Classical Finite Element Analysis Research Articles

Tailoring the extension-bending-twisting coupling in composite laminates using carbon nanotube hybridization

The existence of extension-bend-twist coupling of deformations in composites is a complex problem. Ability to tailor the coupling response as per the requirement is desirable to harness the high strength-to-weight ratio of composites in many structural applications. Here we report a feasible design strategy to tune the extent of deformation coupling in composite laminates. To this end, carbon nanotube (CNT) grafted lamina is incorporated in the lay-up of conventional composites. Classical laminate theory (CLT) and finite element analysis show that the coupling extent of extension-twist, extension-bending and extension- bending-twist can be suitably designed by varying the number, location and distribution of CNT grafted lamina in a laminate configuration. Theoretical and computational results reveal maximum extension-twist coupling when a single CNT grafted lamina is placed closer to the mid-plane in a 16 ply antisymmetric laminate. Symmetrical placement of CNT grafted lamina avoids the extension-bend coupling. Finite element analysis shows that the lateral bending of composite cantilever beam under combined axial and bending loads can be designed by suitably choosing the configuration of the modified laminate. These findings will significantly contribute in designing structural composites for advanced applications.

Composite Plate Optimization: Integrating Analysis Techniques and Design Iterations for Enhanced Mechanical Performance

This essay delves into the comprehensive analysis of composite plate behavior under various loading conditions, focusing on uniaxial loading and the effects of layup design on safety factors. Through a comparative study between Classical Laminate Plate Theory (CLPT) calculations and Finite Element (FE) analysis, discrepancies in stress and strain predictions are identified, attributing them to assumptions made in each method. Furthermore, the essay explores failure prediction using Tsai-Wu criteria and Maximum Stress theory, determining the safety of laminates under different loading scenarios. Additionally, Finite Element analysis is employed to assess the impact of layup design variations on safety factors, leading to recommendations for optimized designs. The limitations of FE models compared to physical tests are discussed, along with alternative approaches such as advanced manufacturing techniques and novel fiber architectures to further enhance safety factors and alter failure modes.

Multicell Thin-walled Method for Solid Multimaterial Beams

In this paper we developed the Multicell Thin-walled Method for Solid Multimaterial Beams, which combines structural idealization used in aircraft components, thin-walled beam theory and homogenization techniques from composite materials applied to discrete models, to obtain the cross-section stress fields of solid beams made of multiple orthotropic and isotropic materials. This method idealizes a solid multimaterial cross-section as a multicell thin-walled section to accurately obtain complex stress fields while significantly reducing the solution time, as well as the computational cost, when compared to classical 3D finite element analyses. This method was implemented in a computer program and three examples were analyzed to validate results with the finite element method. Both methods show almost identical results in regions not affected by local disturbances.

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.

Isogeometric-based mapping modeling and buckling analysis of stiffened panels

Modeling and analysis of stiffened panels are two key technologies in the design of aerospace thin-walled structures. For the stiffened panels with complex geometry, classical finite element analysis (FEA) and conventional isogeometric analysis (IGA) based on explicit geometry usually require time-consuming and labor-intensive geometric processing, and additional coupling matrices to be ready for analysis. In this study, a new method for modeling and buckling analysis of stiffened panels is proposed, which provides a more efficient and simpler way. During the modeling process, the stiffeners are treated as curves on surfaces, which is not explicitly defined using the control-point-based representation of curves, but implicitly defined using parameter curves in the parametric space of the surface. Mapping modeling provides more accurate geometric description and transfer the complex modeling problems (three-dimensional space) of stiffeners on free-form surface into simple modeling problems in the regular parametric space (two-dimensional space). During the buckling analysis process, a new mapped stiffener element based on mapping modeling is proposed, which can model the section of the eccentric stiffener without changing the geometry. The precise normal information of the Non-Uniform Rational B-Splines (NURBS) surface can ensure that the stiffeners are perpendicular to the skin. In addition, the coupling of the stiffener and the skin is automatic, without any additional coupling matrix. This buckling analysis framework realizes the complete integration of modeling and analysis. Furthermore, for the stiffened panels with cutouts, the trimmed surface analysis (TSA) method is extended to be used for the numerical integration of the trimmed stiffeners, which means that no additional geometric process is required. Finally, four numerical examples of different types of stiffened panels are constructed, involving metal, trimmed surface, classical grid-stiffener, free-form surface, variable-stiffness composites, and curvilinear grid-stiffener. Several numerical examples of static and buckling analysis of stiffened panels with high fidelity demonstrate the effectiveness of the proposed framework.

Local Refinement in Isogeometric Analysis of Detailed Tire Models

AbstractIsogeometric Analysis (IGA) and its unconventional basis functions bring undeniable benefits to the numerical analysis of solid bodies with a complex geometrical shape such as pneumatic tires. This approach erases barriers between the stage of design and the computational environment. Preservation of the exact geometrical description of the real body and the nature of functions at hand allow for higher precision of simulations for different physical phenomena.This contribution is aimed to show further developments in the framework for rolling simulation of tires using IGA. The large support of Non‐Uniform Rational B‐Splines (NURBS) provides continuous variable fields along the contact patch. Truncated hierarchical B‐splines (THB‐splines), implemented into an in‐house Finite Element Analysis (FEA) code, improve the modeling of tires by locally refining the contact zone. Global extraction operators bring the hierarchical concept as close as possible to a standard FEA code structure, flattening the set of nested layers of mesh into a sequence of single‐level elements. Furthermore, an algorithm for the computation of the accelerations at material points based on the relative velocities is adapted. The outlook of this development is the intention to use this algorithm in possible combination with analytical models for the in‐situ estimation of forces and to capture certain mechanical behavior which often are not tracked in experiments or hard and too costly to reproduce.The sampling procedure within the hierarchically nested basis is elaborated with attention to required adjustments for the nested parent‐child layered analytical meshes created via the introduction of the selective global multilevel extraction operators. Numerical simulations of rolling tires at steady‐state using IGA are presented. The evaluation and comparison of the developed framework are done using uniformly refined and locally refined models in IGA as well as classical FEA models.

Multi-Attribute Machine Learning Model for Electrical Motors Performance Prediction

Designing an electrical motor is a complex process that needs to deal with the non-linearity phenomena caused by the saturation of the iron at high magnetic field strength, the multi-physical nature of the investigated system and with requirements that may come into conflict. This paper proposes to use geometric parametric models to evaluate the multi-physical performances of electrical machines and build a machine learning model that is able to predict multi-physical characteristics of electrical machines from input geometrical parameters. The focus of this work is to accurately estimate the electromagnetic characteristics, motor losses and stator natural frequencies, using the developed machine learning model, at the early-design stage of the electrical motor, when the information about the housing is not available and to include the model in optimisation loops, to speed-up the computational time. Three individual machine learning models are built for each physics analysed, a model for the torque and back electromotive force harmonic orders, one model for motor losses and another one for natural frequencies of the mode-shapes. The necessary data is obtained by varying the geometrical parameters of 2D electromagnetic and 3D structural motor parametric models. The accuracy of different machine learning regression algorithms are compared to obtain the best model for each physics involved. Ultimately, the developed multi-attribute model is integrated in an optimisation routine, to compare the computational time with the classical finite element analysis (FEA) optimisation approach.

Influence of mesoscale friction interface geometry on the nonlinear dynamic response of large assembled structures

Friction interfaces are unavoidable components of large engineering assemblies since they enable complex designs, ensure alignment, and enable the transfer of mechanical loads between the components. Unfortunately, they are also a major source of nonlinearities and uncertainty in the static and dynamic response of the assembly, due to the complex frictional physics occurring at the interface. One major contributor to the nonlinear dynamic behavior of the interface is the mesoscale geometry of a friction interface. Currently, the effects of the interface geometry on the nonlinear dynamic response is often ignored in the analysis due to the high computational cost of discretizing the interface to such fine levels for classical finite element analysis. In this paper, the influence of mesoscale frictional interface geometries on the nonlinear dynamic response is investigated through an efficient multi-scale modeling framework based on the boundary element method. A highly integrated refined contact analysis, static analysis, and nonlinear modal analysis approach are presented to solve a multi-scale problem where mesoscale frictional interfaces are embedded into the macroscale finite element model. The efficiency of the framework is demonstrated and validated against an existing dovetail dogbone test rig. Finally, the effects of different mesoscale interface geometries such as surface waviness and edge radius, are numerically investigated, further highlighting the influence of mesoscale interface geometries on the nonlinear dynamics of jointed structures and opening a new research direction for the design of friction interfaces in friction involved mechanical systems.

Almost-[formula omitted] splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems

Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from Computer-Aided Design models, which is in general a non-trivial and time-consuming task. In this article, we present a novel spline construction, that enables model reconstruction as well as simulation of high-order PDEs on the reconstructed models. The proposed almost-C1splines are biquadratic splines on fully unstructured quadrilateral meshes (without restrictions on placements or number of extraordinary vertices). They are C1 smooth at all regular and extraordinary vertices. Moreover, they are C1 smooth across all edges between regular vertices and C0 smooth across all edges that are adjacent to an extraordinary vertex. The splines thus form H2-nonconforming analysis-suitable discretization spaces. This is the lowest-degree unstructured spline construction that can be used to solve fourth-order problems. The associated spline basis is non-singular and has several B-spline-like properties (e.g., partition of unity, non-negativity, local support), the almost-C1 splines are described in an explicit Bézier-extraction-based framework that can be easily implemented. Numerical tests suggest that the basis is well-conditioned and exhibits optimal approximation behaviour.

Harnessing fiber induced anisotropy in design and fabrication of soft actuator with simultaneous bending and twisting actuations

Most of the soft dielectric elastomer actuators (DEAs) are able to provide either planar or twisting deformations only. Development of a bio-inspired actuator with functionalities similar to the mammalian tongue or octopus tentacles is highly desirable for soft robotics applications. Here, design and fabrication of a multi-layered soft DEA capable of simultaneous bending and twisting actuation is reported through a unified computational and experimental approach. An anisotropic layer is introduced to couple the bending and twisting deformation in the conventional DEA. The fiber spacing and fiber orientation in the anisotropic layer is optimized with classical laminate theory (CLT) and finite element (FE) analysis. A multi-layered DEA with bending-twisting actuation is experimentally fabricated as a ‘proof of concept’. The computational and experimental results suggest that bend-twist coupling in multi-layered DEA can be suitably designed by varying the fiber spacing and orientation in the anisotropic layer. The twisting actuation of DEA enhances at the expense of bending deformation with an increase in the fiber angle. Finally, it is shown that a single anisotropic layer having 2 mm fiber spacing and 45° fiber orientation induces sufficiently large bending and twisting actuations in DEA. The findings of the present study will be a significant step ahead to develop bio-mimicking anisotropic actuators and grippers for soft robotics applications.

Advanced corrective training strategy for surrogating complex hysteretic behavior

Despite the advances in modeling component behavior, high-fidelity finite element simulation remains challenging and is limited by the computational efficiency of large-scale models. A predictive simulation framework based on deep learning is proposed to provide accurate and efficient hysteretic models for structural analysis. The proposed framework is based on the Transformer network architecture and enriched by an advanced corrective training (ACT) strategy. The ACT strategy discovers and activates the corrective ability of the model and significantly improves the prediction accuracy for complex load cases. In addition, a compound prediction strategy is proposed. By incorporating an integrated assessment of absolute and relative losses, the proposed framework provides a sophisticated prediction capability that is profoundly beneficial to global simulation. Its superior accuracy and efficiency are illustrated through case studies on both a refined steel brace model and the Bouc-Wen hysteretic model. Finally, a data-physics coupling driven structural simulation method is developed. The efficiency of the proposed method is two to three orders of magnitude higher than the classical finite element analysis, while the accuracy is almost identical.

3D simulation of complex fractures with a simple mesh

AbstractRock masses are 3D in nature. The contained complex fracture networks pose great difficulty to its computer‐aided design (CAD) modeling and bring meshing burdens to classic finite element analysis (FEA). Considering the efficiency of digital images capturing complex geometries, as an extension of the previous 2D work, the 3D implementation of the image‐based simulation is carried out in this work. Continuous‐discontinuous deformations of complex rock masses are simulated in 3D with a simple structured mesh based on the numerical manifold method (NMM). Characteristics of the developed voxel crack model and its differences with discrete and smeared crack models are summarized. Based on this voxel crack model, the generating algorithm of 3D physical patches to construct the continuous‐discontinuous trial function is introduced in detail. In the developed method, the three spatial resolutions, respectively of the image model, integration voxels, and mathematical elements, are independent. These resolutions can be chosen freely by trading off the accuracy need and the computational expenses. Numerical examples investigate the accuracy and convergence of this method. Its 3D simulation capability of complex rock masses is demonstrated by calculating the continuous‐discontinuous deformation of El Capitan rock located in the Yosemite National Park with assumed complex fracture networks.

Finite Element Modeling of Diffusion in Fractured Porous Media by Using Hierarchical Material Properties

AbstractFractured porous media challenge modeling approaches due to high computational costs and excessive mesh refinement imposed by the extreme scale variability of fractures and the heterogeneity of the surrounding porous rock. To overcome such difficulties, we utilize the hierarchical finite element method (Hi‐FEM) that has been developed previously to simulate the electrical potential distribution in complex geologic environments. The method employs the hierarchical basis functions in classical finite element analysis to enable representation of material properties on each dimensional component of a given 3D unstructured finite element, thereby inherently allowing for interactions at the boundary between fracture and a host rock. In this study, we extend its application to transient fluid flow and heat conduction in the Laplace domain. Time‐domain flow solutions are obtained by numerical inverse Laplace transform. We evaluate the accuracy of the method using different flow models and demonstrate its robustness for large‐scale, rock mass models featuring complex fracture networks. Moreover, for the computation of nodal Darcian velocity fields in fractured porous media where the fractures are represented as 2D features, a new approach that employs the Yeh's Galerkin model for both volume and facet elements is proposed. Results show that Hi‐FEM can produce accurate flow solutions for fractured porous media without any need of coupling or transfer mechanism while still being computationally economical and numerically robust, even for large‐scale simulations.

3D stability analyses of Skjeggestad landslide

In 2015, a sudden landslide caused the failure of one of the pillars supporting the southern lanes of the Skjeggestad Bridge near Mofjellbekken on Expressway E18. The transportation corridor was closed to traffic for 17 months. To investigate the cause of the failure, an assessment of slope stability is necessary. Usually, limit equilibrium analysis of the middle two-dimensional (2D) cross-section is modelled. The Skjeggestad landslide geometry was not close to a 2D case, and three-dimensional (3D) modelling is more appropriate to analyse the slope. The paper calculates the stability of the slope that failed and compares the results of 3D finite element analyses with classical limit equilibrium and 2D finite element analyses. The analyses were run in the Novapoint GeoSuite Stability software. The soil parameters, including their statistical values, were obtained with the GeoSuite Soil Data Interpretation (SDI) module. A companion paper at this conference analyses the pillar neighbouring the landslide with the module GeoSuite Piles. The paper illustrates the importance of 3D effects in a stability analysis. The results of the analyses also illustrate the need to include appropriate consideration of any strain-softening and spatial variation of soil properties.

An isogeometric framework for the modeling of curvilinear anisotropic media

The advent of multi-material additive manufacturing and automated composite manufacturing has enabled the design of structures featuring complex curvilinear anisotropy. To take advantage of the new design space, efficient computational approaches are quintessential. In this study, we explored a new NURBS-based Isogeometric Analysis (IGA) framework for the simulation of curvilinear fiber composites and we compared it to standard Finite Element Analysis (FEA).We showed that, thanks to the exact geometric representation and the enriched continuity between elements, NURBS-based IGA outperforms classical FEA in terms of computational efficiency, run-time, and estimation quality of field variables for the same number of degrees-of-freedom. To further demonstrate the use of the IGA framework, we performed optimization studies aimed at identifying the fiber paths minimizing stress concentration and Tsai-Wu failure index. The model showed that curvilinear anisotropy can be effectively harnessed to reduce the stress concentration of up to 82% compared to unidirectional composites without affecting the overall plate stiffness significantly.

Stochastic finite element method based on point estimate and Karhunen–Loéve expansion

The present study proposes a new stochastic finite element method. The Karhunen–Loeve expansion is utilized to discretize the stochastic field, while the point estimate method is applied for calculating the random response of the structure. Two illustrative examples, including finite element models with one-dimensional and two-dimensional stochastic fields, are investigated to demonstrate the accuracy and efficiency of the proposed method. Furthermore, two classical finite element analysis methods are used to validate the results. It is proved that the proposed method can model both the one-dimensional and the two-dimensional stochastic finite element problems accurately and efficiently.

The High Frequency Flexural Ultrasonic Transducer for Transmitting and Receiving Ultrasound in Air

Flexural ultrasonic transducers are robust and low cost sensors that are typically used in industry for distance ranging, proximity sensing and flow measurement. The operating frequencies of currently available commercial flexural ultrasonic transducers are usually below 50 kHz. Higher operating frequencies would be particularly beneficial for measurement accuracy and detection sensitivity. In this paper, design principles of High Frequency Flexural Ultrasonic Transducers (HiFFUTs), guided by the classical plate theory and finite element analysis, are reported. The results show that the diameter of the piezoelectric disc element attached to the flexing plate of the HiFFUT has a significant influence on the transducer's resonant frequency, and that an optimal diameter for a HiFFUT transmitter alone is different from that for a pitch-catch ultrasonic system consisting of both a HiFFUT transmitter and a receiver. By adopting an optimal piezoelectric diameter, the HiFFUT pitch-catch system can produce an ultrasonic signal amplitude greater than that of a non-optimised system by an order of magnitude. The performance of a prototype HiFFUT is characterised through electrical impedance analysis, laser Doppler vibrometry, and pressure-field microphone measurement, before the performance of two new HiFFUTs in a pitch-catch configuration is compared with that of commercial transducers. The prototype HiFFUT can operate efficiently at a frequency of 102.1 kHz as either a transmitter or a receiver, with comparable output amplitude, wider bandwidth, and higher directivity than commercially available transducers of similar construction.

Mechanical properties of natural fibre-reinforced hybrid composites

A study on the hybrid composites reinforced by two types of short natural fibres is presented. The material properties of short natural fibre composites were obtained by Mori–Tanaka method. Three-point bend test was simulated by the classical beam theory and finite element analysis. Both asymmetric and sandwich hybrid composites were studied. From the results, the following conclusions can be drawn: 1. A general rule is that one lamina of higher stiffness should be placed on the tensile face of a hybrid composite in order to obtain improved flexural strength. 2. For the sandwich-type hybrid composites, the higher stiffness material should be placed in the core, and the lower stiffness material should be the skin.

A posteriori error estimation for isogeometric analysis using the concept of Constitutive Relation Error

The paper deals with the Isogeometric Analysis (IGA) technology, which has received much attention over the last decade due to its increased flexibility, accuracy, and robustness in many engineering simulations compared to classical Finite Element Analysis (FEA). In this context, we present a verification method, based on duality and the concept of Constitutive Relation Error (CRE), that enables to derive fully computable a posteriori error estimates on the numerical solution provided by IGA. Such estimates, which can be used for a wide class of structural mechanics models, thus constitute effective and practical tools to quantitatively control the numerical accuracy and drive adaptive algorithms. The focus is here on the construction of so-called admissible flux fields which is a key ingredient of the CRE concept, and which was until now almost exclusively addressed in the FEA framework alone. We show that this construction can be performed in a similar way for FEA and IGA, provided some technical issues (due to the use of B-Spline/NURBS basis functions instead of Lagrange polynomials) are carefully addressed. We also use the CRE concept along with adjoint techniques and local enrichments in order to derive accurate goal-oriented error estimates. Two- and three-dimensional numerical experiments are presented, for thermal, linear elasticity and nonlinear damage problems, to illustrate the capabilities and versatility of the proposed approach.

Elimination of Scallop-Induced Stress Fluctuation on Through-Silicon-Vias (TSVs) by Employing Polyimide Liner

3-D modeling of through-silicon-via (TSV) with sidewall scallops, combined with an element birth and death technique, is explored in finite-element analysis (FEA) in this paper to evaluate and improve the thermo-mechanical reliability. Compared with the classic FEA, the proposed modeling and simulation method takes into account the process sequence and, hence, can accurately characterize the stress distribution and fluctuation phenomenon of TSVs, which agrees pretty well with X-ray experimental data. In order to solve the stress fluctuation problem, the process-friendly polyimide dielectric liner is employed to replace the SiO2 liner, which smoothens the sidewalls, reduces the average stress values, and eliminates the local stress fluctuation. The average stress on TSVs with a polyimide liner along the silicon-liner interface and copper-barrier interface are both lower than TSVs with an SiO2 liner and the fluctuation magnitude is also dramatically decreased, which demonstrates that the TSV with a polyimide liner has higher reliability and lower risks in interfacial delamination. Furthermore, the keep-out zone size is also decreased by using a polyimide liner, which is beneficial to realize high-density 3-D integration.