing gear structure of braided composites

Two simplified methods for progressive failure prediction of structures made of braided composites, mainly subjected to uniaxial in-plane loading or bending, were proposed, in order to bypass the complexity associated with meso- and micro-mechanics without losing much accuracy. One method models braided composites as equivalent one-dimensional material with different tensile and compressive strengths, for structures mainly subjected to uniaxial loading. The other more general method models braided composites using equivalent laminates, used together with Hashin’s progressive damage model. The parameters required in two methods were calibrated using stress-strain curves generated through the multi-scale approach, which combines micromechanics of failure (MMF) and meso-mechanical models describing the geometries of braided composites. Good agreement was observed in the moduli and strengths estimated using both proposed methods and the multi-scale approach, for braided composites with braiding angles ranging from 15 to 75 degrees subjected to uniaxial tension and compression. Finally, the proposed methods were utilized to predict the response of a landing gear structure fabricated using braided composites under bending. Reasonable agreement between experimentally acquired load-displacement curve and prediction was achieved.