Iterative Finite Element Analysis Research Articles

Stress–strain curve estimation from load–depth curve of spherical indentation test based on finite element analysis and optimization

A stress–strain curve is one of the most important indicators of material properties for characterizing constitutive behavior. It can be directly obtained from a conventional uniaxial tensile test or load–displacement curve using an instrumented indentation test (IIT). An IIT uses formulations of the effective indentation strain and stress or the iterative finite element analysis (FEA) of the indentation process using a constitutive model, such as a power-law constitutive model. In this study, an iterative FEA is used to obtain the engineering stress–strain curve. However, it focused on considering the realistic plastic flow of specific materials without idealizing the power-law constitutive model. A concept for stress–strain estimation using a master stress–strain curve for specific materials was proposed, and its usefulness was validated via FEA and optimization techniques. In the future, this methodology can be extended to deep learning technology to address the issue of time consumption in iterative optimization methods.

Effects of different intrusion patterns during anterior teeth retraction using clear aligners in extraction cases: an iterative finite element analysis.

Overtreatment design of clear aligner treatment (CAT) in extraction cases is currently primarily based on the clinical experience of orthodontists and is not supported by robust evidence on the underlying biomechanics. This study aimed to investigate the biomechanical effects of overtreatment strategies involving different maxillary anterior teeth intrusion patterns during anterior teeth retraction by CAT in extraction cases. A finite element model of the maxillary dentition with the first premolar extracted was constructed. A loading method of clear aligners (CAs) based on the initial state field was proposed. The iterative method was used to simulate the long-term orthodontic tooth movement under the mechanical load exerted by the CAs. Three groups of CAs were utilized for anterior teeth retraction (G0: control group; G1: incisors intrusion group; G2: anterior teeth intrusion group). Tooth displacement and occlusal plane rotation tendency were analyzed. In G0, CAT caused lingual tipping and extrusion of the incisors, distal tipping and extrusion of the canines, mesial tipping, and intrusion of the posterior teeth. In G1, the incisors showed minimal extrusion, whereas the canines showed increased extrusion and distal tipping tendency. G2 showed the smallest degree of posterior occlusal plane angle rotation, while the inclination tendency of the canines and second premolars decreased. 1. In CAT, tooth displacement tendency may change with increased wear time. 2. During anterior teeth retraction, the incisor intrusion pattern can provide effective vertical control for the lateral incisors but has little effect on the central incisors. Anterior teeth intrusion patterns can alleviate the inclination of canines and second premolars, resulting in partial relief of the roller-coaster effect.

Experimental characterization and finite element investigation of SiO2 nanoparticles reinforced dental resin composite

In this study, a commercial dental resin was reinforced by SiO2 nanoparticles (NPs) with different concentrations to enhance its mechanical functionality. The material characterization and finite element analysis (FEA) have been performed to evaluate the mechanical properties. Wedge indentation and 3-point bending tests were conducted to assess the mechanical behavior of the prepared nanocomposites. The results revealed that the optimal content of NPs was achieved at 1% SiO2, resulting in a 35% increase in the indentation reaction force. Therefore, the sample containing 1% SiO2 NPs was considered for further tests. The morphology of selected sample was examined using field emission scanning electron microscopy (FE-SEM), revealing the homogeneous dispersion of SiO2 NPs with minimal agglomeration. X-ray diffraction (XRD) was employed to investigate the crystalline structure of the selected sample, indicating no change in the dental resin state upon adding SiO2 NPs. In the second part of the study, a novel approach called iterative FEA, supported by the experiment wedge indentation test, was used to determine the mechanical properties of the 1% SiO2-dental resin. Subsequently, the accurately determined material properties were assigned to a dental crown model to virtually investigate its behavior under oblique loading. The virtual test results demonstrated that most microcracks initiated from the top of the crown and extended through its thickness.

Evaluating the tensile properties of high-strength stainless steels using small punch testing.

Accurately measuring the mechanical properties of high-strength stainless steels is of great significance for ensuring structural safety, predicting long-term performance and optimizing design. However, the standardized tensile test specimens used to obtain strength properties must be fabricated from bulk materials from an in-service structure or component, result in the loss of structural integrity or a reduction in remaining service life. Small punch tests require only miniscule material samples and are widely used to estimate in-service component material characteristics. This study performed small punch tests on three high-strength stainless steels-X17CrNi15-2, 15-5PH, and PH13-8Mo-to obtain the correlations between the small punch tests and the uniaxial tensile test results for each material. The estimated yield stresses obtained from the small punch tests were distributed within a factor of 1.5 on both sides of the unity line when compared with those obtained from the uniaxial tensile tests; the ultimate strength values estimated from the small punch tests correlated quite well with those obtained from the uniaxial tensile tests. An iterative finite element analysis was subsequently established to simulate the small punch tests and thereby obtain the coefficients for a Ludwik power law correlation representing the true stress-strain properties. The finite element predicted force-deflection curves agreed well with the small punch test results, which were also compared with the predictions obtained from empirical equations proposed in previous studies. Finally, the fracture mechanisms of the small punch test specimens were characterized through scanning electron microscopy, indicating that the dimple fracture mechanism dominated the failure mode. The results of this study are expected to inform the application of small punch test to evaluate in-service high-strength stainless steel materials.

A Problem-Independent Machine Learning (PIML) enhanced substructure-based approach for large-scale structural analysis and topology optimization of linear elastic structures

Structural analysis for structures composed of highly heterogeneous materials which often involves the solution of large-scale linear algebraic equations is very time-consuming even within the linear elastic regime. Furthermore, the tremendous computational cost of iterative large-scale finite element analysis also prevents the widespread use of topology optimization as a powerful design tool especially when the desired design resolution is very high. In order to break the bottleneck hindering the efficient solutions of large-scale structural analysis and design optimization problems, in the present article, a general machine learning (ML) enhanced substructure-based framework is proposed. The essential idea is resorting to the classical substructure-based finite element analysis approach and establishing an implicit mapping between the parameters characterizing the material distribution within a substructure and the corresponding condensed stiffness matrix/numerical shape functions through offline trained deep neural networks. In contrast to most of the existing ML enhanced approaches, the proposed framework is truly independent of the forms of structural geometry, boundary condition and external load, and can be applied to solve various boundary value problems governing by the same type of partial differential equation once the offline training is completed. Armed with modern artificial intelligence techniques, the proposed approach in some sense revives the classical substructure approach in finite element analysis. Compared with the traditional paradigm, it can achieve 104–105 times solution efficiency for tested large-scale examples with satisfactory accuracy. The effectiveness of the approach was also validated for the non-adjoint topology optimization problems, i.e., 3D compliant mechanism design. Finally, to demonstrate the proposed approach’s capability in dealing with extremely large-scale three-dimensional problems, a three-dimensional topology optimization problem with about 109 design variables and 3×109 degrees of freedom (Dofs) is solved on a laptop without resorting to any parallel computing techniques.

Design optimization of an optical fiber air-backed concentric hybrid mandrel hydrophone by an iterative design and finite element analysis for submarine passive array applications

The optical fiber hydrophones are well suited for the submarine passive sonar applications taking into consideration of their high sensitivity, fully electrically passive characteristics etc. and are definitely an equivalent replacement for Lead Zirconate and Lead Titanate ceramic hydrophones. In this paper, finite element analysis of several sets of cases of concentric hybrid material-based air-backed OF mandrel hydrophones are analysed and tuned to their geometric dimensions and their mechanical properties for design optimization, suitable for submarine sonar applications. A finite element method is adopted for analysis, strain and sensitivity calculations using ANSYS software. An inverse dependency of the sensitivity and the natural frequency were observed and was overcome by an innovative method where a hybrid inner hollow tube, combining both Aluminium and high-density polyethylene materials, were used, improving both the stiffness property and compliance of the mandrel and thereby improving both the natural frequency and pressure sensitivity. The harmonic analysis was carried out at 5 KHz acoustic pressure, by adding hydrostatic pressures of 2 MPa, 3 MPa and 4 MPa and obtained satisfying results. The acoustic directivity of this OF mandrel hydrophone was estimated, plotted and an omni directional pattern was obtained.

Accumulated biomechanical effects of mandibular molar mesialization using clear aligners with auxiliary devices: an iterative finite element analysis

BackgroundThe biomechanics generated by the clear aligner (CA) material changes continuously during orthodontic tooth movement, but this factor remains unknown during the computer-aid design process and the predictability of molars movement is not as expected. Therefore, the purpose of this study was to propose an iterative finite element method to simulate the long-term biomechanical effects of mandibular molar mesialization (MM) in CA therapy under dual-mechanical systems.MethodsThree groups including CA alone, CA with a button, and CA with a modified lever arm (MLA) were created. Material properties of CA were obtained by in vitro mechanical experiments. MM was conducted by the rebound force exerted by CA material and the mesial elastic force (2N, 30° to the occlusal plane) applied to the auxiliary devices. Stress intensity and distribution on periodontal ligament (PDL), attachment, button and MLA, and displacement of the second molar (M2) during the iterations were recorded.ResultsThere was a significant difference between the initial and cumulative long-term displacement. Specifically, compared to the beginning, the maximum stress of PDL decreased by 90% on average in the intermediate and final steps. The aligner was the main mechanical system at first, and then, the additional system exerted by the button and MLA dominated gradually. The stress of attachments and auxiliary devices is mainly concentrated on their interfaces with the tooth. Additionally, MLA provided a distal tipping and extrusive moment, which was the only group that manifested a total mesial displacement of the root.ConclusionsThe innovatively designed MLA was more effective in reducing undesigned mesial tipping and rotation of M2 than the traditional button and CA alone, which provided a therapeutic method for MM. The proposed iterative method simulated tooth movement by considering the mechanical characteristic of CA and its long-term mechanical force changes, which will facilitate better movement prediction and minimize the failure rate.

Identification of Hyperelastic Material Parameters of Elastomers by Reverse Engineering Approach.

Simulating the mechanical behavior of rubbers is widely performed with hyperelastic material models by determining their parameters. Traditionally, several loading modes, namely uniaxial tensile, planar equibiaxial, and volumetric, are considered to identify hyperelastic material models. This procedure is mainly used to determine hyperelastic material parameters accurately. On the contrary, using reverse engineering approaches, iterative finite element analyses, artificial neural networks, and virtual field methods to identify hyperelastic material parameters can provide accurate results that require no coupon material testing. In the current study, hyperelastic material parameters of selected rubbers (neoprene, silicone, and natural rubbers) were determined using an artificial neural network (ANN) model. Finite element analyses of O-ring tension and O-ring compression were simulated to create a data set to train the ANN model. Then, the ANN model was employed to identify the hyperelastic material parameters of the selected rubbers. Our study demonstrated that hyperelastic material parameters of any rubbers could be obtained directly from component experimental data without performing coupon tests.

Iterative Finite Element Analysis of Concrete-Filled Steel Tube Columns Subjected to Axial Compression

Since laboratory tests are usually costly, simulating methods using computers are always under the spotlight. This study performed a finite element analysis (FEA) using iterative solutions for simulating circular and square concrete-filled steel tube (CFST) columns infilled with high-strength concrete and reinforced with a cross-shaped plate (comprising two plates along the columns that divide the hollow columns into four equal sections) with and without opening. For this reason and for validation purposes, the columns had length of 900 mm, width/diameter of 150 mm and wall thickness of 3 mm. In this study, unlike in some other studies, the cross-shaped plate was assumed to be fixed at the top and the bottom of a column, and the columns were subjected to axial compression pointed in the center. The outcomes revealed that the cross-shaped plate could improve the axial strength of both circular and square CFST columns; however, the structural performance of the square CFST columns changed: local outward buckling was observed after inserting the cross-shaped plate. By inserting an opening on the cross-shaped plate, the bearing capacity of the circular CFST columns was further improved, while the square CFST columns experienced a decline in their ultimate bearing capacity compared with the corresponding models without the opening. The lateral deflection also improved for the circular CFST columns by adding the reinforcement. However, for the square CFST columns, while it initially improved, increasing the thickness of the cross-shaped plate inversely influenced the lateral deflection of the square CFST columns. The results were also compared with some available codes, and a good agreement was achieved with those outcomes.

A High-Consolidation Electron Beam-Curing Process for Manufacturing Three-Dimensional Advanced Thermoset Composites

Abstract This paper describes the application of a new manufacturing process for low-cost and rapid consolidation and curing of advanced thermoset composites that avoids the use of expensive prepreg, autoclaving, and thermally induced curing. The process, called VIPE, uses a novel tooling design that combines vacuum infusion (VI) of a dry preform with resin, a rigidly backed pressure focusing layer (P) made of an elastomer to consolidate the wet preform with uniform pressure, and high-energy electron beam curing (E). A VIPE tool is engineered and fabricated to manufacture 3D laminate bicycle seats composed of woven carbon fiber textile and an electron beam-curable epoxy acrylate. Details of the tooling design discussed include computational fluid dynamics (CFD) simulation of the vacuum infusion, iterative structural finite element analysis (FEA) to synthesize the pressure focusing layer (PFL), structural FEA to design the top mold made of a composite sandwich structure for electron beam transparency, and Monte Carlo electron absorption simulations to specify the e-beam energy level. Ten parts are fabricated using the matched tool (bottom aluminum mold covered with silicone layer and top mold with carbon/epoxy skins separated by foam core) after the dry textile preform contained within is infused with resin, the tool halves are clamped under load, and a 3.0 MeV e-beam machine bombards the tool for less than 1 min. Part thickness, part stiffness, surface roughness, and fiber and void volume fractions measurements show that aerospace quality parts with low cycle times are achievable, although there is high variability due to the small number of replicates and need for process optimization.

A Taguchi based iterative wing structural design for a low speed, hybrid UAV

An iterative structural design process for the conventional, composite wing of a low speed, hybrid Unmanned Aerial Vehicle (UAV) is presented in this paper. The relevant design goals are light weight, strength and stiffness derived from the customer specifications, conceptual design and STANAG-4671 airworthiness standards. To achieve the design goals, a modified Taguchi model was applied in conducting iterative Finite Element Analysis of the loads and stresses on the wing model, using ABAQUS CAE. In this analysis, the pitch of the rib and thicknesses of the spar and skin were applied as control factors in three levels, leading to an L9 orthogonal array. Mass, maximum deflection and Tsai-Hill failure index of the wing structure were measured as responses. The result shows that varying the skin thickness had the most impact on the wing mass, failure index and maximum deflection. The design goal of wing mass- less than 2.5kg, deflection of 10% and Tsai-Hill failure index value- less than 1 were achieved after 9 iterations.

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 1—Theory

Abstract Statically admissible stress distributions are necessary to evaluate lower bound limit loads. Over the last three decades, several methods have been postulated to obtain these distributions using iterative elastic finite element analyses. Some of the pioneering techniques are the reduced modulus, r-node, elastic compensation, and linear matching methods, to mention a few. A new method, called the bounded elastic moduli multiplier technique (BEMMT), is proposed and the theoretical underpinnings thereof are explained in this paper. BEMMT demonstrates greater robustness, more generality, and better stress distributions, consistently leading to lower-bound limit loads that are closer to elastoplastic finite element analysis estimates. It also leads us to question the validity of the prevailing power law-based stationary stress distributions. Part 2 of this paper offers several case studies to validate this claim.

Linking Time-Domain Vibration Behaviors to Spatial-Domain Propagating Waves in a Leaf-like Gradient-Index Phononic Crystal Lens

It is known that a propagating wave at a certain spatial point can be decomposed into plane waves propagating at different angles. In this work, by designing a gradient index phononic crystal lens (GRIN PCL) with transverse-continuous leaf-like unit cells, we theoretically and experimentally show that the spatial-domain propagating waves in finite periodic structures can be linked to their time-domain vibration behaviors. The full-field instantaneous focusing behaviors of Lamb waves in the proposed leaf-like GRIN PCL give an example of the wave-vibration linkage in finite periodic structures while allowing a certain complexity. The conclusion in this paper can help one skip iterative time-consuming finite element analysis (e.g., time-stepping solutions) to avoid possible numerical instabilities occurred in calculating transient wave field on practical finite metamaterials or phononic crystals having unit cells with complicated configurations.

Matrix Microcracking Effect on the Structural Response of a Thermal Protection System

The effect of microcracking in the phenolic matrix of a three-dimensional woven thermal protection system (TPS) and resulting material stiffness reduction was studied via a comparison of finite element results from linear and iterative linear analyses. A dual-layer continuous dry weave material with a low-density phenolic resin matrix has been developed for use in extreme environments. Because of high stresses in the through-the-thickness direction, microcracks may form in the matrix. The matrix does not have structural load transfer requirements, and testing has shown that microcracked phenolic resin satisfies thermal requirements. Microcracks in the matrix would result in a reduction of stiffness, which could alter the structural performance. A study was conducted to determine if reduction in material stiffness would change the load paths or structural margins. A linear finite element analysis that did not account for microcracking and an iterative linear finite element analysis that accounted for propagation microcracks were compared. Four subcases were analyzed with results indicating that the assumed propagation strength for the microcracking is the critical parameter for determining the extent of microcracking. Phenolic microcracking does not appear to have an adverse effect on the structural response and is not a critical failure for the modeled TPS.

Mechanical properties characterization of fiber reinforced composites by nonlinear constitutive parameter optimization in short beam shear specimens

This work presents a novel approach to quantify the nonlinear shear stress-strain behavior of carbon fiber reinforced polymer composites without finite element stress calculation. Full-field noncontact deformation measurements using Digital Image Correlation are used to measure surface strains in Short Beam Shear IM7/8552 specimens. The presented spline-based optimization technique solves the inverse problem of generating both axial and shear stress-strain curves without ad hoc assumptions on the material model. Accuracy of the analysis method was verified by finite element analysis (FEA). This method improves on available closed-form and iterative FEA based solutions due to flexibility and accuracy without the computational expense.

Numerical estimation of the influence of joint stiffness on free vibrations of frame structures via the scattering of waves at elastic joints

In the structural design of mechanical products, natural frequencies must be controlled to reduce noise and vibration. In particular, the stiffness of the joints which assemble the structural components affects the natural frequencies. Therefore, it is important to predict the influence of joint stiffness on natural frequencies. Generally, these effects are determined by iterative finite element analyses of assembled structural models. Because this results in high computational costs, the sensitivity of natural frequencies to joint stiffness should be determined by a different approach to make the structural design process more efficient. Therefore, this paper proposes the use of reflection and transmission coefficients of elastic joints to predict the dependency of natural frequencies on joint stiffness. First, we formulate the reflection and transmission coefficients of joint stiffness, and then organize the coefficients using a ray tracing method. These formulations enable us to discuss the mechanisms which determine the natural frequency of a structure based on a wave approach using the phase-closure principle. Therefore, by applying the phase-closure principle to the frame structure, we investigate the formation of bending modes, which suggests that the effects of joint stiffness on natural frequencies correspond to the dependence of the reflection and transmission coefficients on joint stiffness. Therefore, these coefficients are useful indicators for estimating the influence of joint stiffness.

Prediction of surface variation field in face milling via finite element model updating with considering force-deformation coupling

Effective prediction of surface variation is of great helpf for developing and controlling machining process to maintain surface quality during face milling of large-scale component with discontinuous surface. However, the simulation ranges of machined surface error in traditional finite element analyses are far less than those needed in characterization of large-scale face milling with multi-tooth cutter in order to maintain efficiency. To address this issue, this paper attempts to develop a numerical methodology to estimate the field data of machined surface error based on iterative finite element analysis integrated with cutting trajectory reconfiguration. Finite element model updating (FEMU) method is applied to analysis the cutting deformation in each cutting instant while considering both the cutting force variation in face milling and the locally geometrical differences of component. A flexible model is established to predict the residual cutting material in each cutting instant with considering the coupling effect between instantaneous cutting force and cutting deformation. And then a sub-iteration scheme is proposed to calculate the equilibrium deflection and the real residual material of flexible cutting system with a modified Newton-Raphson method. The proposed simulation methodology can be generally applied for predicting surface variation field in face milling of large-scale component with multi-holed surface, especially for flexible component.

3D topology optimization for cost and time minimization in additive manufacturing

As the frontier of modern-day engineering challenges pushes forward, the integration of multiple strategies to reduce manufacturing cost and increase component performance has engineers turning to tools such as topology optimization (TO) and additive manufacturing (AM). Recent focus on these topics has led to the bridging of the gap between these two tools and the making of their integration in the conventional design cycle as seamless as possible. This paper expands upon existing mathematical constructs by providing an algorithm to minimize the cost and time associated with additively manufactured parts within a three-dimensional topology optimization framework. The formulation has been constructed in such a manner to accommodate large-scale topology optimization problems, including a filtering scheme requiring minimal storage of additional mesh information and an iterative finite element analysis solver. A rigorous trade-off analysis is conducted to determine the optimal contribution of additive manufacturing factors to minimize build time. A perimeter method-inspired approach for optimization of the surface area is explored, suggesting benefits for AM-specific process mechanics. Multiple academic example problems included in this work illustrate the applicability of this approach to three-dimensional geometries; physical models of these example problems created via fused filament fabrication serve to validate the numerical results obtained herein.

A Coupled Model for the Prediction of Surface Variation in Face Milling Large-Scale Workpiece With Complex Geometry

Face milling commonly generates surface quality of variation, is especially severe for milling of large-scale components with complex surface geometry such as cylinder block, engine head, and valve body. Thus surface variation serves as an important indicator both for machining parameter selection and components' service performance such as sealing, energy consumption, and emission. An efficient and comprehensive numerical model is highly desired for the prediction of surface variation of entire surface. This study proposes a coupled numerical simulation method, updating finite element (FE) model iteratively based on integration of data from abaqus and matlab, to predict surface variation induced by face milling of large-scale components with complex surfaces. Using the coupled model, three-dimensional (3D) variation of large-scale surface can be successfully simulated by considering face milling process including dynamic milling force, spiral curve of milling trajectory, and intermittently rotating contact characteristics. Surface variation is finally represented with point cloud from iterative FE analysis and verified by face milling experiment. Comparison between measured and predicted results shows that the new prediction method can simulate surface variation of complex components well. Based on the verified model, a set of analyses are conducted to evaluate the effects of local stiffness nonhomogenization and milling force variation on machined surface variation. It demonstrates that surface variation with surface peaks and concaves is strongly correlated with local stiffness nonhomogenization especially in feed direction. And thus the coupled prediction method provides a theoretical and efficient way to study surface variation induced by face milling of large-scale complex components.

Solid riveting process optimization for the reduction of key point distortions caused by locating

PurposeDeterminative locating and riveting distortions are highly coupled at assembly locale. Recent methods only take every tested or assumed locating errors at the mating surface into the process planning for the assemblies in a simple form. However, the growth of part number makes it nearly infeasible to take every locating error at every mating surface into the dimensional precision calculation. This paper aims to provide a solid riveting process planning for the reduction of practical locating-related distortions.Design/methodology/approachLarge-scale metrology firstly measures the determinative coordinates for the locating-deviated key points. Iterative finite element (FE) analyses then calculate the riveting-related key point distortions from every rivet upsetting directions (UDs) and assembly sequence. These key points on the actual assembly contour and relative FE nodes yield two virtual planes. Virtual plane manipulation adds the riveting distortions into the locating-deviated coordinates. Finally, optimal algorithm integrates the iterative FE analyses with virtual plane manipulation.FindingsCase studies validate that the virtual plane manipulation coincides with the test well, and the proposed method has good compensation of practical locating distortion.Research limitations/implicationsThe optimized rivet UDs may be set in a chaotic distribution, which may complicate the abundant riveting operations and the assembly appearance. Therefore, the use of automatic riveting systems can overcome the operational complexity, and the industrial design of rivet UD distribution will improve the assembly appearance.Practical implicationsThe optimized UDs and assembly sequence are for assembly workers or automatic riveting systems.Originality/valueThe proposed method is the first to reduce the determinative locating distortion by a novel and efficient solid riveting process planning in detail, and the solid riveting process designed is conservative and accurate for practice.