Nonlinear Finite Element Method Research Articles

Construction of multi-component finite element model to predict biomechanical behaviour of breasts during running and quantification of the stiffness impact of internal structure.

This study aims to investigate the biomechanical behaviour and the stiffness impact of the breast internal components during running. To achieve this, a novel nonlinear multi-component dynamic finite element method (FEM) has been established, which uses experimental data obtained via 4D scanning technology and a motion capture system. The data are used to construct a geometric model that comprises the rigid body, layers of soft tissues, skin, pectoralis major muscle, fat, ligaments and glandular tissues. The traditional point-to-point method has a relative mean absolute error of less than 7.92% while the latest surface-to-surface method has an average Euclidean distance (d) of 7.05mm, validating the simulated results. After simulating the motion of the different components of the breasts, the displacement analysis confirms that when the motion reaches the moment of largest displacement, the displacement of the breast components is proportional to their distance from the chest wall. A biomechanical analysis indicates that the stress sustained by the breast components in ascending order is the glandular tissues, pectoralis major muscle, adipose tissues, and ligaments. The ligaments provide the primary support during motion, followed by the pectoralis major muscle. In addition, specific stress points of the breast components are identified. The stiffness impact experiment indicates that compared with ligaments, the change of glandular tissue stiffness had a slightly more obvious effect on the breast surface. The findings serve as a valuable reference for the medical field and sports bra industry to enhance breast protection during motion.

The influence of lateral pressure on ultimate strength of ship structure

ABSTRACT The lateral pressure influences the ultimate strength of double-bottom structure. In the midship section of bulk carrier, upward bottom local loads typically exceed downward loads, resulting in increased longitudinal thrust in the outer bottom plating and a reduction in the ultimate strength of the hull girder during hogging conditions. In the present research, the typical stiffened plate and double bottom structures of the Kamsarmax type bulk carrier are taken as the research objects. The nonlinear finite element method is considered to analyze the collapse behaviour of the stiffened plate and double-bottom structure under the longitudinal thrust/bending and lateral pressure, respectively. The influence of lateral pressure on buckling modes, stress distribution, collapse mode and ultimate strength is systematically demonstrated and analyzed. This research contributes significantly to the safety design of hull structures.

A Nonlinear Mixed Finite Element Method for the Analysis of Flexoelectric Semiconductors

Abstract In this paper, we develop a nonlinear mixed finite element method for flexoelectric semiconductors and analyze the mechanically tuned redistributions of free carriers and electric currents through flexoelectric polarization in typical structures. We first present a macroscopic theory for flexoelectric semiconductors by combining flexoelectricity and nonlinear drift-diffusion theory. To use C0 continuous elements, we derive an incremental constrained weak form by introducing Langrage multipliers, in which the kinematic constraints between the displacement and its gradient are guaranteed. Based on the weak form, we established a mixed C0 continuous nine-node quadrilateral finite element as well as an iterative process for solving nonlinear boundary-value problems. The accuracy and convergence of the proposed element are validated by comparing linear finite element method results against analytical solutions for the bending of a beam. Finally, the nonlinear element method is applied to more complex problems, such as a circular ring, a plate with a hole, and an isosceles trapezoid. Results indicate that mechanical loads and doping levels have distinct influences on electric properties.

Post-Buckling Behavior of Variable-Arc-Length Elastica Pipe Conveying Fluid Including Effects of Self-weight and Pressure Variation

This paper investigated the post-buckling behaviors of a variable-arc-length (VAL) elastica pipe caused by internal transporting fluid motion, accounting for the effects of the self-weight and variation of internal fluid pressure. Both weak-form and strong-form formulations of the VAL elastica pipe were developed. The weak-form formulation was derived by the virtual work principle, and later solved using the nonlinear finite element method (FEM). The strong-form formulation was derived using equilibrium of the force and moment equations, the geometrical relationship of the differential pipe segment, and the energy conservation of the transported fluid. Because of the large displacement analysis, the variation in the internal pressure inside the pipe was considered, which was taken into account by energy conservation based on the Bernoulli principle. Then, the set of nonlinear governing first-order differential equations, corresponding to the two-point boundary value problem, was conveniently solved using the shooting optimization method (SOM). The numerical results obtained from the presented FEM and SOM analyses independently verified each other, with good agreement between these two methods. The parametric study considered the effects of gravity load (pipe and fluid self-weights) and internal fluid pressure on the post-buckling characteristics of the VAL pipe. The numerical results showed that without the pipe and internal fluid weights, the transporting fluid exerted an axial compressive force on the pipe, causing post-buckling phenomena. Beyond the critical state, the support rotation and the length of the VAL pipe increased as the internal fluid velocity decreased. Finally, by including the effect of self-weight, the mode exchange of the odd buckling modes (1st and 3rd modes) was found from the load-displacement path.

Non-bracket oblique traction-hoisting construction strategy for cable-truss structures

This study describes the non-bracket oblique traction-hoisting construction strategy for cable-truss structures, which is to assemble the upper and lower radial cables, hoop cables, sling cables, and compression rods without stress at a low altitude, then hoist the cable-strut system to a high altitude by oblique traction of the upper radial cables through the jack fixed on the upper radial anchorage nodes, and finally actively tension the lower radial cables to achieve the designed shape and prestress level of the entire structure. This strategy assembles at a low altitude, requires simple operations, results in high tensioning efficiency, and does not require brackets, which could guarantee both quality and quantity in terms of completing the construction of cable-truss structures. The semilune-shaped canopy of Yueqing Stadium is constructed using this strategy. The construction simulation and disturbance stability analyses of the structure in the traction-hoisting state and prestress tensioning state are conducted using a nonlinear dynamic finite element method. In the traction-hoisting stage, the deformation changes sharply, and the hoop cables and upper radial cables make up the primary bearing substructure, while the lower radial cables are in a suspended hanging state. In the forming process, the forces of the radial and hoop cables increase gradually, and the structure finally reaches the designed state. For cable-trusses with crossed upper and lower radial cables, the additional stabilizing tooling ropes should be tied at the top of the middle rods to ensure geometric stability because they are susceptible to excessive out-of-plane displacement or even overturning, which is the least desirable at the beginning of traction hoisting.

Effect of Corrosion-Induced Structural Degradation on the Ultimate Strength of a High-Tensile-Steel Ship Hull

Standard structural assessments of ship hulls include the evaluation of the elastic structural response. Elastic analysis neglects extreme and unpredicted loadings, which can produce catastrophic outcomes, such as the loss of the ship’s ultimate strength. Moreover, hull elements are considered unaffected by age-related degradation. Therefore, this study models and quantifies the effect of corrosion-induced structural degradation on the ultimate strength of a high-tensile-steel (HTS) cargo ship using progressive collapse and nonlinear finite element methods. Uniform and pitting corrosion are modeled through selected scenarios, which hull elements might encounter during exploitation, producing a total of 148 calculation models. The findings show that corrosion-induced degradation can significantly decrease the ultimate strength of the hull (up to 30% for the most severe scenarios assessed). Furthermore, ultimate strength decreases almost proportionally to the amount of wastage considered. It was found that stiffener corrosion has a significant effect on the total ultimate strength. This study’s aim is to emphasize the vast importance of including ultimate strength along with ageing effects in industry-standard structural assessments of large HTS ship structures, designed to last for several decades whilst exposed to excessive and unpredicted bending moments.

Non-linear behavior of functionally graded elastoplastic beam under torsion

The torsional behavior of beams graded in one and two directions under large displacements and angular deformations was analyzed using the power law and sinusoidal functions. Functionally graded material is elastoplastic, consisting of ceramic and metal. A nonlinear finite element method with isoparametric hexahedral elements was used. The finite element formulation was made using the updated Lagrangian formulation based on the virtual displacement principle. An iterative solution using Newton-Raphson and updated Newton-Raphson methods was used to solve the nonlinear equation system. The propagation of the plastic zone was calculated based on the flow theory of plasticity. Elastoplastic behavior and effective material properties were determined according to the TTO model. Numerical investigations have shown that functionally graded beams behave quite differently from homogeneous beams under torsion. Yielding of the material starts at the outer boundaries of the section of the homogeneous beams, and the plastic zone propagates symmetrically. On the other hand, yielding and propagation of plastic zones tend to shift to regions with more ceramic volume with higher effective Young modulus in functionally graded beams. Unlike homogeneous beams, the largest shear stresses can occur within the section rather than at the outer boundaries of the section. In beams graded from ceramic to metal using the power law, the section moves along the transverse direction in addition to the rotation. This transverse displacement occurs in the grading direction, and its magnitude is about 3% of the thickness at 12.5° rotation angle. Also, the shear stresses are not zero in the section's midpoint. The effects of material distribution on displacements, stresses, and plastic zone propagation were examined, and essential points were reported.

Numerical evaluation of the internal fracture mechanism of the single PBL shear connector considering the effects of position and strength of the transverse rebar

AbstractThe perfobond (PBL) shear connector reinforced with transverse rebar effectively contributes to sufficient ductility, bearing capacity, and anti‐fatigue behavior to hybrid structures. The construction practice involves the placement of the transverse rebar at the bottom position within the concrete dowel, whereas past studies employed transverse rebar in the center of the dowel; hence, there exists a gap between literature and design practices. Furthermore, there is no specific information in the design guidelines for hybrid structures on the influence of the position of the transverse rebar. Therefore, the current research deals with the analytical investigations employing the coupled Rigid Body Spring Model (RBSM) and the nonlinear solid Finite Element Method (FEM) that encompass the internal fracture behavior of concrete with the various parameters of transverse rebar, particularly the position and strength, to recognize the failure mechanism. It was determined that the numerical model accurately captured the test shear capacity and failure modes. The internal failure process of a specimen with transverse rebar at the bottom position, identical to actual field practice, revealed that as the height of the concrete region above the rebar rises, more compressive stresses in a trapezoidal manner are being generated, leading to an enhancement of the deformation capacity. Furthermore, it was confirmed that the specimen with the transverse rebar inserted at the bottom generates the greatest axial force, which is followed by the greatest shear capacity.

Estimating welding deformation of ultra-thin mild steel bead-on-plate joints by means of inherent strain method

The inherent strain method as an efficient computational tool has been widely used to predict welding deformation for large and complex structures with thin and medium-thick plates. For ultra-thin plate welded structures, geometric non-linear phenomena often arise during welding because of the low stiffness. In this study, the welding deformation of 0.8 mm thick bead-on-plate mild steel joints was studied by both experimental method and thermal-elastic-plastic finite element method (T-E-P FEM), and the influences of weld lengths on Tendon force, transverse shrinkage and angular distortion were examined experimentally and numerically. Meanwhile, a non-linear elastic finite element method based on the inherent strain theory using ABAQUS software as a platform was developed to reproduce the welding deformation of the ultra-thin bead-on-plate joints with different weld lengths, and the adaptability of the inherent strain method to ultra-thin plate weldments was clarified.

Behavior of helical reinforced concrete columns subjected to cyclic loading

AbstractHelical concrete columns are a new type of structural members which arose in new twisted buildings to satisfy architectural purposes. Helical concrete columns have a unique geometry which depends on the values of twist angle (ϕ) and the tilt distance of the center of rotation. According to the ACI T1.1R-01:2001 guidelines, a combined effect of axial load and lateral cyclic displacement protocol was applied to twelve specimens. Nonlinear finite element method was used to conduct the analysis and the numerical simulation for the helical reinforced concrete columns. The findings of the study revealed that the value of the buckling load, lateral displacement and the drift angle of helical concrete columns are significantly affected by the tilting distance of the rotation center and the twist angle.

Comparative analysis of nonlinear dynamic behaviors of hyperelastic curved structure modelled by different constitutive laws

This work focuses on conducting numerical studies and comparisons on the nonlinear dynamic behaviors of hyperelastic curved structures subjected to external dynamic loadings. A numerical model of the hyperelastic structure is developed using the nonlinear finite element method, which considers both the geometric nonlinearity resulting from large deformations and the material nonlinearity due to hyperelasticity. Four commonly used hyperelastic constitutive laws, namely the Mooney-Rivlin model, the neo-Hookean model, the Yeoh model, and the Ogden model, are employed to describe the nonlinear stress-strain relationship of the hyperelastic material. The convergence performance of the numerical model with respect to grid element and time step is thoroughly examined through several numerical examples. Subsequently, based on the developed numerical model, the nonlinear dynamic behaviors of the hyperelastic curved structures excited by uniform pressure loadings with single and dual frequencies are studied and compared using various constitutive laws. The material constants used in these constitutive laws are estimated based on the well-known Treloar's test data on vulcanized rubber material. Additionally, comprehensive parametric analyses are conducted on the nonlinear dynamic behaviors of the hyperelastic structure simulated by different constitutive laws. The deformation evolution process, resonance curves, time-frequency analysis, bifurcation diagrams, and phase portraits are employed to demonstrate the similarities and differences in the nonlinear dynamic behaviors (i.e., super- and sub-harmonic resonance, internal resonance, chaotic motion and bifurcations) of the hyperelastic structure modeled by different constitutive laws.

Array analysis on a seawall type of deformable wave energy converters

There has been a significant interest in developing Flexible Wave Energy Converters (FlexWECs) that utilise structural deformations to generate electricity and mitigate destructive wave loads to the devices. In the meantime, FlexWECs are most likely to operate in an array format to enhance space usage and power output, as well as provide convenience for maintenance. In this context, the present paper develops a high-fidelity computational model to investigate the interaction of ocean surface waves with an array of seawall-type FlexWECs, which can meanwhile serve coastal engineering purposes. The fluid field is solved using the Navier-Stokes equations, and structural deformations are predicted using a nonlinear finite-element method. Hydroelastic interactions of up to seven deforming FlexWECs with the surrounding wave fields are demonstrated through systematic simulation cases. Based on the simulation results, analyses are conducted to investigate how the wave farm energy output is influenced by the gap between individual devices and the number of devices deployed. Accordingly, empirical design suggestions are provided. Overall, this work innovatively simulates the hydroelastic interactions between waves and multiple deforming structures, and the provided insights are useful for promoting the development of FlexWECs and their wave farms.

Analysis of Position Effect of Vertical Load-Bearing Elements for Reinforcement of Steel Reinforced Concrete Floor Structures

The paper deals with the problem of stress in the connection detail of vertical supporting structures with a flat slab and possible methods for its analysis. It mainly focuses on the problem of non-axial connection of columns and walls, which is typical for today's architectural designs. The parametric study compares the effect of the distance of the connected vertical support structures on reinforcement in the discontinuity region. Three different computational methods are used to stress analysis of this region - linear Finite Elements Method in SCIA Engineer software, 2D Strut-and-Tie Model and 2D non-linear Finite Elements Method in IDEA StatiCa software. The conclusion of the study is a comparison of the accuracy of different calculation methods and also a comparison of the solved design variants in terms of shear and bending stress and specific form of reinforcement.

Effects of Mosquito-Imitated Microneedle’s Reciprocating Rotations on Puncture Resistance Forces—Evaluations by Puncturing Experiments and Nonlinear FEM Analyses—

Development of a low-invasive microneedle is currently desired in the medical field to mitigate the patients’ stress and pain. We have paid attention to mosquitoes that puncture the skin without giving humans no feelings of pain. We have observed mosquitoes and found that when their proboscis punctures human skin, they make the following three behaviors: apply tension to human skin; rotate their proboscis; vibrate their proboscis. In our previous studies, we developed a bundled set of three microneedle imitating the mosquito’s proboscis and experimentally proved the usefulness of their alternate vibrations, which is one of the mosquito’s puncturing behaviors. However, the setting of three needles with proper clearances from each other was difficult, making their driving system too complex to practically use it. Therefore, we have developed a simplified microneedle by reducing the number of needles from three to two or one. This paper has focused on the effects of the rotations of a single needle. Using our developed microneedle with a diameter of 90 µm and the thinnest commercial microneedle with a diameter of 180 µm, we evaluated the effect of reciprocating rotation, one of the mosquitoes’ puncturing behaviors, by puncture experiments using artificial skin and nonlinear finite element method (FEM) analysis. As a result, it was found that the reciprocating rotation suppresses the puncture resistance force and the skin deflection.

Research on Structural Collapse of a Containership under Combined Bending–Torsion by Oblique Waves

Large waves cause a great number of collapsed-ship accidents, resulting in the loss of many lives and properties. It has been found that most of these collapses are caused by encountering oblique waves. As a result, the ship structure experiences a complex collapse under combined bending and torsion. This paper utilizes a numerical hydroelasto-plastic approach, coupling CFD (Computational Fluid Dynamics) with the nonlinear FEM (Finite-Element Method), to study the structural collapse of a containership in oblique waves. First, a 4600 TEU containership was selected to study its collapse mechanism under oblique waves. Second, a hydroelasto-plastic numerical coupling of CFD and nonlinear FEM is used to co-calculate the wave loads and structural collapse of containership. The hydrodynamic model is constructed and used to solve wave loads in the CFD solver, and a nonlinear FEM model of containership with finer meshes is also modeled to solve the structural collapses, including plasticity and buckling. Third, several oblique-wave cases involving heading angles of 120°, 135°, 150°, and 180° are determined and calculated. Typical cases are discussed for time-domain stress histories and collapsed courses. Finally, the influence of oblique-wave parameters on structural collapse is discussed, and the collapse mechanism of containerships under the action of oblique waves is obtained, which provides a new understanding of ship structure design.

The displacement mechanism of the cracked rock – a seismic design and prediction study using XFEM and ANNs

Materials with sufficient strength and stiffness can transfer nonlinear design loads without damage. The present study compares crack propagation speed and shape in rock-like material and sandstone when subjected to seismic acceleration. The nonlinear extended finite element method (NXFEM) has been used in numerical simulation. It assumes the model has a pre-existing crack at 0° from the horizontal. The mechanical properties of the model, crack propagation shape, and crack speed were selected as the main parameters. The nonlinear stress and strain along the crack have been compared in two simulated models. NXFEM and Artificial Neural Networks (ANNs) were used to predict the displacement. The simulation results illustrate that the materials’ crack propagation mechanism and mechanical properties control the stress, strain, and displacement at the selected points in the model. In addition, crack propagation in materials is related to elastic-plastic stresses and strains along the crack path. The speed and shape of the crack are associated with the mechanical properties of the materials. The prediction of crack paths helps to understand failure patterns. Comparison of the seismic response of the rock-like material with sandstone helps to assess the stress, strain, and displacement levels during cracking. This study’s findings agree with the literature report and field observations.

Strength Reduction Method for the Assessment of Existing Large Reinforced Concrete Structures

This work presents a new developed assessment methodology based on strength reduction and finite element methods which is suitable for existing large reinforced concrete structures commonly used in hydraulic constructions. The methodology is based on a reloading phase of the finite element model and is preceded by an intermediate reduction phase of concrete tensile strength and an initial loading phase up to service level. Rosenblueth’s point estimate method was used to compute a global resistance factor and to deduce a design resistance value of the structure. After validations, the methodology was applied to two existing complex and large hydraulic structures: a spiral case and a draft tube. If compared with existing methodologies using sophisticated non-linear finite element methods, the developed approach is simpler, more practical, and provides results that are on the conservative side. Considering the difficulties in characterizing the tensile peak and post-peak strength of concrete, along with uncertainties regarding the damage conditions of facilities, the developed methodology is deemed robust and well suited for assessing existing critical large reinforced concrete infrastructures.

Experimental and numerical studies on the ultimate bending moment of welded plate girder with perforated web

ABSTRACT Combined opening girders with high stiffener webs used in the superstructure areas of passenger ships are prone to complex buckling phenomena under combined longitudinal and vertical loads caused by overall longitudinal bending and vertical forces from the deck cargo. In addition, the deformation and stress induced during structural assembly and welding make the buckling behaviour more difficult to predict. In response to this situation, thermal elastic–plastic and nonlinear finite element methods were used to simulate the welding and loading process and related experiments were conducted to provide a comparison. We further extended the investigation of the buckling behaviour of girders to the combined opening plate frame and investigated the buckling behaviour using experiments. This research on the buckling behaviour of combined opening girders and plate frames could provide a reference for the optimal design of these members in actual ship structures.

Experimental and Numerical Studies on the Ultimate Bending Strength of Welded Plated Grillage with Combined Openings

Plated grillage with combined openings was susceptible to complex failure behaviors as the main load-bearing structure of the superstructure on passenger ships subjected to deck loads. Additionally, the deformation and stresses generated during the welding of the plated grillage complicated the prediction of its failure behavior. In this case, a new partitioned inherent strain method and nonlinear finite element method were used to simulate the welding and loading process, and experiments were designed and carried out to make comparisons, unveiling the influence regulations between the failure behavior of the structure and the loading condition, the initial welding state. This research on the failure mode analysis of plated grillages could provide references for the optimization of the structural form of plated grillages and the cargo loading scheme on the deck of a real ship.

Analysis of Ice-shedding induced flashover accident on a transmission line in mountainous terrain

Transmission lines are essential infrastructure for modern society. Large amplitude vibration of conductors due to ice shedding may cause electrical faults, resulting from insufficient clearance among different phases and phase conductors and ground wires. A flashover fault on a 500kV transmission line located in a mountainous area, which is caused by ice shedding, is analysed in this paper. The approximate reason and history of the flashover accident were restored by the nonlinear finite element method with the help of ANSYS software. The key physical parameters such as conductor ice thickness and amount of ice shedding at the moment of the accident were analysed. The study in this paper helps to gain a deeper understanding of the ice-shedding–induced disasters of transmission lines and provides important reference for the design of transmission structures.