Finite Element Analysis Solutions Research Articles

A chronological catalog of methods and solutions in the Space–Time Computational Flow Analysis: I. Finite element analysis

AbstractThe Space–Time Computational Flow Analysis (STCFA) started in 1990 with the inception of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method. The DSD/SST was introduced as a moving-mesh method for flows with moving boundaries and interfaces, which is a wide class of problems that includes fluid–particle interactions, fluid–structure interactions (FSI), and free-surface and multi-fluid flows. The first 3D computations were reported in 1992. The original DSD/SST method is now called “ST-SUPS,” reflecting its stabilization components. As the STCFA evolved, advanced mesh moving methods, FSI coupling methods, and problem-class-specific methods were introduced to increase its scope and the ST Variational Multiscale was introduced to upgrade its stabilization components to the VMS. Complementary general-purpose methods developed in the evolution of the STCFA include the ST Isogeometric Analysis (ST-IGA) and the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods. The ST-IGA delivers superior accuracy through IGA basis functions not only in space but also in time. The ST-SI enables high-fidelity moving-mesh computations even over meshes made of patches with nonmatching meshes at the interfaces between those patches. The ST-TC enables high-fidelity moving-mesh computations even in the presence of topology changes in the fluid mechanics domain, such as an actual contact between moving solid surfaces. The STCFA brought first-of-its-kind solutions in many classes of problems, ranging from fluid–particle interactions in particle-laden flows to FSI in parachute aerodynamics, flapping-wing aerodynamics of an actual locust to ventricle-valve-aorta flow analysis to car and tire aerodynamics with near-actual geometries, road contact, and tire deformation. With the success we see in so many classes of problems, we can conclude that the STCFA has reached a level of remarkable sophistication, scope, and practical value. We present a chronological catalog of the methods and solutions in the STCFA. In Part I of this two-part article, we focus on the methods and solutions in finite element analysis.

Numerical Prediction and Experimental Verification of Inherent Defect Influences on Frequencies of Adhesively Bonded Joint

The vibrational response of adhesively bonded joints with and without defects in the adhesive layer is predicted by simulation for the different overlapping lengths in this work. The eigenvalue extraction method (Block Lanczo’s) is employed within the finite element analysis (FEA) framework to predict the modal values of adhesively bonded joints. The numerical analysis has adopted a solid 20-node quadratic brick elements with reduced integration (C3D20R) to predict the realistic values. The predicted eigenvalues of adhesively bonded joints using an FEA solution are compared with published data and verified the accuracy of the FEA model through experimentation considering defective and non-defective joints. Additionally, simulation solutions are predicted for different overlap lengths (i.e., 25, 30, 35 and 40 mm) by changing the boundary conditions, adhesive bond thickness aspect ratio, adherend thickness ratio, defect position, and defect aspect ratio. The geometries of the adhesive and adherend significantly affect vibration responses through the dampening effect and structural weight, enhancing the stiffness. Defect position and geometry have negligible impact on the natural frequency values for all overlapping lengths except when located around the overlapping edges.

Ultra‐fast finite element analysis of coreless axial flux permanent magnet synchronous machines

AbstractLarge‐scale design optimisation techniques enable the design of high‐performance electric machines. Electromagnetic 3D finite element analysis (FEA) is typically employed in optimisation studies for accurate analysis of axial flux permanent magnet (AFPM) machines, which require extensive computational resources. To reduce the computational burden, a FEA‐based mathematical method relying on the geometric and magnetic symmetry of coreless AFPM machines is proposed to estimate the machine performance indicators using the least number of FEA solutions, thereby significantly lowering the running time. This method is generally applicable to AFPM machines with low saturation effects and cogging torque as exemplified for a printed circuit board (PCB) stator coreless AFPM machine. To further reduce the computation time, a systematically simplified equivalent 3D FEA model for planar PCB coils integrated with this machine is also proposed. The practical implementation of the introduced method is elaborated based on an example optimisation study, and an analytical method for fast design scaling is also discussed. The results of the proposed approach are compared with detailed transient FEA results, and a prototype 26‐pole PCB stator coreless AFPM machine was also used to validate the results experimentally.

CRUD deposition induced multi-physics effects analysis in PWR

In PWR, the deposition of corrosion products from the steam generator leads to the formation of Chalk River Unidentified Deposits (CRUD) on the surface of fuel rods. CRUD deposition can cause issues such as CRUD induced localized corrosion, axial power anomaly and deterioration of cladding heat transfer. A new multi-physics program named CIFF (CRUD Induced eFFects analysis) is developed to analyze the effects caused by CRUD deposits. CIFF is a 1.5D model and can be used to simulate the variations in surface temperature, cladding corrosion and fuel deformation caused by CRUD deposition. A three-node CRUD deposition model is developed based on mass transfer theory and chemical equilibrium. The calculations of heat transfer, mechanical deformation, oxide layer growth, CRUD deposition and fission gas behavior are fully coupled based on finite element analysis and numerical solution technology. Axisymmetric element is used to solve the deformation of fuel rod under thermal expansion, gas pressure, creep and radiation swelling. The performance of CIFF is validated through IFA-513, ANO-2, Oconee and PCCL cases. The DBN-1 case is used to explore the influence of CRUD. The results indicate that CRUD deposition and CRUD induced local corrosion deteriorate the heat transfer of cladding, resulting in a three-stage increase of cladding temperature and accelerated growth of the oxide layer. CRUD deposition also leads to a relative increase in the gap pressure exceeding the coolant pressure by 8.4 %, a relative increase in the fuel rod strain by 10 % and a relative decrease in the gap size by 11 %, which indirectly leads a premature pellet-cladding mechanical interaction by 90 days.

Generation of Tow Paths on a Curved Shell in Three-Dimensional Space for Fiber Steering

A multimesh framework to optimize two-dimensional, flat-steered fiber laminates for a given loading condition is extended to include complex curved laminates in three-dimensional (3D) space. The optimal fiber angle distribution solution is used by a tow path planner to generate (steered) tow paths in curved laminates in 3D space. The framework utilizes two meshes in the optimization step: i) a coarse quadrilateral element-based manufacturing mesh (MM) used to discretize the fiber angle distributions with nodal values; and ii) a fine triangular element-based stress mesh used in the finite-element-based stress analysis to ensure a converged solution. Lagrangian interpolation functions are used to determine the fiber angles at the centroid of each finite element analysis (FEA) mesh element within a given MM. The number of design variables is minimized without jeopardizing the accuracy of the FEA solution. A third mesh, the tessellation mesh, is used to project the generated tow paths onto the curved laminates in 3D space accurately. This paper presents all the steps needed to go from optimized fiber angles to tow paths. In conclusion, a methodology is proposed and implemented to optimize variable-stiffness laminates on complex curved structures.

Analyzing the continuity of the mild solution in finite element analysis of semilinear stochastic subdiffusion problems

<abstract><p>This paper aimed to further introduce the finite element analysis of non-smooth data for semilinear stochastic subdiffusion problems driven by fractionally integrated additive noise. The mild solution of this stochastic model consisted of three different Mittag-Leffler functions. We analyzed the smoothness of the solution and utilized complex integration to approximate the error of the solution operator under non-smooth data. Consequently, optimal convergence estimates were obtained, and we also obtained the continuity conditions of the mild solution. Finally, the influence of the fractional parameters $ \alpha $ and $ \gamma $ on the convergence rates were accurately demonstrated through numerical examples.</p></abstract>

Experimental and numerical analysis of different vertical connections of precast shear walls with special regard towards deformability

AbstractNowadays precast concrete multi‐story dual system structures require Finite Element Method structural analysis. The stiffness of the vertical connections between wall panels influences the internal forces distribution. European standard EN 1992‐1‐1 recommends verification of strength and deformability of precast connections to be assisted by testing. Six different connection layouts were tested under pure shear with a special attention towards deformability. All connections showed close to/equivalent monolithic initial stiffness. Depending on the connection layout, the post‐cracking stiffness is reduced. The equation for shear resistance of interfaces between concrete cast at different times according to EN 1992‐1‐1 can lead to significant estimation errors due to its weak physical meaning (in disagreement with experimental observed failure mechanisms). A non‐linear finite element analysis solution strategy is validated by experimental results that shows how stochastic parameters can inflict large variation in terms of strength and stiffness.

Data-driven hyperelasticity, Part II: A canonical framework for anisotropic soft biological tissues

In this work, we present a novel anisotropic data-driven hyperelasticity framework for the constitutive modeling of soft biological tissues that allows direct incorporation of experimental data into the constitutive model, without requirement of a predetermined mathematical formula for the strain–energy density function. The data-driven framework is constructed through a dispersion-type anisotropic formulation based on a generalized structure tensor in the sense of Holzapfel et al. (2015) that take into account in- and out of plane dispersion. The partial derivatives of the strain energy density functions are replaced with appropriate B-spline interpolations where the control points are calibrated against experimental data obtained from uniaxial tension, triaxial shear, and (equi)biaxial tension deformations. The model calibration phase incorporates the normalization condition and the polyconvexity condition is enforced through the control points of the B-splines in order to ensure a stable constitutive response that allows unique solution in finite element analysis. The predictive capabilities of the proposed model are shown against linea alba, rectus sheath, aneurysmal abdominal aorta, and myocardium tissues. On the numerical side, the stress and moduli expressions of the model are derived and implemented into the finite element method. The performance of the model is demonstrated through representative boundary value problems.

Finite Element Analysis (FEA) of a Premaxillary Device: A New Type of Subperiosteal Implant to Treat Severe Atrophy of the Maxilla.

Extreme atrophy of the maxilla still poses challenges for clinicians. Some of the techniques used to address this issue can be complex, risky, expensive, and time consuming, often requiring skilled surgeons. While many commonly used techniques have achieved very high success rates, complications may arise in certain cases. In this context, the premaxillary device (PD) technique offers a simpler approach to reconstruct severely atrophic maxillae, aiming to avoid more complicated and risky surgical procedures. Finite element analysis (FEA) enables the evaluation of different aspects of dental implant biomechanics. Our results demonstrated that using a PD allows for an optimal distribution of stresses on the basal bone, avoiding tension peaks that can lead to bone resorption or implant failure. ANSYS® was used to perform localized finite element analysis (FEA), enabling a more precise examination of the peri-crestal area and the PD through an accurate mesh element reconstruction, which facilitated the mathematical solution of FEA. The most favorable biomechanical behavior was observed for materials such as titanium alloys, which helped to reduce stress levels on bone, implants, screws, and abutments. Additionally, stress values remained within the limits of basal bone and titanium alloy strengths. In conclusion, from a biomechanical point of view, PDs appear to be viable alternatives for rehabilitating severe atrophic maxillae.

Theoretical solutions for 2D mode-I crack-tip stress fields in power-law plastic materials based on the stress factor derived from the developed median-energy–density equivalence method

This study presents the energy density equivalence equation, demonstrating that the strain energy density of an arbitrary representative volume element (RVE) under a complex stress state equals to that under a uniaxial stress state when volume change is neglected. Based on the developed median-energy–density equivalence method, the analytical solution for equivalent stress of the RVE at the energy density equivalence point in power-law plastic materials is derived in a new method and the concept of stress factor is proposed. Additionally, novel special functions are introduced to accurately describe the angular distributions of stresses in this study. By combining the stress factor, integral theoretical solutions for mode-I crack tip stress fields in power-law plastic materials under finite plane conditions are proposed. Finally, parameterized studies are conducted on bending and tension specimens under plane-strain and plane-stress conditions. The results of stress distributions and contour lines predicted by the integral theoretical solutions are compared with the finite element analysis and HRR solutions for five mode-I plane specimens, providing verification of the solutions’ applicability.

Experimental investigation of doubly-symmetric built-up I–girders subjected to high moment gradient

Recent analytical studies have shown that the AISC 360-16 Specification overpredicts the flexural resistance of certain built-up steel I-girders. The largest overpredictions were observed in I‑girders subjected to a high moment gradient having unstiffened webs with a large web slenderness ratio. The objectives of the current research are to provide experimental validation of these strength overpredictions, validate the accuracy of full-nonlinear shell finite element analysis (FEA) solutions, and further investigate the behavior of these susceptible built-up I-girders. To accomplish the objectives, six largescale experimental tests targeted web slenderness ratios ranging from 77 to 192 and a moment gradient factor, Cb, of 1.74 (single curvature (SC) bending) and 2.31 (reverse curvature (RC) bending), calculated using common design equations. Additionally, full nonlinear shell FEA simulations were conducted to evaluate the correlation with the experiments. The tests showed flexural strengths smaller than the predicted resistances from AISC 360, with the predicted resistances ranging from 4% to 16% unconservative for SC members and 9% to 32% unconservative for RC members. Furthermore, the FEA simulation strengths were similar to the strengths measured in the experiments. The results indicate that there are two main phenomena leading to the overpredictions by AISC 360: web distortion effects exacerbated by web shear and the direct scaling of the uniform LTB strength curve by Cb up to the plateau resistance, overestimating the strength gains from moment gradient due to insufficient accounting for the onset of yielding.

Multi-stage thermoelectric coolers for cooling wearables

• Multi-stage TECs are shown to perform better than single-stage TECs for use against skin. • Multi-stage TECs can achieve lower temperature, while maintaining power requirement. • Results are validated using experiment, finite element analysis and analytical solutions. Over the last decade, there has been significant interest in the use of thermoelectric coolers (TECs) in cooling wearables. While there has been notable work on optimizing single-stage TECs for use against human skin, much less attention is given to multi-stage TECs. In this contribution, analytical computations are performed to show that multi-stage TECs can achieve lower cold side temperatures while maintaining the coefficient of performance as compared to single-stage TECs when used against human skin. The findings are confirmed with detailed FEA analysis and experiments. The results therefore imply that multi-stage TECs have the potential of providing more cooling sensation to the human skin, while maintaining the power required per unit cooling power provided. This paper provides a detailed parametric studies on how key design parameters of the TECs (number of stages, current ratio, fill factor, aspect ratio and leg area) affect the performance of the multi-stage TECs. A guideline on the optimal design parameters is provided to guide the design of multi-stage TECs for use in cooling wearables.

A Fast 3-D Winding Inductance Estimation Method for Air-Cored Resonant Induction Machines

The air-cored resonant induction machine removes the magnetic core, so the fields produced by the windings are truly 3-D in nature. The end-windings normally regarded as a nonactive and leakage source in conventional iron-cored machines now become an active part and contribute to the torque production. Therefore, the electromagnetic modeling can no longer be reduced to a 2-D analysis, and the 3-D inductance calculation becomes a key problem. The 3-D finite element analysis (FEA) can solve the 3-D magnetic field, but, first, the validity of its solution depends on the precision in geometry modeling. In particular, representing the end-winding region avoiding conductor clashing can be very complicated. Second, 3-D FEA solutions are computationally slow, and therefore inefficient as an “internal routine” of an optimization procedure. This article proposes a fast analytic 3-D winding inductance estimation method for air-cored resonant induction machines. The approach breaks down the real coils into straight conductors and represents them by single filaments located at their centers, then uses closed-form expressions derived from Neumann integrals to calculate the coil self and coil-to-coil mutual inductances, which are then collected into winding phase self and mutual inductances. All the independent coil-pair contributions are isolated, so as to eliminate redundant calculations. Good accuracy of the calculated results is confirmed by validation against both 3-D FEA and experimental results, including winding inductance breakdown and overall machine tested performance.

Analytical solution for quick decision of tied–arch bridge parameters at early-design stage based on Hellinger–Reissner variational method

The tied-arch bridge is the combined system of an arch, a beam and suspenders. There have been a few methods applied in the design stage of the analysis of tied-arch bridges including finite element analysis and approximate solutions. The approximate solution based on the Ritz method has been very popular in the analysis of hybrid bridges during the early design stages for its high efficiency. The disadvantage of the Ritz method is that it only directly determines the deformation values while the forces in the structural members should be decided through the obtained deformation values, which highly decreases the accuracy of the force values. Based on the Ritz method, the Hellinger–Reissner (H–R) variational principle is introduced here to improve the approximate solution. It analyzes both the deformation and forces of the tie-arch bridge directly. This is the first time of the application of this method in the analysis of the tied-arch bridges. The advantage of the H–R variational principle is that it provides the forces and deformation values independently and directly which highly enhances the accuracy of the results. For verification, the material properties of the tied-arch bridge of the second-stage project of Line No.1 in Wuhan railway transportation are applied here. And the results from H–R variational method show good agreement with finite element analysis. Hence, the presented method could be a relatively good alternative to use in the early-design stage of the tied-arch bridges.

Quantification of the resistance modeling uncertainty of 19 alternative 2D nonlinear finite element approaches benchmarked against 101 experiments on reinforced concrete beams

AbstractNineteen 2D nonlinear finite element analysis (NLFEA) solution strategies were benchmarked against a wide variety of 101 experiments on reinforced concrete beams failing in bending, flexural shear, or shear compression. The relatively high number of solution strategies was motivated by the conviction that choices for the constitutive models, the finite element kinematics and equilibrium settings will interact, and must therefore be tested in conjunction. Modeling uncertainty distribution parameters are presented for the 19 solution strategies, using all beams, and using beams with and without stirrups separately. The resulting statistics are discussed against the correctness of the simulated failure modes and failure loads, revealing that rotating crack models perform well for the relatively ductile failures in beams with stirrups, while fixed crack models perform better for the more brittle failures in beams without stirrups. The tailored solution strategies that predict failure modes correctly, imply a log‐normal distribution of the modeling uncertainty with relatively low coefficients of variation. The outlook is that these estimates of the statistical properties of the modeling uncertainties could serve as a basis within safety formats.

Fatigue crack growth in metallic components: Numerical modelling and analytical solution

The paper presents innovative approaches for the simulation of fatigue crack growth (FCG) in metallic compact tension (CT) specimens using finite element (FE) analysis and analytical solution. FE analysis is performed in ABAQUS using the extended finite element method (XFEM) coupled with the direct cyclic low-cycle fatigue (LCF) approach. Novel methods are developed for the computation of the numerical crack growth by processing the analysis outputs. The numerical modelling is validated by considering past experimental data. The analytical solution for the fatigue life evaluation is formally reviewed, and novel fatigue damage descriptors are defined. The influence of the main sample/testing features on numerical and analytical fatigue life is extensively assessed by a parametric study. The discrepancy between the numerical and analytical estimations of the fatigue life of the components is investigated and correlated to the features of the testing/modelling. A statistical-based correction factor is finally proposed in order to enhance the analytical solution.

Evaluation of ductile fracture in welded tubes with tensile, hardness, flaring tests

A continuum damage model (CDM) based on local hardness in welds is developed to predict fracture of welded tubes. A regression function of hardness distribution in the welds is proposed to establish hardness continuously through hardness mapping method in the finite element model. A constitutive model of the weld zone is determined by the rule of mixture, which estimates the flow stress of the welds from the hardness ratio. Coefficients of the flow stress model in the welds are validated by comparing finite element analysis (FEA) solution and experimental load - displacement data of tensile specimens. Softening after necking is considered by Lemaitre CDM. A damage parameter is newly given as a function of hardness ratio varying with angular position. Coefficients of damage parameter are obtained by the inverse FEA of tensile and flaring tests. The proposed method finely predicts the ductile fracture of welded tubes by considering local plastic properties and damage evolution.

Numerical study of the square cup stamping process: a stochastic analysis

The industrial demand for products with better quality and lower production costs have encouraged the widespread application of the finite element analysis (FEA) in the development and optimization of sheet metal forming processes. To ensure that the FEA solutions are reliable and robust it is important to take into account the uncertainties that inevitably arise in a real industrial environment. In this context, a numerical study on the influence of the material and process uncertainty in the stamping results of a square cup is presented. In this analysis, it is assumed uncertainty in the elasticity properties, hardening law parameters, anisotropy coefficients, blank thickness, friction coefficient and in the blank holder force. The effect of the uncertainty in these input parameters is evaluated in the punch force, equivalent plastic strain, thickness and cup geometry. Firstly, quasi-Monte Carlo method was used to evaluate the variability in the simulation outputs, considering the uncertainty of the input parameters. This analysis shows that the geometry is the output most sensitive to the uncertainty of the input parameters. Afterwards, a variance-based sensitivity analysis was carried out to identify the input parameters that most influence the output variability. It was concluded that the hardening law parameters and the anisotropy coefficients have the most influence in the stamping results variability of a square cup.

Swage autofrettage FEA incorporating a user function to model actual Bauschinger effect

An ‘exemplar’ Finite Element Analysis (FEA) solution for swage autofrettage (SA) incorporating Bauschinger effect (BE) for a real steel (A723) is presented. This is derived via a new user programmable function (UPF). Datum geometries for tube and swage were selected in order to permit comparison with previous work.The FEA UPF solution methodology was developed and validated to demonstrate that a 3D analysis will fully replicate a uniaxial tension-compression test on a real material (A723 steel) exhibiting BE, designated UPF(U).A refined formulation designated UPF(S) was then used to obtain a solution for the full 3D axisymmetric SA process. It is first applied to an idealized (BKIN) material; to permit direct comparison with two existing BKIN SA solutions. Finally the UPF(S) formulation is used to obtain a solution for full 3D SA applied to a standard steel (A723) whilst incorporating BE during unloading.The near-bore BE SA solution is compared to an equivalent BE hydraulic autofrettage (HA) solution. Near-bore SA hoop residual stresses are shown to be more compressive and deeper than HA. Conversely SA produces tensile axial stresses, whereas HA generates compression. Finally, it is shown that a subsequent material removal process, applied to the SA tube, may significantly improve near-bore stress profiles.

Numerical analysis of large deflection of the cantilever beam subjected to a force pointing at a fixed point

In many cable-driven compliant mechanisms, the need for controlled motion in the flexible structure often demands the actuation cables to pass through a fixed point (e.g. a cable routing channel in a segment disk or a fixed pulley) to constrain the force angle on the cable. This condition can be modeled as the large deflection problem of a cantilever beam with two parameters, namely the distal slope and the force angle, which is more complex than the regular one-parameter deflection problem of cantilever beams. In order to solve this mechanics problem, a numerical method based on variable transformation and heuristic cuckoo search (CS) algorithm is presented to analyze the large deflection shape of a beam subjected to a tip force pointing at a fixed point. Firstly, a two-parameter second-order differential equation governing the cantilever beam with large deflection and tip force constrained to a particular point is established. Secondly, a new variable is defined to replace the two parameters based on the variable transformation, allowing the governing equation to be simplified to a one-parameter second-order differential equation. Thirdly, this mathematical problem is written as a one-parameter optimization problem that can be solved by the CS algorithm. The proposed approach is then verified by commercial finite element analysis solution. Comprehensive simulation results and analysis are presented under different combinations of critical parameters, leading to potentially more accurate model-based design for compliant structures under the studied force constraint.