Conventional Finite Element Method Research Articles

Variational damage model: A new paradigm for fractures

The computational modeling of fracture in solids using damage mechanics faces challenges with complex crack topology. This can be addressed by using a variational framework to reformulate the damage mechanics. In this paper, we propose several mathematically elegant variational damage models (VDMs) for fracture mechanics without explicitly using damage variables. Based on the energy density ϕ, the fracture energy density is formulated as ϕ^=ϕ(1+ℓϕ/Gc) and the damage variable is expressed as s = ϕ/(ϕ + Gc/ℓ), which satisfy ϕ^∣ϕ→∞=Gc/ℓ and s∣ϕ→∞ = 1 as ϕ approaches infinity. These limits demonstrate that the new energy density converges to the Griffith energy release rate at full-damage state. The VDM profoundly modified the energy functional, implicitly incorporating the damage field. As a generalization of previous model, we propose a family of VDMs of varying orders. Additionally, we develop a multi-damage model to account for different types of energy densities, such as elastic thin plate and gradient elasticity. Using this functional, it is straightforward to deduce the governing equation for automatically evolving fractures. These formulations can be employed in conventional finite element method or other numerical methods with minimal modifications. Compared to the phase field method with the same mesh density, a sharper crack interface can be achieved. We demonstrate the capabilities of the proposed variational damage formulations using representative numerical examples.

An educational computational program for nonlinear geometric analysis of truss structures using the Finite Element Method based on Positions

This study describes an educational computational program for the analysis of truss structures using the Finite Element Method based on Positions (FEMP). FEMP adopts the nodal positions of discretized elements as degrees of freedom, in contrast to the displacements used in conventional Finite Element Method (FEM). This approach enables FEMP to straightforwardly and naturally incorporate geometric nonlinearity into its positional formulation, simplifying the nonlinear geometric analysis of structures. The developed educational program provides a range of functionalities, allowing users to conduct both static and dynamic analyses of truss structures.

High electromechanical coupling factor Lamb wave resonator

Lamb wave resonators (LWRs) based on lithium niobate on insulator (LNOI) substrates operating in an A1 mode at frequencies above 5 GHz typically exhibit high electromechanical coupling coefficients (K2) ranging from 20% to 30%. This makes them promising candidates to replace current bulk acoustic wave technology in next-generation broadband RF filters. However, the K2 of conventional LWRs still struggles to meet application requirements for bandwidths exceeding 1 GHz, such as WiFi-6E. This paper presents an analytical optimization approach for rapid and comprehensive scanning of the full 3D Euler space to find the maximum effective K2 of LWR devices. Such a full scan is difficult to achieve by the conventional time-consuming finite element method (FEM). The K2 results for a selected subset of Euler angles obtained through this analytical approach align with FEM simulation results. The optimized results show that LWRs on LNOI can achieve the highest K2 of 59.92% at Euler angles of (0, −151°, −60°), providing bandwidths exceeding 1 GHz at 5 GHz. To validate this optimization approach, LWRs with various orientations were fabricated on both 41° YX-cut and Z-cut LNOI wafers, with measured K2 values at different Euler angles agreeing well with both analytical and FEM results. The proposed K2 optimization method serves as a valuable guideline for selecting substrate cuts and device orientations in the design of ultra-broadband filters for next-generation telecommunications.

A Special Corner Element for Solving Heat Conduction Problems

A hybrid Trefftz finite element method is proposed for solving heat conduction problems in a domain with concave or convex angles. In this method, two temperature fields are independently assumed, one of which is the intra-element field defined inside the element and the other is the frame field defined on the boundary. The corner effects embed in the truncated complete solutions which are used to construct the internal interpolation function for approximating the intra-element field. It is able to accurately analyze the problems with particular corners. The key characteristics lie in the finite element formulation which is evaluated along the element boundary. Compared with the conventional FEM, the corner element does not lose any accuracy by using a small number of elements. Numerical examples demonstrate that the proposed method exhibits low sensitivity to mesh distortion. Compared with ABAQUS, the proposed method also exhibits higher accuracy and a faster convergence rate.

Implementation and Application of Cell-Based S-FEM Based on the Object-Oriented Programming Framework

The object-oriented programming is widely used in different fields of finite element analysis (FEA). The commonly used object-oriented codes were almost written by C++. Due to the inability to automatically manage memory and the lack of gigantic standard library and a third-party library for C++, building matrix classes are needed and a strong programming ability for program developers is also necessary. The conventional FEM method still has many disadvantages such as poor accuracy, hard stiffness matrix, mesh dependence and lack of upper bound solution. The smoothed FEM (S-FEM) method proposed by Liu et al. can efficiently overcome these disadvantages and is therefore widely used in FEA. In this work, the elastic-plastic CS-FEM method is extended and implemented using Python programming based on the framework proposed [H. Li and Y. Xiao, Implementation and numerical simulation on object-oriented elastic-plastic finite element method based on Python, J. Syst. Simul. 36(5) (2024) 1107–1117] The resulting object-oriented elastic-plastic CS-FEM framework is then applied to FEA of elastic-plastic mechanics problems. The correctness of the resulting framework and the high computational accuracy and good mesh adaptability of CS-FEM models have been verified by comparing the corresponding results with an analytical solution or ABAQUS results. The object-oriented elastic-plastic CS-FEM framework provides a more efficient and adaptable approach to FEA, and can also overcome many limitations of the conventional FEM method and C++ programming. The use of Python and the CS-FEM method offers improved computational accuracy, mesh adaptability and development efficiency, and this will make it a valuable tool for solving practical problems in mechanics and engineering.

Experimental and numerical study on the torsional behavior of rectangular hollow reinforced concrete columns strengthened By CFRP

This paper reported a series of hysteretic torsion experiment to investigate the torsional behavior of rectangular hollow reinforced concrete (RHRC) column strengthened by fiber reinforced polymer (FRP). Six RHRC column specimens with different number of longitudinal reinforcements, spacing of stirrup and strengthening method using FRP were designed. One was not strengthened, four were strengthened with CFRP, one was strengthened with CFRP and GFRP. The experimental results showed that the primary failure modes of specimens were the spalling of surface concrete with the detachment of FRP. In details, under the hysteretic torsional load, the interaction between adhesive and concrete caused the intersecting diagonal cracks in the internal concrete. Compared with the hysteretic curve of specimen without FRP strengthening, FRP strengthening can significantly improve the initial stiffness by 50 % and peak torsional strength by 70 %. For RHRC column without strengthening, the fullness was poor because of the weak torsional energy dissipation. The FRP strengthening can also enhance the torsional energy dissipation and seismic behavior of RHRC column. To predict the complex torsional behavior of RHRC column strengthened by FRP, a finite element (FE) model and a constitutive model were developed. The FE model considered potential cracks in concrete and FRP–concrete interface based on the application of the cohesive zone model (CZM), whereas the constitutive model accounted for interface damage and plasticity. The results of the performed simulations indicated that the proposed model can effectively represent the hysteretic mechanical behavior of columns under torsional load, which cannot be achieved using conventional FE methods.

A novel Bayesian updating finite element model using enhanced unscented Kalman filter for time-dependent estimation of rockfill dam structure deformation

Due to the time-dependent effect of rockfill dams, the conventional time-invariant finite element method (FEM) can hardly meet practical engineering requirements. This paper proposes an updating Bayesian FEM method for accurate long-term deformation analysis. A combined FEM model is introduced accounting for both instantaneous and creep behaviors. The FEM model is then updated using a Bayesian algorithm, unscented Kalman filter (UKF). The UKF calibrates the prior FEM predictions by incorporating real-time measurement data, thus iteratively reducing discrepancies between model predictions and actual observations. To further enhance the algorithm accuracy, a power-law-based fading memory factor is proposed to mitigate measurement noise in standard UKF. For parameter identification, a slice approach of the high-dimensional covariance confidence ellipsoid is developed. The methodology is validated in Qingyuan rockfill dam, in Guangdong province, China. Results show that the updated FEM is more consistent with the actual monitoring data. The fading memory improves standard UKF performance with a lower relative root-mean-square error (RRMSE). Additionally, the slice method reveals that a specific three-parameter configuration behaves better than the others. The proposed approach can also be extended to other fields including slope and tunneling.

Elastodynamic analysis of rotating solids by novel nodal position finite element method

This study develops a novel 8-node isoparametric hexahedral element using the Nodal Position Finite Element Method (NPFEM) for elastodynamic analysis of rotating solids. The element also incorporates the flexural modes directly into its element shape function to alleviate the shear locking when modeling the bending deformation of solids. Unlike conventional displacement-based finite element methods, which require the decoupling of elastic deformation from rigid-body motions, the NPFEM eliminates this process by directly representing strain and kinetic energies through nodal position coordinates, which avoids potential approximation errors in the decoupling process. To validate the accuracy and efficacy of this new NPFEM solid element, numerical simulations of a beam under static and dynamic loads are conducted and benchmarked against the theoretical solutions. Then, dynamic analysis of a rotating blade demonstrates that the NPFEM element can directly account for the centrifugal stiffening effect and superharmonic resonance of rotating blades without resorting to conventional methods. The successful implementation of this NPFEM element in complex simulations highlights its potential to provide significant advancements in computational mechanics.

An optimal penalty method for the joint stiffening in beam models of additively manufactured lattice structures

Additive manufacturing is revolutionizing structural design, with lattice structures becoming increasingly prominent due to their superior mechanical properties. However, simulating these structures quickly and accurately using the finite element method (FEM) remains challenging. Recent research has highlighted beam element simulation within FEM as a more efficient alternative to traditional solid FE simulations, achieving similar accuracy with reduced computational resources. However, a significant challenge is managing the lack of rigidity at nodes and the prevalence of low aspect ratio beams. While various methodologies have been proposed to address these issues, there is still a gap in the comprehensive evaluation of their limitations. An optimal node penalization methodology is required to expand the limited range of accurately represented lattice behavior. A preliminary study investigates lattice geometries through comparative analysis of solid and beam FE simulations. Built on this, we developed a methodology suitable to linear, dynamics and nonlinear beam FE simulations, contributing to enhanced computational speed and accuracy. Several lattice structures were printed using material jetting and quasi-static compressive tests were conducted to validate the methodology’s accuracy. The numerical results reveal a good accuracy between the proposed beam FE methodology and the experimental data, offering a better alternative to conventional FEM for energy absorption in terms of computing time.

Variational damage model: A novel consistent approach to fracture

The computational modeling of fractures in solids using damage mechanics faces challenge when dealing with complex crack topologies. One effective approach to address this challenge is by reformulating damage mechanics within a variational framework. In this paper, we present a novel variational damage model that incorporates a threshold value to prevent damage initiation at low energy levels. The proposed model defines fracture energy density (ϕ˜) and damage field (s) based on the energy density (ϕ), crack energy release rate (Gc), and crack length scale (ℓ). Specifically, if ϕ≤Gc2ℓ, then ϕ˜=ϕ and s=0; otherwise, ϕ˜=−Gc24ℓ21ϕ+Gcℓ and s=1−Gc2ℓ1ϕ. Furthermore, we extend the model with a threshold value to a higher-order version. Utilizing this functional, we derive the governing equation for fractures that evolve automatically with ease. The formulation can be seamlessly integrated into conventional finite element methods for elastic solids with minimal modifications. The proposed formulation offers sharper crack interfaces compared to phase field methods using the same mesh density. We demonstrate the capabilities of our approach through representative numerical examples in both 2D and 3D, including static fracture problems, cohesive fractures, and dynamic fractures. The open-source code is available on GitHub via the link https://github.com/hl-ren/vdm.

Response prediction and damage assessment of CFST column after explosion via ANN

Concrete-filled steel tubes (CFSTs) have been extensively employed in pressurized structural members, such as high-rise buildings, large-span bridges or offshore structures. Accurately and reliably assessing the damage of CFST column subjected to explosion is helpful for designers to optimize the structural performance and construction cost. Currently, peak displacement, the damage indicator, is generally estimated via finite element method (FEM) and single degree of freedom (SDOF) oscillator model. However, the computational overhead of FEM is high, while the computational accuracy of SDOF model is low. In this paper, artificial neural network (ANN) is used to overcome the above drawbacks. A dataset of 270 experiments and numerical simulations is collected from existing literatures to develop the ANN model. The performance of this model is compared with the conventional methods, i.e., FEM and SDOF model. And its prediction accuracy and efficiency are better in the comparison by experimental results. The damage evaluation and parameter research are carried out to reveal insight into the factors on the CFST column under explosion, including the property of column and its cross-section properties, the axial compression condition, and the explosive. To support the explosion resistance design of a CFST column, an explicit equation and an excel calculation table are introduced based on the ANN model.

A novel hybrid boundary element for polygonal holes with rounded corners in two-dimensional anisotropic elastic solids

A novel hybrid boundary element is developed for polygonal holes in finite anisotropic elastic plates based on two different special fundamental solutions for holes. Since these special fundamental solutions satisfy traction-free condition along the hole's boundary, there is no mesh required on the boundary of polygonal holes. Various types of polygonal holes with rounded corners, such as triangles, rhombuses, ovals, pentagons, are considered by adding proper perturbation to an elliptical hole. The developed hybrid element is a mixture of two special boundary elements: one is based on the special fundamental solution derived through nonconformal mapping and the other is based on the solution derived through perturbation technique with conformal mapping. The special boundary element methods are combined through submodeling technique. First, the global model is solved using the perturbation solution. Then, using the displacements obtained from global model, an auxiliary submodel is set up and the results are evaluated with the nonconformal solution. The present method is compared and validated with conventional boundary element method and finite element method. The effect of hole curvature, material anisotropy, and loading condition on the stress distribution around the hole is presented.

Analysis of micro-defect-induced cracking in the IPyC layer of TRISO particle with the XFEM

PurposeWe use the extended finite element method (XFEM) to model the whole process of initiation and propagation of cracks in the inner dense pyrolytic carbon (IPyC) layer of tri-structural isotropic (TRISO) particle induced by the microdefect in an irradiation-induced thermomechanical coupling environment and study the effect of microdefect sizes on the propagation path.Design/methodology/approachThe irradiation-induced thermal–mechanical coupling analysis is first conducted for the representative volume element (RVE) of the TRISO particle by using the conventional finite element method (CFEM) so that the stress distribution is obtained. The stress results are then restored for the enriched elements, and the simulation of crack initiation and propagation is eventually carried out by using the XFEM.Findings1. As a crack initiates in the IPyC layer, it will terminate at the free edge of the RVE TRISO particle in the end. 2. The size of the microdefect has a significant impact on the propagation path.Originality/valueThe ceramic dispersion microencapsulated (CDM) fuel is a good accident-resistant fuel whose safe operation is crucial to the safety and reliability of the whole nuclear reactor. It is of great scientific significance and practical value to study the irradiation-induced thermomechanical coupling stress distribution and cracking behavior in the IPyC layer of TRISO particles for the CDM fuel. Crack initiation and propagation analysis is challengeable for this complex multi-layer structure. This can help understand the failure mechanism of TRISO particles and evaluate the operation safety of the reactor.

Temperature-Driven Instabilities in High-Pressure Vessel Flat Plates: A Thermal Buckling Study

In the realm of high-pressure vessel simulation, conventional finite element method (FEM) approaches, as per ASME standards, may inadequately predict the behavior of flat surfaces under elevated temperatures. This study challenges the efficacy of shell-type mesh modeling for high-temperature flat plates, demonstrating that the thermal conditions within such high-pressure vessels can induce thermal instability and buckling, not accounted for by traditional FEM methods recommended by ASME. Through comprehensive analytical investigations, we reveal that traditional shell-type meshing techniques, while suitable for certain applications, fail to capture the intricate thermal stresses and deformation patterns inherent in high-temperature flat plate configurations. Our analysis delineates distinct stability regimes governed by key design parameters, including plate thickness, operating temperature, and geometric dimensions, profoundly impacting the structural integrity of heating plates under thermal loading. Specifically, we found that increasing the plate thickness enhances resistance to thermal buckling, clamping the plate edges raises the critical buckling temperature, and selecting materials with lower thermal expansion coefficients improves stability. These findings provide engineers with critical insights necessary for optimizing the design and performance of high-temperature equipment. This includes the design of high-pressure vessels with flat surfaces for heating materials, flanges in high-temperature environments, and fins in heat exchangers across various industries such as oil and gas, pyrolysis, and power plants. The findings presented herein serve as a valuable reference for engineers seeking to comprehend and mitigate instability phenomena in solid mechanics, offering practical guidance for developing robust and reliable high-temperature structures in demanding industrial environments.

Dynamic Analysis of 2D FG Porous Thick Cylindrical Shells Under Thermal Shock

In this research, a thick hollow cylindrical shell made of bidirectional functionally graded open cell porous materials under internal thermal shock according to the classical theory of linear thermo-elasticity is examined for the first time. The cylinder is made of a porous cellular material and its porosity varies along both radial and axial directions continuously. The governing motion equations are obtained by using 2D-axisymmetric theory of linear thermo-elasticity rather than shell theories. This theory represents thickness stretching and gives more precise results. Graded finite element method is employed to model the problem. Applying this method rather than conventional FEM leads to more accurate results, especially for dynamic analyses. The cubic higher order element is used for dividing the solution domain. To obtain transient temperatures, Crank–Nicolson algorithm is used and then the Newmark procedure is used to derive time responses of displacement and stress components. The time history of displacements and stress components for different radial and axial power law exponents, porosity coefficient, boundary conditions, length-to-thickness ratio and two different porosity patterns are investigated in detail. The obtained results show that thermal-induced vibration is generally caused by hoop stress, and frequency and amplitude of vibrations and velocity of stress waves are considerably influenced by the porosity distribution, porosity coefficient and power law exponents in both directions.

On the isogeometric analysis of vibration and buckling of bioinspired composite plates using inverse hyperbolic shear deformation theory

Inspired by the remarkable energy absorption and damage tolerance capabilities observed in mantis shrimp crustaceans, this study delves into the intricate realm of biological composites with helicoidal structures. However, the effect of the relative orientation of fibers within the helicoidal structure matrix on the buckling and vibration characteristics still warrants comprehensive investigation for the better design of the bioinspired structures. For the first time, a Non-Uniform Rational B-Splines (NURBS)-based isogeometric analysis (IGA) framework termed NURBio is proposed to investigate the vibration and buckling characteristics of bioinspired laminated composite structures. The framework employs NURBS basis functions for exact complex geometric representation and field approximation and offers superior computational accuracy and efficiency as compared to conventional finite element method (FEM). The present analysis is underpinned by an inverse hyperbolic shear deformation theory (IHSDT) capable of accurately capturing the interlaminar stress distribution. This research investigates the performance of various bioinspired layup configurations encompassing recursive, exponential, semicircular, and Fibonacci helicoidal designs and compares them with those of unidirectional, and cross-ply laminates. A series of numerical examples on the buckling and vibration response of bioinspired composite plates are presented to demonstrate the versatility and efficacy of the proposed isogeometric framework. The influence of different layups, loading and boundary conditions, and geometric properties on the response of different bioinspired plate structures are meticulously examined. The study offers valuable insights into the design and optimization of high-performance bioinspired structures.

A review of curved crease origami: design, analysis, and applications

Origami structures with morphing behaviours and unique mechanical properties are useful in aerospace deployable structures, soft robots and mechanical metamaterials. Curved-crease origami, as one of the variants in the origami family, has a curve that connects two vertices as a crease compared to the straight crease counterpart. This feature couples the crease folding and facet bending during the folding process, providing versatile design space of mechanical metamaterials with tunable stiffness, multi-stability properties and morphing behaviours. However, current design techniques are mostly for simple geometries with intuitive construction, the modelling technique focuses on using the conventional finite element method, and the intrinsically complex geometries make specimens difficult to manufacture, which further hinders the development of curved-crease origami structures. Thus, it is valuable to review the state-of-the-art in curved-crease origami. This paper presents a review on the design methodology, analytical methods, and applications of curved-crease origami over the years, discusses their strengths, identifies future challenges and provides an outlook for the future development of the curved-crease origami concept.

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

In this study, a carefully designed enriched finite element method (EFEM) is presented to improve the solution accuracy of the conventional FEM by analyzing the dynamic behavior of the magnetic-electric-elastic (MEE) composite structures, which are frequently used in designing various smart and intelligent devices. By formulating the proper EFEM with ideal numerical performance, different enrichment functions are considered and the corresponding solution quality of different versions of the EFEM is compared and examined in great detail. When the Lagrange polynomial basis functions together with the harmonic trigonometric functions are used as enrichment functions, the obtained EFEM shows extremely powerful and ideal numerical performance, which is obviously better than the other versions of EFEM and the conventional FEM, in studying the free vibration and harmonic frequency responses of the MEE structures. Nearly exact numerical solutions for three-phase physical fields of MEE structures can be generated by the proposed EFEM even if very coarse mesh patterns are used. Intensive numerical studies are conducted to confirm and verify the excellent properties of the proposed EFEM in performing dynamic analysis of the MEE structures.

High-strain dynamic model of large-diameter pipe piles with soil plug for vertical vibration analysis

A rigorous analytical model is developed for simulating the vibration behaviors of large-diameter open-ended pipe piles (OEPPs) and surrounding soil undergoing high-strain impact loading. To describe the soil behavior, the soil along pile shaft is divided into slip and nonslip zones and the base soil is modeled as a fictitious-soil pile (FSP) to account for the wave propagation in the soil. True soil properties are adopted and slippage at the pile-soil interface is considered, allowing realistic representation of large-diameter OEPP mechanics. The developed model is validated by comparing with conventional models and finite element method (FEM). It is further used to successfully simulate and interpret the behaviors of a steel OEPP during the offshore field test. It is found that the variation in the vertical vibrations of shaft soil along radial direction is significant for large-diameter OEPPs, and the velocity amplitudes of the internal and external soil attenuate following different patterns. The shaft soil motion may not attenuate with depth due to the soil slippage, while the wave attenuation at base soil indicates an influence depth, with a faster attenuation rate than that in the pile. The findings from the current study should aid in simulating the vibration behaviors of large-diameter OEPP-soil system under high-strain dynamic loading.

A comparative study of emerging material point method and FEM for forming simulation of textile reinforcements

For forming simulations of fabric composites, nonlinear Finite Element Method/FEM has been a long-standing tool to predict and mitigate defects such as wrinkling. However, small-time step requirements in explicit FEM codes, numerical instabilities, and large computational time are among challenges reported. This study presents an alternative fast forming simulation technique through an application of the so-called Material Point Method/MPM, which enables the use of much larger time steps along with fewer numerical instabilities. As a preliminary step towards assessment of this method, both standard 2D deformation modes and 3D hemispherical forming setups were employed, using a plain fabric weave at dry condition. The MPM results were compared to the conventional FEM simulations, as well as to the physical experiments. Notably, the MPM method showed a runtime 20 times faster than its FEM counterpart (under a comparable mesh size), yet with the same reliability in forming predictions as verified by experiments.