Bending Stress State Research Articles

A hybrid continuum-beam optimisation model: the virtual extensometer method for efficient optimisation of lattice materials

AbstractAdditive manufacturing (AM) enables the fabrication of complex lattice structures that are infeasible with traditional manufacturing processes. These structures are typically implemented with constant cross-sectional strut elements; this strategy is expedient but leads to sub-optimal structural efficiency. Numerical continuum models allow robust mechanical modelling of complex lattice geometry but provide equally complex data fields that are ill-suited for traditional optimisation techniques. By contrast, numerical beam models represent the fundamental tensile and bending stress states but are incapable of capturing nuanced geometrical effects that lead to local stress concentrations. In this research, a hybrid continuum-beam method is proposed for the systematic optimisation of strut cross section: a representative unit cell is simulated by continuum elements, and the local strut stress tensor is acquired by embedded beam elements that act as virtual extensometers. By integrating a computationally inexpensive beam model into a more robust continuum model, the volume and the quality of data returned are significantly increased whilst being provided in a readily usable format for optimisation techniques, for a trivial increase in computational cost. The presented method is generalised and can be applied to any strut-based lattice structure. Body-centred cubic (BCC) and BCC with z-strut (BCCZ) lattice structures optimised by the proposed method are fabricated using laser-based powder bed fusion (LB-PBF) in AlSi10Mg and are mechanically evaluated. On average, performance for BCC lattice structures improves by 33% and 26% for relative yield strength and relative Young’s modulus respectively. BCCZ lattice structures saw a performance improvement of 25% and 19% for relative yield strength and relative Young’s modulus respectively, thus confirming superior performance at lower relative densities when compared to incumbent designs.

Scale modeling of thermo-structural fire tests of multi-orientation wood laminates

The stacking sequence of laminated wood significantly impacts the composite mechanical behavior of the material, especially when scaling down thermo-mechanical tests on plywood. In previous research, we developed a scaling methodology for thermo-structural tests on samples with similar cross sections, however this paper focused on testing plywood samples with different stacking sequences between the scales. Plywood samples at ½-scale and ¼-scale were subjected to combined bending and thermal loading, with the loading scaled to have the same initial static bending stresses. While the ¼-scale 4-layer [0°/90°]s laminate and the ½-scale 8-layer [0°/90°/90°/0°]s laminate had an equal number of 0° and 90° layers, as the char front progresses, the sections behave differently. Thus, modeling becomes essential to extrapolating the data from the smaller ¼-scale test to predict the behavior of the larger ½-scale test. Reduced cross-sectional area models (RCAM) incorporating classical laminated plate theory were used to predict the mechanical response of the composite samples as the char front increased. Three methods were proposed for calibrating the RCAM models: Fourier number scaling, from detailed kinetics-based pyrolysis GPyro models, and fitting to data from fire exposure thermal response tests. The models calibrated with the experimental char measurements produced the most accurate predictions. The experimental char models validated to predict the behavior of the ¼-scale tests within 2.5%, were then able to predict the ½-scale test behavior within 4.5%.

Theory and Empirical Analysis of Bridge Load Limitation Under the Action of Typical Heavy-Duty Vehicles

Abstract With the continuous growth of transportation demands, in-service highway bridges face greater challenges in their long-term operational lifespans, and bridge collapse accidents caused by vehicle overloading occur from time to time. Additionally, under the influence of loads and environmental factors, various wear patterns inevitably lead to degraded reinforced concrete bridges. In view of this problem, it is reasonable and feasible to limit the vehicle loads passing over highway bridges, and the key basis for limitation is determining the load limit value of a bridge. To determine a reasonable load limit value of a bridge, this paper has carried out the following research: Based on a classification of vehicle types, this paper explores the load parameters of several heavy-duty vehicles with large traffic volumes through traffic flow information and summarizes the load spectra of typical heavy-duty vehicles. On the basis of the theory of structural reliability, a method for determining the limit load of bridges is proposed. Given a structural target reliability index, the theoretical load limit value of a bridge can be calculated. To ensure the rationality of the theory of bridge load limit value, by relying on the engineering example, the theoretical load limit value is calculated. By comparing actual bridge load test data with the finite element model results, the rationality of the bridge load limiting theory is verified. Finally, the paper notes that it is safer and more reliable to define the load limit value according to the bending stress state for bridges.

Significant improvement of bending properties for WE43 magnesium alloys under the coupling effects of weak basal texture and high deformation temperature

Significant improvement of bending properties (approximately 64.7%) for WE43 magnesium alloy was realized by weakening the basal texture and raising the deformation temperature. The mechanisms for such improvement were investigated in detail by combining the experiment and finite element model. The results concluded that the coupling effects of weak basal texture and high deformation temperature was the key reason producing the above improvement of bending properties. Specially, the TD sample with weak basal texture was more conducive to activating basal slip than the RD sample, resulting in its higher strain hardenability and consequently more significant bending properties. Based on weak basal texture, raising the deformation temperature could further improve the bending properties. This improvement mechanism was attributed to the abundant activations of non-basal slip instead of basal slip, which could increase the independent slip systems and efficiently delay the development of the strong basal texture. Moreover, the occurrence of partial DRV and DRX relieved the stress concentrations by consuming the dislocations, further improving the bending properties. The activations of these deformation mechanisms matching the corresponding bending stress states caused the crystal rotation and the texture variety in the bending samples. Basal slip activation aligned the (0002) basal planes parallel to tensile stress in the outer region or perpendicular to compressive stress in the inner region. Additionally, prismatic slip activation induced crystal rotation around the c-axis, developing <10-10>//LD texture in the outer region but <10-10>⊥LD texture in the inner region.

Interlaminar Response of LSI-Produced C/SiC Ceramic Matrix Composites: Experiments and Modelling

This work investigates the interlaminar properties of a C/SiC composite produced by Liquid Silicon Infiltration, combining experiments based on Double Cantilever Beam tests and numerical analyses. Experimentally, a method to obtain pre-cracks with sharp tips at precise locations is proposed, and specimens with different thickness are used to investigate the effects of bending stress states in the delamination process. The properties of tri-linear Cohesive Zone Models for the modelling of delamination are identified numerically, by using automatic regression techniques without requiring additional assumptions or testing. Fiber bridging effects were observed and modelled, including the evaluation of the process zone lengths with different experimental, analytical, and numerical methods. Overall, the work provides a qualitative insight in the delamination process of long fiber reinforced C/SiC laminates produced with a cost-affordable technique and proposes an experimental and numerical protocol to characterize and model delamination phenomena, taking into account the scattering of material properties.

Bending of Bi-directional inhomogeneous nanoplates using microstructure-dependent higher-order shear deformation theory

In contrast of experimental analysis in the mechanical behavior of the complicated structures, the progress of theoretical research has many difficulties, especially with regard to the modelling of structures. The main objective of this research is to analyze analytically the static problem of a new model of functionally graded materials, namely the “bi-coated FGM” plate. The materials are graded continuously through 2-directional by using a power law function. Two types of coated FG plates are investigated, Hardcore and Softcore FG plates. Based on the generalized field of displacement, a Quasi-3D higher-order shear deformation plate theory is proposed in this work by reducing the number of variables from six to five variables. The equilibrium equations are performed based on the principle of virtual work and solved using the Galerkin method to cover different boundary conditions. The nonlocal strain gradient theory is employed to capture the microstructure-dependent effect. The model is validated compared to recent relevant research interests. Numerical results are performed to present the impact of hardcore and softcore distributions, gradation indices, and boundary conditions on static bending deflection and stresses of bi-coated FGM plate.

Effect of Carbon Nanofibers on the Viscoelastic Response of Epoxy Resins.

Two epoxy resins with different viscosities were enhanced up to 1 wt.%, applying a simple method with carbon nanofibers (CNFs). These were characterized in terms of static bending stress, stress relaxation, and creep tests. In bending, the contents of 0.5 wt.% and 0.75 wt.% of CNFs on Ebalta and Sicomin epoxies, respectively, promote higher relative bending stress (above 11.5% for both) and elastic modulus (13.1% for Sicomin and 16.2% for Ebalta). This highest bending stress and modulus occurs for the lower viscosity resin (Ebalta) due to its interfacial strength and dispersibility of the fillers. Creep behaviour and stress relaxation for three stress levels (20, 50, and 80 MPa) show the benefits obtained with the addition of CNFs, which act as a network that contributes to the immobility of the polymer chains. A long-term experiment of up to 100 h was successfully applied to fit the Kohlrausch-Williams-Watts (KWW) and Findley models to stress relaxation and creep behaviour with very good accuracy.

Buckling prediction for composite laminated cylindrical shells in underwater environment

This paper presents buckling solutions for composite laminated cylindrical shells in the underwater environment. Under the equilibrium governing equation of the bending stress state, two calculation formulas are proposed to predict the buckling pressure for the underwater composite cylinders with different boundary conditions. The validation of the proposed solutions in the elastic range is proved by comparison with experimental data. The influences of the geometrical imperfections generated from the process are considered by correcting the stiffness coefficients of the proposed analytical model. The results, compared with the finite element method, show that the evolution trend of the buckling pressure calculated by the developed model is close to the finite element analysis. Therefore, the proposed analytical solutions can provide a practical and efficient way for the designers to evaluate the buckling pressure of the composite shells in the design stage.

P‐29: Influence of the Static Bending Stress on LTPS TFT

We investigated the degradation behavior of p‐channel LTPS TFTs on PI substrate under the static bending stress. In order to evaluate the bending durability of flexible LTPS TFTs, device‐bending tests under different bending strains and directions have been performed. The performance of TFT under tensile bending stress degraded (ΔVth≈ 0.38V) worse than compressive bending stress (ΔVth ≈0.07V), which might be originated from both the generation of interface trap states (ΔNit) and channel boundary trap density (ΔNtrap) under tensile bending stress much higher than compression‐bent. In the meanwhile, the stress distribution has also been simulated. According to the results of test and simulation, we speculated the mechanical stress near the source and drain electrodes caused the traps in gate insulator, which in turn cause electron trapping.

SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR ANISOTROPIC PLATES AND SHELLS BY BOUNDARY ELEMENTS METHOD

Modern mechanical engineering sets the tasks of calculating thin-walled structures that combine lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of anisotropic materials and plastics seems justified. The problems of the theory of plates and shells belong to the class of boundary value problems, the analytical solution of which, due to various circumstances (nonlinearity of differential equations, complexity of geometry and boundary conditions, etc.), cannot bedetermined. Numerical methods help to solve this problem. Among numerical methods, undeservedly little attention is paid to the boundary element method. In this regard, the further development of indirect method of compensating loads for solving problems of the anisotropic plates and shells theory based on the applicationof exact fundamental solutions is relevant.The paper considers the application of the indirect boundary element method for solving of an anisotropic plates and shells nonlinear deformation problem. Since the kernels of the system of singular integral equations to which the solution of the problem is reduced are expressed in terms of the fundamental solution and itsderivatives, first of all, the article provides a method for determining the fundamental solutions to the problem of bending and the plane stress state of an anisotropic plate. The displacement vector is determined from the solution of linear equations system describing the bending and plane stress state of an anisotropic plate. The solution of the system is performed by the method of compensating loads, according to which the area representing the plan of the shallow shell is supplemented to an infinite plane, and on the contour that limits the area, compensating loads are applied to the infinite plate. Integral equations of indirect BEM are given. In this paper, the study of nonlinear deformation of anisotropic plates and shallow shells is carried out using the deflection load dependencies. The deflection at a given point on the median surface of the shell was taken as the leading parameter.

Nonlinear response under several multiaxial loading states in fibre reinforced polymer laminates

The present work includes a summary of the doctoral thesis entitled &quot;Complexity of the structural response of fibre reinforced polymer matrix composites&quot;. This PhD thesis focused on analyzing the nonlinear mechanical response of a set of stacking sequences, with main interest in angle-ply laminates, to detail the stress-strain behaviour under a range of loading states: uniaxial tension/compression, loading-unloading-reloading tensile tests, three-point bending and plane stress states. The aim is to delve into the mechanisms of coupling and damage and their influence on the mechanical behaviour, in some cases highly nonlinear, aiming to achieve that the material withstands large strains with the consequent delay of the final failure and the increase in energy absorption capacity. Thanks to the characterization through standard testing, it is possible to calibrate material models based on progressive damage, providing two different numerical approaches which are tested against the different experimentally generated states of plane stress. In addition, it is worth mentioning the biaxial tests on cruciform specimens under different loading ratios, which provide experimental data closer to the actual response of composite structures in service. These tests, due to their greater complexity and lack of standardization, are analyzed in detail by applying numerical simulations and analytical models that ensure the validity of the results, highlighting the possible instabilities generated in the presence of compressive loads.

Numerical Evaluation of Safety Wall Bending Strength during Hydrogen Explosion

The main aims of this study are to assess numerically the stress state of a solid wall which is installed at the hydrogen fueling station in order to protect personnel from the consequences of the accidental hydrogen explosion, define the bending stress values in the foot of the wall exposed to explosion wave pressure forces and located at different distances from explosion epicenter in order to choose appropriate construction material of the wall and assess the minimum thickness of the wall satisfying bending strength condition. A three-dimensional mathematical model of hydrogen-air mixture explosion is used to define the distribution of the maximum overpressure on the wall surface. To assess the bending stress state at the foot of the wall, the design scheme of a cantilever beam is considered. It is assumed that the maximum overpressure force field influences the wall at the same time to assess the worst possible scenario. Actually, the computer-based methodology of how to resolve a coupled problem of explosion gas dynamics and defense wall strength is suggested. This technique allows evaluating of the construction parameters of the wall, which protects the personnel against consequences of the explosion wave exposure, without the destruction of the wall.

5‐2: Enhanced Bending Endurance with Transverse Tensile Strain and 4‐Terminal Double Gate LTPS TFTs for flexible AMOLED

This letter investigates the degradation behavior of p‐channel LTPS TFTs on PI substrate under the static bending stress. During 1hr bend, the threshold voltage shifts positively and the subthreshold slope increases slightly. In transverse compressive strain, the field effect mobility increases abruptly with the decrease of the effective channel length and the off state leakage current. This is attributed to the generation of the strain‐induced GI defects near the source and drain terminals, resulting in the trapping of electrons and a shrinkage of the effective channel length and the H passivation of the strained Si bonds in the channel. By inserting the bottom metal layer to block the H diffusion from PI substrate, the controllable normal NBTI behavior is observed in a strained LTPS TFT on PI. These transverse tensile strained and 4‐termianl double gate LTPS TFTs on PI shows as a stable switching TFTs on PI for the flexible system‐on‐panel display.

A Refined Model for Analysis of Beams on Two-Parameter Foundations by Iterative Method

It is of great significance to study the interactions between structures and supporting soils for both structural engineering and geotechnical engineering. In this paper, based on the refined two-parameter elastic foundation model, the bending problem for a finite-length beam on Gibson elastic soil is solved. The effects of axial force and soil heterogeneity on the bending behaviours and stress states of beams on elastic foundations are discussed, and the parameters of the physical model are determined reasonably. The beam and elastic foundation are treated as a single system, and the complete potential energy is obtained. Based on the principle of minimum potential energy, the governing differential equations for the beam bearing axial force on the Gibson foundation are derived, and the equations for attenuation parameters are also defined. The problem of the unknown parameters in foundation models being difficult to determine is solved by an iterative method. The results demonstrate that this calculation method is feasible and accurate, and that the applied theory is universal for the analysis of interactions between beams and elastic foundations. Both axial force and soil heterogeneity have a certain effect on the deformation and internal force of beams on elastic foundations, and the vertical elastic coefficient of foundations is mainly determined by the stiffness of the surface soil. Additionally, attenuation parameters can be obtained relatively accurately by an iterative method, and then the vertical elastic coefficient and shear coefficient can be further obtained. This research lays a foundation for the popularisation and application of the two-parameter elastic foundation model.

Application of Physical Methods for the Detection of a Thermally Degraded Recycled Material in Plastic Parts Made of Polypropylene Copolymer.

The paper deals with the possibility of applying physical methods to detect a thermally degraded recycled material in plastic parts made of polypropylene. Standard methods of evaluating the mechanical properties of the material under static tensile and bending stress, as well as under dynamic impact stress using the Charpy method, were used for the experimental measurements. The rheological properties of materials were monitored using a method involving measuring the melt flow index, while their thermal properties and oxidative stability were monitored using differential scanning calorimetry. Based on the methods used, it can be clearly stated that the most suitable technique for detecting thermally degraded recycled material in polypropylene is the method involving establishing the melt flow index. The bending test seems to be the most suitable method for detecting recycled material by measuring the material’s mechanical properties. Similarly to the melt volume flow rate (MVR) method, it was possible to unambiguously detect the presence of even a small amount of recycled material in the whole from measuring the material’s bending properties. It is clear from the results that in the short term, there may be no change in the useful properties of the parts, but in the long term the presence of degraded recycled material will have adverse consequences on their lifespan.

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets.

A novel functionally graded (FG) polymer-based nanocomposite reinforced by graphene nanoplatelets is proposed based on a new distribution law, which is constructed by the error function and contains a gradient index. The variation of the gradient index can result in a continuous variation of the weight fraction of graphene nanoplatelets (GPLs), which forms a sandwich structure with graded mechanical properties. The modified Halpin–Tsai micromechanics model is used to evaluate the effective Young’s modulus of the novel functionally graded graphene nanoplatelets reinforced composites (FG-GPLRCs). The bending and elastic vibration behaviors of the novel nanocomposite beams are investigated. An improved third order shear deformation theory (TSDT), which is proven to have a higher accuracy, is implemented to derive the governing equations related to the bending and vibrations. The Chebyshev–Ritz method is applied to describe various boundary conditions of the beams. The bending displacement, stress state, and vibration frequency of the proposed FG polymer-based nanocomposite beams under uniformly distributed loads are provided in detail. The numerical results show that the proposed distributions of GPL nanofillers can lead to a more effective pattern of improving the mechanical properties of GPL-reinforced composites than the common ones.

Investigation of Guidewire Deformation in Blood Vessels Based on an SQP Algorithm

This paper proposes a solution to the simulated deformation of guidewires when they come in contact with the blood vessel in an interventional surgery simulation training system. Starting from the principle of minimum energy, the guidewire is evenly dispersed into a rigid light bar articulation model. A sequential quadratic programming (SQP) algorithm is used to nonlinearly optimize the deflection angle of each light bar. When the elastic potential energy of the guidewire reaches a minimum, we can get the guidewire deformation we want to solve. The method proposed in this paper avoids necessity of delving into contact deformation caused by the contact force between the guidewire and the blood vessel wall, while solving the problem of the deformation of the guidewire due to the pose of the contact points. We use an ABAQUS (finite element software) simulation to verify that this solution has a theoretical simulation accuracy of 5.11%, and the designed experiments prove that the actual simulation accuracy is about 11%. Moreover, we also simulated the bending stress state of the guidewire by using the deflection angle of each bar. In addition, in order to achieve the most suitable simulation results, we discuss the discrete density of the guidewire model from the perspective of algorithm time consumption and simulation accuracy.

Stress validation of finite element model of a small-scale wind turbine blade

Wind turbine blades are the first mechanical part of a wind turbine that interacts with the wind and hence play a key role in wind power generation. It is important that the wind turbine blade is tested for structural integrity in accordance to design code IEC 61400-23 such as strain limits, fatigue life, blade tip clearance limit, and surface stress. This paper aims to focus on the calculation and validation of static bending stresses in the blade; it presents the experimental and simulated stress analysis of a small-scale wind turbine blade. The simulation and 3D design software ANSYS, version 19.0 is used in the finite element analysis (FEA). By using FEA, we aim to capture the stress generated on the blade geometry under static loading and unloading conditions. As a first step towards this, the finite element results were validated against experimental results on a kestrel E230i turbine blade. The wind turbine blade was fixed at one end, loaded, and unloaded statically at three selected points. The finite element results are calculated within a 25% error margin of the experimental results. A reverse engineering procedure was used to determine the appropriate ANSYS model blade properties that were used as the exact material properties were not available from the manufacturer.

Bond durability of steel-FRP composite bars embedded in seawater sea-sand concrete under constant bending and shearing stress

The combination of the new steel-FRP composite bar (SFCB) and natural seawater and sea-sand concrete (SWSSC) has good prospects to be applied in development along the ocean coast and offshore islands. However, at present, there is still a lack of clear understanding on the durability of this new combination under actual marine service conditions. Therefore, in this paper, the interfacial bond durability, which is critical to the overall durability of SFCB reinforced SWSSC structures, was evaluated by accelerated aging tests. A new type of eccentric pullout test was designed to take into account the bending and shearing stress states of the concrete. The experimental results showed that the bond strength of SFCBs decreased by 5% after 9 months of aging in a 40 °C seawater wet-dry cycling environment and decreased by 26.2% after 9 months of aging in a 50 °C seawater immersion environment. Due to the surface degradation of the basalt fiber reinforced polymer (BFRP) after exposure, the sheared failure layer gradually transferred from the interface to the inner layer. Based on Fib Bulletin 40, the predicted bond strength retentions of SFCBs with SWSSC were 84% to 96% after 50 years of service.

Accurate prediction of springback after coining operation

A common approach used to reduce springback in flanging operations is to apply additional coining around the bent regions. In this strategy, the sheet metal part is compressed between two rigid dies having a clearance less than the sheet thickness. The aim is to bring additional compressive stresses especially around bending dominated regions. These stresses are slightly larger than the current yield stress of the material. By this way, the dominant bending stress state is reduced leading to less springback. The shell elements which are the state of the art in productive utilization of finite element simulations lack the ability to consider normal deformation which occurs during coining. Hence, it is not possible for process planners to decide on the degree of coining and to predict the springback results beforehand. In order to address this problem a set of experiments were performed, whereby deep drawn cups were coined around the punch radius region and cup bottom. To investigate the changed state of residual stresses, drawn cups were cut into halves and springback was measured. The same procedure was also simulated with the new thick shell elements which are improved to incorporate the normal stresses in thickness direction. It was seen that, by the help of this enhancement, the springback prediction is improved as compared to the conventional shell elements.