Linear Elastic Finite Element Research Articles

Numerical analysis of fixed-end hollow rectangular beam under uniformly distributed load

The purpose of using opening in the reinforced concrete (RC) rectangular beam is the reduction of self-weight, cost, displacement, and strain. Therefore, this research performs linear elastic finite element analysis by using ETABS for fixed-ended RC hollow and solid rectangular beams under uniformly distributed loadings with variable beam lengths, compressive strengths, and opening sizes.The solid and hollow beams are considered to be a 2-nodded line element for the numerical analysis. The maximum range of validation result in case of hollow beam is found to be (3.9 to 7.9) %, which may indicate good accuracy of numerical analysis. The 50 × 50 mm opening size is suitable for 300 × 300 mm RC rectangular beam because of showing the positive normalized deflection of (0–1.45) % and lower strain rates (i.e. 0.13 % and 0.17 %) to compare the solid beam. This research may help professional engineers to use suitable opening size for design and construction works. Although, there is a scope to enhance this research in future by performing nonlinear analysis.

Finite element analysis of macro-crack behavior in the cortical bone of a human tibia

The bone is a biological tissue that possesses a highly complicated hierarchical structure; hence, the tissue components of the bone exhibit variable mechanical proper-ties and a complex bone geometry. This is why the creation of a three-dimensional mod-el through CAD software facilitates the study of the mechanical behavior of bones. Com-bining the concepts of linear elastic fracture mechanics and finite element analysis pro-vides a practical solution to study the fracture behavior of the tibial bone. The objective of this study is to analyze the behavior of cracks in the cortical bone of the human tibia us-ing stress intensity factors in mode I, II, and III as rupture criteria to assess the bone damage response. The tibial bone is one of the most common sites for lower limb stress fractures, which pose problematic injuries. The results investigating the effect of the crack position in the bone demonstrate that the risk of crack propagation is mainly due to mode I opening and is highly favored in the distal zone compared to the middle and proximal regions, regardless of bone density. For the second case study, it is observed that regardless of the crack size, the maximum values of stress intensity factors KI are obtained in the distal zone. Regarding the effect of crack orientation, the results indicate the dominance of mode II for angles α = – 45°, 30°, 45°, leading to high values of stress intensity factors KII.

Parametric Analysis of Moment-Resisting Timber Frames Combined with Cross Laminated Timber Walls and Prediction Models Using Nonlinear Regression and Artificial Neural Networks

The light weight and moderate stiffness of multistorey timber buildings make them susceptible to increased lateral displacements and accelerations under service-level wind loading. Therefore, the fulfilment of serviceability requirements is a major challenge. In this study, linear elastic finite element analysis was used to perform a parametric study of moment-resisting timber frames combined with cross laminated timber walls. In the parametric study, various mechanical and geometrical parameters were varied within practical ranges. The results of the parametric study were used to derive simplified analytical expressions and to train artificial neural networks which can be used to estimate fundamental frequency, mode shape, top floor displacement, maximum inter-storey drift, and wind-induced acceleration. The analytical expressions and the artificial neural networks can be used for the preliminary assessment of serviceability performance of moment-resisting timber frames with and without cross laminated timber walls, under service-level wind loading.

Fatigue crack propagation life analysis of propeller

Fatigue crack fracture is a common failure mode in structures. For the propeller with initial crack, the hydrodynamic effect cannot be ignored when studying the fatigue crack propagation behavior. Taking the full-size KP505 propeller as the research object, its hydrodynamic performance is simulated and verified. By using the fluid-structure interaction (FSI), the pressure distribution and stress distribution of propeller under different working conditions are analyzed comprehensively, and the position of propeller hot spot stress is obtained. According to the principal stress and its direction of the hot spot stress, the location and orientation of possible macroscopic crack initiation are determined. By using the linear elastic fracture mechanics and finite element method (FEM), the propeller fatigue crack propagation law and life are calculated. The analysis results show that the Forman-Newman-de Koning (FNK) model predicts more complete fatigue crack propagation life than Paris model. The fatigue crack propagation of propeller has two stages, steady propagation stage, and accelerated propagation stage. The crack breaking blade thickness is the dividing point between the two stages. In addition, the effects of the advance coefficient, stress ratio, and initial crack size on the computed results are also analyzed, which provide reference for ship driving and propeller maintenance.

Impact of stress regime change on the permeability of a naturally fractured carbonate buildup (Latemar, the Dolomites, northern Italy)

Abstract. Changing stress regimes control fracture network geometry and influence porosity and permeability in carbonate reservoirs. Using outcrop data analysis and a displacement-based linear elastic finite-element method, we investigate the impact of stress regime change on fracture network permeability. The model is based on fracture networks, specifically fracture substructures. The Latemar, predominantly affected by subsidence deformation and Alpine compression, is taken as an outcrop analogue for an isolated (Mesozoic) carbonate buildup with fracture-dominated permeability. We apply a novel strategy involving two compressive boundary loading conditions constrained by the study area's NW–SE and N–S stress directions. Stress-dependent heterogeneous apertures and effective permeability were computed in the 2D domain by (i) using the local stress state within the fracture substructure and (ii) running a single-phase flow analysis considering the fracture apertures in each fracture substructure. Our results show that the impact of the modelled far-field stresses at (i) subsidence deformation from the NW–SE and (ii) Alpine deformation from N–S increased the overall fracture aperture and permeability. In each case, increasing permeability is associated with open fractures parallel to the orientation of the loading stages and with fracture densities. The anisotropy of permeability is increased by the density and connectedness of the fracture network and affected by shear dilation. The two far-field stresses simultaneously acting within the selected fracture substructure at a different magnitude and orientation do not necessarily cancel each other out in the mechanical deformation modelling. These stresses affect the overall aperture and permeability distributions and the flow patterns. These effects – potentially ignored in simpler stress-dependent permeability – can result in significant inaccuracies in permeability estimation.

Artificial neural networks-based J-integral prediction for cracked bodies under elasto-plastic deformation state –cyclic loading

The study builds upon a prior modeling framework designed for monotonic loading to compute the cyclic J-integral encompassing a crack tip experiencing elastic–plastic deformation due to cyclic loads. The proposed modeling approach extends the authors' earlier time-efficient method for computing the J-integral by combining artificial neural networks (ANNs) with finite element (FE) analyses. The ANN-FE integration allows efficient and accurate prediction of elastic–plastic stresses, strains and displacement fields for a crack body under cyclic loadings from the linear elastic FE solution. In the context of cyclic loading, stress, strain, and displacement fields near the crack tip of stainless steel (SS304) are determined by FE analyses under both elastic and elasto-plastic states for various crack sizes and R-ratios. ANNs models are developed to establish the nonlinear relationship between these two states. Consequently, the proposed approach enables the prediction of the elasto-plastic cyclic J-integral through the equivalent domain integral method, based on the elastic FE solution bypassing the need of a complicated elasto-plastic FE solution under cyclic loadings. The results show that this approach can effectively predict elasto-plastic cyclic J-integral while avoiding the complex computation of elastic–plastic deformation fields around the crack tip during cyclic loadings.

Study on the applicability of a modified strain approach to predict the fatigue life of HFMI-treated transverse stiffeners under variable amplitude loading

AbstractThis paper analyses the applicability of a modified strain approach to predict the fatigue life of HFMI-treated transverse stiffeners under variable amplitude loading (VAL) with random load sequences of a p(1/3) and linear shaped spectrum. Local stresses are determined using linear-elastic finite element analyses. The measured weld geometry and component imperfections are considered. From the hardness of the HFMI-treated zone and the base material, the elastic–plastic material behaviour and Coffin-Manson parameters to describe the damage parameter Woehler curve are estimated. Based on a hysteresis counting method (HCM), the damage for each closed hysteresis is calculated. The applied notch strain approach includes the impact of residual stresses and the influence of surface roughness. Thus far, the application of similar approaches has only been validated for welded components with comparatively low residual stresses and HFMI-treated welds subjected to constant amplitude loading. To validate the accuracy of the approach for HFMI-treated welds under variable amplitude loading, the approximated fatigue life is compared to the number of cycles derived from experimental investigations. In this study, it is shown in conjunction with experimental results that it is essential to consider the strength of the base material near the weld when assessing the service life. This area can be more critical than the HFMI-treated weld toe.

A Comparative Investigation of the Reliability of Biodegradable Components Produced through Additive Manufacturing Technology.

Using the linear elastic finite element method, we investigated how defects significantly influence the integrity of 3D-printed parts made from biodegradable material by experimental techniques and numerical simulations. A defective flaw was incorporated into the tensile test dog-bone sample using Computer-Aided Design and processed by slicing software. Three distinct raster angles examine two sets of samples, one featuring intact specimens and the other with the introduced defects. An open-source 3D printer was used to fabricate both sets of samples, utilizing biodegradable PLA material. In finite element analysis, we employed a highly detailed model that precisely accounted for the geometry and dimensions of the extruded 3D-printed filament, accurately replicating the actual configuration of the 3D-printed samples to an extent. Our study involved a thorough comparative analysis between the experimental results and the FEA simulations. Our findings uncovered a consistent trend for the intact and defective samples under tensile load. Specifically, in the intact case, the samples with a zero-degree raster orientation presented the highest resistance to failure and displayed minimal elongation. Remarkably, these conclusions paralleled our observations of the defective samples as well. Finite element analysis revealed that the stresses, including Principal, Max shear, and Von Mises, were remarkably higher at the 3D-printed samples' outer surface than the inner layers, reflecting that the failure starts at the outer surface since they exceeded the theoretical values, indicating a significant discrepancy between the simulated and anticipated values.

Structural Performance of Large-Scale 3D-Printed Walls Subjected to Axial Compression Load

Despite the growing incorporation of additive manufacturing in the construction industry, a significant gap persists in the availability of design guidelines and comprehensive structural assessments for 3D-printed components. This research employs experimental methods to evaluate the performance of large-scale hollow unreinforced 3D-printed masonry walls under axial compressive load. Furthermore, a design methodology tailored for 3D-printed masonry walls under compressive loads is proposed in compliance with both American and Canadian masonry standards. This methodology is supported by the application of linear elastic 3D finite element analysis. Moreover, supplementary insights into material behavior are garnered through the examination of small specimens extracted from an additional 3D-printed wall. The results reveal that 3D printing reduces stiffness and compressive strength. The 3D-printed infills played an important role in redistributing stress after cracking. All full-scale 3D-printed masonry walls examined in this research exceeded the performance criteria set by the American masonry standard for load-bearing walls.

Study on Nanomaterials Coated Natural Coir Fibers as Crack Arrestor in Cement Composite

The process of inclusion of carbon nanotubes as fibers in cement paste has been proved to have optimistic effect as it enhances the tensile property of cement paste composite. Coir fibers have exceptional mechanical qualities and are thus employed as reinforcement in cement composites. Epoxy resin, which has a high Young’s modulus, is an ideal component for bonding carbon nanotubes (CNTs) to coir fiber. This paper describes a novel kind of nanocomposite made of L-12 epoxy resin and CNTs at the nanolevel, along with coir fibers at the microlevel which operate as crack arrestors. To remove surface contaminants, coir fibers are first treated with sodium hydroxide (NaOH). Epoxy/CNTs polymer coatings were developed at varying CNTs fractions (0.05, 0.1, 0.15, and 0.2 wt.% of cement). Multiwalled CNTs were combined in distilled water, followed by epoxy resin and hardener (9 : 1 v/v) polymer in an ultrasonic sonicator for 90 min to ensure full dispersion of CNTs within the epoxy polymer. This blend is now coated on the treated clustered coir fiber (length 10 cm, 10 strands) and reinforced along the length of a cement composite beam 20 mm × 20 mm × 80 mm in size. Tensile and three-point tests were performed to evaluate the mechanical characteristics of the hybrid composite. The linear elastic finite element analysis is employed to distinguish their failure phenomena via fatigue or fracture behavior. The microstructure behavior and the effect of coating material on the coir fibers were investigated using scanning electron microscope and EDX analysis. The reinforcing impact of nanopolymer coated coir fiber in cement composite diminished the tensile and flexural strength after 0.1 wt.% of CNT fraction but increased the composite’s durability and Young’s modulus. Fourier transform infrared spectroscopy analysis was carried out to assess the chemical interaction between the epoxy/CNTs and the coir fibers. The simulation was performed using ANSYS workbench, and the modeling results were within an acceptable 10% range of the experimental data. Nevertheless, it can be concluded that the hybrid composite is capable of enhancing the composite’s stress and strain capacity by regulating the fracture propagation process at the crack’s end.

Fretting Behavior of WC-Co-Cr Coatings Against QT Steel in Bolted Joint

Fretting damage on contacting surfaces introduces major challenges in mechanical assemblies. Thermal sprayed hardmetal coatings are extensively used for surface modification in tribological applications under demanding conditions and may also be subjected to fretting-inducing loading. In the present work, the fretting behavior of High Velocity Oxy-Fuel (HVOF) and High Velocity Air–Fuel (HVAF) sprayed WC-10Co-4Cr coatings against quenched and tempered (QT) steel was studied by using a single bolt joint-type fretting experiment. This experimental approach was selected to obtain realistic data on the fretting fatigue performance of the contact pairs (both coating-to-steel and coating-to-coating). Experimental results were completed with continuum-scale linear elastic finite element method (FEM) calculations.

Using the Point Method to estimate failure loads in 3D printed graphene-reinforced PLA notched plates

This work estimates failure loads in Fused Filament Fabrication (FFF) printed graphene-reinforced PLA (polylactic acid) plates containing different types of stress risers. With this aim, firstly, several notched plates are tested and conducted to fracture. Then, linear elastic Finite Element (FE) analyses are completed to define the corresponding stress profiles and, finally, the Point Method (PM) is applied to establish the failure criterion. This approach asserts that fracture conditions are achieved when the stress level equates the inherent strength (σ0) at a distance from the notch tip equal to L/2, so both parameters (related to each other through the material fracture toughness, Kmat) have been defined beforehand. The estimations of fracture loads obtained following this approach agree with the experimental results. Thus, the present work demonstrates the accuracy of the PM to estimate failure loads in this 3D printed material.

Feasibility of outrigger structural system for tall timber buildings: A numerical study

Tall timber buildings are prone to serviceability problems (e.g. lateral displacements and wind-induced accelerations). This article investigates the feasibility of timber outrigger system to build up to 20 storeys using linear elastic finite element analysis and relevant European and international standards such as EN 1990, EN 1991-1-1, EN 1991-1-4, EN 1995-1-1 and ISO 10137. The location of up to two outriggers was optimised based on different serviceability criteria. Various outrigger layouts were investigated, and their stiffness demands were discussed. The efficiency of outrigger structures in reducing lateral displacements and wind-induced accelerations is highlighted. A feasibility study considering serviceability requirements was performed using different basic wind velocities, number of storeys and gravity loads. Although the focus of the article is on serviceability requirements, some ultimate limit state considerations (forces and stresses) were briefly discussed. The results demonstrate the feasibility of building up to 16 storeys under medium to high wind velocities.

Structural analysis and optimization of steel truss bridge based on finite element method

In view of the defects of the current mainstream structural safety analysis method of Truss bridge, the safety analysis method at the component level should be further developed. Therefore, it is necessary to carry out the overall safety analysis and structural optimization at the structural level. Based on the concrete data of the actual steel truss beam bridge, this paper uses ABAQUS and MIDAS finite element software to model the truss structure. First of all, the static analysis is carried out, and then the structural analysis and optimization of the steel truss beam bridge is carried out with the elastic modulus reduction method. Based on the linear elastic finite element method, the bearing state of each component is solved, and the ultimate bearing capacity of the whole structure is calculated iteratively. Thus, the limitation of incremental nonlinear finite element method is overcome, and higher calculation accuracy and efficiency are realized.

Assessment of residual stresses in welded T-joints using contour method

Welded T-joints are commonly used in manufacturing of stiffened panels or crossbeams. However, welding of web-to-flange joint induces residual stresses and distortions resulting in significant challenges during both manufacturing and service. These issues can ultimately impact the structural performance, including fatigue and stability, and lifetime of the weldment. The purpose of current paper is determining the distribution and magnitude of manufacturing-induced longitudinal residual stresses in welded T-joints. Influence of hot rolling, thermal cutting, prestressing, welding, etc. are all included using the so-called contour method. Deformed surfaces are measured using coordinate measuring machine after wire electrical discharge machining of specimens. An inverse linear elastic finite element analysis is carried out for assessing residual stresses after data smoothing. Two-dimensional longitudinal residual stress patterns are evaluated in representative cross-sections clearly indicating high stress peaks near the welds, even exceeding yield strength of the base material. In addition, longitudinal membrane residual stresses are determined based on through-thickness stresses. In addition, a simplified residual stress model, satisfying the requirement for equilibrium of internal forces and bending moments, is developed for welded T-joints with double-sided fillet welds based on contour method results.

Investigation of anchorage plate opening on bursting force

Three-dimensional (3D) Finite Element analyses were performed to investigate transverse stresses and bursting forces at the anchorage zone in post-tensioned concrete beams. The behavior of the concrete beam was investigated through linear elastic Finite Element analyses. To validate the Numerical modeling results, an experimental study was performed on a beam and results are compared in terms of ultimate strength. The effect of duct hole and eccentricity are investigated by varying diameter and eccentric distances on the concrete beam. Furthermore, the results are validated for bursting stress and bursting force. Altogether, the equation of bursting force in IS 1343:2012 hasn’t considered the effect of duct hole and eccentricity, the results are compared with IS 1343:2012, and an equation is presented considering the effect of duct and eccentricity.

Data-driven artificial neural network for elastic plastic stress and strain computation for notched bodies

An integration of artificial neural network (ANN) and finite element (FE) analysis was developed to predict elastic–plastic stress and strains at notch locations based on a linear elastic FE analysis solution. Two FE models were created for different materials and multiaxial load cases to produce hypothetical elastic and elastic–plastic stress and strain datasets. One model was based on an elastic state, and the other was based on an elastic–plastic state. The ANN was trained with the elastic stress data from the linear elastic FE model as input and the elastic–plastic stress–strain data from the nonlinear elastic–plastic FE model as output. The dataset was divided into three groups: training, verification, and testing data. The ANN was trained using the training data, evaluated using the verification data, and tested for generalizability using the testing data. The results showed that the proposed methodology can predict elastic–plastic stress and strain fields for notched bodies under multiaxial loadings accurately and efficiently using only the elastic FE analysis solution.

A Numerically Efficient Method to Assess the Elastic–Plastic Strain Energy Density of Notched and Imperfective Cast Steel Components

The fatigue strength of cast steel components is severely affected by manufacturing process-based bulk and surface imperfections. As these defect structures possess an arbitrary spatial shape, the utilization of local assessment methods is encouraged to design for service strength. This work applies the elastic–plastic strain energy density concept to study the fatigue strength properties of a high-strength cast steel alloy G12MnMo7-4+QT. A fatigue design limit curve is derived based on non-linear finite element analyses which merges experimental high-cycle fatigue results of unnotched and notched small-scale specimens tested at three different stress ratios into a unique narrow scatter band characterized by a scatter index of 1:TΔW¯(t)=2.43. A comparison to the linear–elastic assessment conducted in a preceding study reveals a significant improvement in prediction accuracy which is assigned to the consideration of the elastic–plastic material behaviour. In order to reduce computational effort, a novel approximation is presented which facilitates the calculation of the elastic–plastic strain energy density based on linear–elastic finite element results and Neuber’s concept. Validation of the assessment framework reveals a satisfying agreement to non-linear simulation results, showing an average root mean square deviation of only approximately eight percent in terms of total strain energy density. In order to study the effect of bulk and surface imperfections on the fatigue strength of cast steel components, defect-afflicted large-scale specimens are assessed by the presented elastic–plastic framework, yielding fatigue strength results which merge into the scatter band of the derived design limit curve. As the conducted fatigue assessment is based solely on linear–elastic two-dimensional simulations, the computational effort is substantially decreased. Within the present study, a reduction of approximately 400 times in computation time is observed. Hence, the established assessment framework presents an engineering-feasible method to evaluate the fatigue life of imperfective cast steel components based on rapid total strain energy density calculations.

A linear elastic finite element approach to fatigue life estimation for defect laden materials

This work assumed that the stress-life behaviors of defect-laden materials converge at a certain low life cycle and attempted to estimate fatigue life by applying relative knock-downs to the endurance limit of a reference stress-life data. Linear elastic finite element analysis on small cracks initiated from defects was performed to evaluate the effect of defect size, aspect ratio, and location on endurance limit. While for internal defects size and shape are both influential, size and depth were found to be more important for surface defects. These findings were validated against the fatigue lives of laser powder bed fused Ti-6Al-4V specimens.

Simultaneous shape and topology optimization of wings

This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are evaluated by the means of a source-doublet panel method for the aerodynamic response and linear elastic finite elements for the structural response, which are one-way coupled. At each design iteration, a mapping procedure is applied to map the current wing shape and corresponding pressure loads to the unfitted finite element mesh covering the design domain. Wings of small fixed-wing airplanes both with and without a stiffening strut are optimized. The resulting wings show internal topologies with struts and wall-truss combinations, depending on the design freedom of the shape optimization. The lift distributions of the optimized wings show patterns like the ones obtained when performing optimization of wing shapes with constraints on the bending moment at the root.