High-order Element Research Articles

Life Prediction and Reliability Evaluation of Reinforced Concrete Frame Structures Considering the Collision Response Under Earthquake Conditions

Firstly, in this study, we utilize the high-order element model (truss link model) simulation method in OpenSees (3.7.0) software and verify the feasibility of this method by comparing it with the shaking table test. Secondly, the structural dynamic response of adjacent structures with different performance levels, spacing, and layout forms under large earthquakes is analyzed, and the corresponding structural failure probability is studied. Furthermore, the life distribution within the design service life of the structure is predicted according to the nonparametric Kaplan–Meier estimation model. Finally, the reliability of adjacent structures is evaluated by using the joint engineering demand parameters. The analysis method of replacing the theoretical analysis based on engineering experience and certainty in the current specification with probability analysis is proposed, which provides a more reliable theoretical basis for decision-making regarding the reinforcement, maintenance, or demolition of structures in the later stage.

Dynamic insights into thermal shock response of double-layer cylinders with FGM main layer and viscoelastic holder via generalized Green-Naghdi theory

This study investigates the dynamic thermoelastic response of a hollow cylinder composed of two distinct layers: a Functionally Graded Material (FGM) as the primary layer and an isotropic viscoelastic material as the supporting layer. Utilizing a power function, the material properties of the FGM layer are determined, while the viscoelastic layer follows the Kelvin-Voigt model. The research employs the generalized Green-Naghdi theory to formulate the heat transfer equation, capturing the energy dissipation and thermoelastic wave propagation within this novel configuration. Highly coupled equations governing both layers are derived, incorporating appropriate boundary and continuity conditions. The Chebyshev collocation element (CCE) method is utilized for the spatial solution, significantly reducing the computational effort by requiring only two higher-order elements. The Newmark time marching approach is employed to solve the resulting ordinary differential equations (ODEs). The model's accuracy is validated against existing literature, and parametric studies are conducted to evaluate the impact of thermal shock on the FGM layer. It has been observed that the presence of the viscoelastic barrier effectively impedes the full penetration of stress waves, thereby reducing the potential for shock-induced damage.

An accurate and locking-free geometric exact beam formulation on the special orthogonal group SO(3)

An accurate and locking-free geometric exact beam formulation (GEBF) on the special orthogonal group SO(3) is developed for slender beams with large deformations and large rotations. Due to the nonlinear nature of the spatial rotations, the classical GEBFs usually have a non-constant mass matrix and complex expressions of inertia forces; meanwhile, the singularity and locking issues are also key matters of concern. Aiming at resolving these drawbacks, two main contributions are achieved in the present work. First, the angular velocity is independently interpolated, resulting in a constant mass matrix and explicitly representable inertial forces, which can offer significant advantages for efficient dynamic simulations. Second, inspired by the assumed natural strain method in shell theory, the stretch-shear strain is interpolated to obtain simplified and locking-free elastic forces, which is a new attempt to alleviate the locking problems for the GEBFs. In addition, the special orthogonal group SO(3) is utilized for updating incremental rotation vectors to eliminate singularities, and objective strain measurement is achieved by employing relative rotation vector interpolation. The effectiveness and superiority of the developed low-order and high-order elements are demonstrated through numerical simulations of standard benchmark examples. The present work contributes to the advancement of accurate and reliable formulation for slender beams; the constant mass matrix, the locking-free characteristics, and the elegant form of the formulation make it particularly suitable for multibody dynamic analysis.

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

Minimal surface-guided higher-order mesh generation for CAD models

This paper presents a novel method for generating higher-order meshes for CAD surfaces by leveraging minimal surface theory to improve element shapes. We explore the concept of higher-order mesh distortion through deformation gradients and introduce an energy function designed to minimize the surface area of these meshes, providing a theoretical justification for its effectiveness in untangling. The process of mesh generation starts with segmenting CAD surfaces into linear elements, followed by the insertion of higher-order nodes within these elements. These nodes are then projected onto the CAD surface to form the initial higher-order elements. By optimizing energy functions related to minimal surfaces and the projection distances, we achieve high-quality, geometrically accurate higher-order surface meshes. Our method has been validated on complex geometries, showcasing its potential in creating effective higher-order meshes for industrial CAD models.

A frequency domain analysis method for the dynamic response of a submerged floating tunnel under wave action

To investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves, a modal superposition method in the frequency domain was established, and the amplitudes of the modals were determined using the generalized wave loads and hydrodynamic coefficients of the structural modals. In this model, the SFT was simplified as a constant-cross-section Euler–Bernoulli beam with multiple anchor cables, and its structural modals were resolved using the finite element method (FEM). The generalized wave loads and generalized hydrodynamic coefficients were obtained using the Fourier expansion strategy of the modal function, by which the hydrodynamic problem can be converted into 2D problems with the modified Helmholtz controlling equation and solved using the matched higher-order boundary element method (HOBEM) and eigenfunction expansion. The effects of the diameter of the anchor cables and length of the SFT on the stiffness of the structure and the dynamic response of an SFT with anchor cables under wave action were investigated. Furthermore, the effects of different added mass calculation methods on the structural response were studied. In addition, the wave exciting forces were calculated using potential flow theory or linearized Morison equations according to the wave scale. Finally, the effects of the incident wave frequencies and incident angles were investigated in detail to reveal the combined resonance mechanism.

Mitochondrial Genome Characteristics and Phylogenetic Analysis of Fulmekiola serrata (Kobus) (Thysanoptera: Thripidae)

Sugarcane thrips, Fulmekiola serrata (Kobus) (Thysanoptera: Thripidae), is a common foliar pest that infests sugarcane and is found throughout tropical and subtropical countries. In this study, we obtained and analyzed the complete mitochondrial genome of F. serrata for the first time and explored the phylogenetic relationships of the higher-order elements of Thysanoptera members at the mitochondrial level. The complete mitochondrial genome of F. serrata is 16,596 bp in length and includes 13 protein-coding genes (PCGs), 22 transfer RNA (tRNA) genes, 2 ribosomal RNA (rRNA) genes, and 1 noncoding control region. A+T accounted for 75% of the total bases in the mitochondrial genome of F. serrata, revealing an obvious AT bias. Among the 13 PCGs, except for nad5, which had a start codon of TTG, the remaining genes had ATNs typical of insects (ATA, ATT, ATC, and ATG); nad1, nad2, nad3, and atp8 had incomplete termination codons of TA or T. The remaining nine PCGs were complete with the termination codon TAA. Of the 22 tRNA secondary structures, all were typical cloverleaf secondary structures except for trnS1, which was missing the DHU arm. Compared with the hypothetical ancestral gene arrangement of arthropods, F. serrata presented extensive gene rearrangement, with 23 translocated genes, 8 inverted genes, and 5 shuffled genes. Both maximum likelihood (ML) and Bayesian inference (BI) phylogenetic trees resulted in similar topologies: ((Thripidae + (Stenurothripidae + Aeolothripidae)) + Phlaeothripidae), with Thripidae, Aeolothripidae and Phlaeothripidae being monophyletic groups, whereas F. serrata is closely related to Thrips palmi, and the two are sister groups.

Experimental and numerical investigation of wave loads on land-based multi-chamber OWC converters

Capturing more wave energy in a cost-effective principle has become a challenging task. Multi-chamber oscillating water column (OWC) devices are gradually gaining favour due to their potentially efficient characteristics. However, there is relatively limited research on dynamic analysis which is crucial for the safety and survival of multi-chamber OWC devices. In the study, model experiments of the hydrodynamic pressures for single-, dual- and three-chamber devices were conducted at a wave flume. A two-dimensional fully nonlinear numerical model for the interaction between waves and the OWC devices was established based on the higher-order boundary element method. The numerical results well cross-validated the experimental data. The wave forces and moments exerted on the devices were numerically calculated. The results indicate that the multi-chamber configurations not only generally reduce the wave loads on front and rear walls in high-frequency waves, but also avoid the sloshing motion of the water column inside the chamber, which induces large wave loads on the converter. However, the additional internal walls impose a redoubled burden on the junction of the top ceiling and the rear wall. The OWC converters sustain the horizontal forces much more than vertical forces. The front lip (i.e., the bottom edge of the front wall), the rear wall and the connection between the seabed and the device are relatively dangerous positions for configurations with any number of chambers.

Mixed displacement–pressure formulations and suitable finite elements for multimaterial problems with compressible and incompressible models

Multimaterial problems in linear and nonlinear elasticity are some of the least explored using mixed finite element formulations with higher-order elements. The fundamental issue in adapting the mixed displacement–pressure formulations with linear and higher-order continuous elements for the pressure field is their inability to capture pressure and stress jumps across material interfaces. In this paper, for the first time in literature, we perform comprehensive studies of multimaterial problems in elasticity consisting of compressible and incompressible material models using the mixed displacement–pressure formulation to assess the performance of different element types in accurately resolving pressure fields within the domains and pressure jumps across material interfaces. In particular, inf–sup stable displacement–pressure combinations with element-wise discontinuous pressure for triangular and tetrahedral elements are considered and their performance is assessed along with the Q1/P0 element and Taylor–Hood elements using several numerical examples. The results show that Taylor–Hood elements fail to capture the stress jumps due to the continuity of DOFs across elements, the Crouzeix–Raviart (P2b/P1dc) element yields substantially poor pressure fields despite a significant increase in pressure degrees of freedom and that the P3/P1dc element produces superior quality results fields when compared with the P2b/P1dc element.

A hp-adaptive finite element approach for 3D controlled source electromagnetic forward modeling

Accurate and efficient 3D controlled-source electromagnetic (CSEM) forward modeling is crucial for deciphering CSEM responses in complex geological contexts and for assessing the efficacy of survey designs. It also serves as the foundation for 3D inversion, a critical technique for interpreting CSEM data. We present a novel hp-adaptive finite element method for 3D CSEM forward modeling. This method enhances the traditional h-adaptive approach, which only refines the mesh while keeping the polynomial degree of the basis functions constant, by enabling simultaneous refining mesh and increasing polynomial degree of basis functions. High-order elements yield superior approximations when the solution exhibits sufficient smoothness, while mesh refinement enhances accuracy in regions with less smooth solutions. The adaptive refinement process is guided by a goal-oriented error estimator that relies on the residual of the governing equation and the continuity of electromagnetic fields. The hp-adaptive strategy, which determines whether to refine elements or increase their polynomial degree, is based on the refinement levels of the elements. Constraints are applied to hanging nodes, introduced during the refinement process, to ensure the continuity of the finite element space. We validate the accuracy, efficiency, and convergence of the hp-adaptive method through tests on two layered models. Further simulations on a topographic model and a realistic model corroborate its effectiveness. Our findings indicate that the hp-adaptive method outperforms the traditional h-adaptive method in terms of accuracy, convergence rate and computational cost, making it a promising technique for 3D CSEM forward modeling.

In-Plane and Out-of-Plane Bending Vibration Analysis of the Laminated Composite Beams Using Higher-Order Theories

In this paper, higher-order shear deformation theories for a thorough analysis of the in-plane and out-of-plane vibrational characteristics of laminated composite beams have been presented. Through the introduction of new displacement fields and the consideration of rotary inertia and Poisson's effect, the kinetic and potential energies of the beams have been derived. This formulation, displaying significant generality, accommodates arbitrary stacking sequences. Utilizing the finite element method, a new element has been presented for calculating the beam's vibrational characteristics. Featuring three nodes, each with seven degrees of freedom, this higher-order element provides a detailed representation of complex behaviors. Mass and stiffness matrices have been derived using the energy method and apply boundary conditions through the penalty approach. The results exhibit a high degree of consistency and alignment with those obtained from the 3D commercial software ANSYS, validating the accuracy and reliability of the proposed methodology for structural analysis. This comprehensive approach contributes to advancing the understanding and modeling of laminated composite beams in diverse engineering applications. The effects of different parameters on the in-plane and out-of-plane vibration analysis of laminated composite beams have been investigated in detail.

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.

Are There an Infinite Number of Passive Circuit Elements in the World?

We found that a second-order ideal memristor [whose state is the charge, i.e., in ] degenerates into a negative nonlinear resistor with an internal power source. After extending analytically and geographically the above local activity (experimentally verified by the two active higher-integral-order memristors extracted from the famous Hodgkin–Huxley circuit) to other higher-order circuit elements, we concluded that all higher-order passive memory circuit elements do not exist in nature and that the periodic table of the two-terminal passive ideal circuit elements can be dramatically reduced to a reduced table comprising only six passive elements: a resistor, inductor, capacitor, memristor, mem-inductor, and mem-capacitor. Such a bounded table answered an open question asked by Chua 40 years ago: Are there an infinite number of passive circuit elements in the world?

Wave Propagation for Structural Health Monitoring (WaveProSHM): open software with GUI

Guided wave–based SHM methods have been explored extensively in recent decades. The wave propagation modelling including piezoelectric transducers and various damage types helps understand intricacies of guided wave behavior and for designing a robust SHM system. However, modelling aspects are still challenging. Moreover, commercially available software for the modelling of guided waves often lacks appropriate high-order elements and code optimization for fast GPU computations. This research aimed to develop and disseminate to the SHM community the open software based on highly efficient vectorised code of the time domain spectral element method which can be run on GPU. The developed code is written in MATLAB with Graphical User Interface (GUI) and communicates with GMSH – open source finite element mesh generator. It can model signals of propagating guided waves in structures which are excited and registered by an array of piezoelectric transducers. The capabilities of the software are shown in an example of a large-scale problem of interacting guided waves with delamination.

Mesh objective characteristic element length for higher-order finite beam elements

The use of fracture energy regularization techniques can effectively mitigate the mesh dependency of numerical solutions caused by the strain softening behavior of quasi-brittle materials. However, the successful regularization depends on the correct estimation of the crack bandwidth in Finite Element solutions. This paper aims to present an enhanced crack band formulation to overcome the strain localization instability especially for the higher-order elements developed in the framework of Carrera Unified Formulation (CUF). Besides, a modified Mazars damage method incorporating fracture energy regularization is employed to describe the nonlinear damage behavior of the concrete. To evaluate the efficiency of the proposed crack band formulation, three experimental concrete benchmarks are selected for the numerical damage analysis. By comparing numerical and experimental results, the proposed method can guarantee mesh objectivity despite varying finite element numbers and orders, indicating perseved fracture energy consumption within proposed higher-order beam models.

High-order elements in position-based dynamics

High-order elements in position-based dynamics

Floating wind turbine response in uni- and multi-directional nonlinear waves by numerical and experimental investigations

Natural sea waves are typically multi-directional. However, the existing studies on the interaction of waves and structures mostly concentrate on uni-directional waves. In this study, using a higher-order boundary element method based on the nonlinear potential flow theory and the perturbation expansion technique, a numerical model is developed to investigate the hydrodynamic performance of a semi-submersible wind turbine foundation in uni- and multi-directional waves. Comprehensive validations with the wave-tank experiment are conducted. It is found that the significant platform response increases with the peak wave period in uni-directional irregular waves, while the high-frequency “energy” ratio changes little. The significant wave height hardly influences motion responses from either the time- or the frequency-domain perspective. In multi-directional irregular waves, the translational motions exhibit monotonicity with wave directionality. The energy concentration around the primary direction leads to a dominant wave-frequency motion and an increase in the high-frequency “energy” ratio. Although the individual modal motion responses are variable functions of wave nonlinearity, their averaged translational and rotational motions are nearly constant, indicating an energy transition or a trade-off relationship among the modal motions. In addition, unlike the uni-directional wave case, the low- and high-frequency “energy” ratios increase quadratically and decrease linearly with the significant wave height in multi-directional waves, respectively. All these findings demonstrate that wave directionality can change the wave–structure interaction properties and therefore needs to be adequately considered in engineering applications.

Real-world data-supported and higher-order element theory-enabled progressive damage model assembly

Real-world data-supported and higher-order element theory-enabled progressive damage model assembly

Analysis and simulation of the (2 + 1)-dimensional Fisher’s reaction-diffusion equation with higher order finite element method

In this article, a finite element analysis of Fisher’s reaction-diffusion equation is performed, by using quadratic shape elements. The higher-order elements in the finite element method (FEM) are known to yield better results in the approximation of solutions. However, such elements are less explored in the literature. Therefore, quadratic shape functions are taken into consideration for the finite element analysis of Fisher’s reaction-diffusion equation. A priori error estimates for the semi-discrete solution are derived by applying the Galerkin approximation. For the fully discrete solution, a priori error estimates are derived using the Crank-Nicolson method and the predictor-corrector scheme. Also, the stability of the time-discrete scheme is analyzed by the energy technique. Third-order convergence for space discretization in L 2 ( Ω ) norm and second-order convergence in H 1 ( Ω ) norm are observed. Furthermore, second-order convergence for time discretization is also found. Finally, we validate our theoretical results by considering a variety of numerical examples in one and two-dimensional spaces, which also illustrate the reliability of the developed finite element algorithm. Through comparison tables, 3D plots, and convergence plots, the results of the current study are compared with the results from the existing literature.

Numerical Investigation on a High-Speed Transom Stern Ship Advancing in Shallow Water

A high-speed advancing ship will cause significant squats in shallow water, which could increase the risk of grounding. To this end, a program based on the Rankine higher-order boundary element method (HOBEM) is developed to investigate a high-speed displacement ship with a transom stern moving in shallow water. The nonlinear free surface condition is satisfied by adopting an iterative algorithm on the real free surface. The transom condition is considered by implementing a modified transom condition. Computations of wave-making resistance, sinkage and trim in deep water are first performed, and satisfactory agreement is achieved by comparing with the experimental results; the simulations are then extended to the shallow water case. It indicates that the present method can provide a suitable balance of practicability and robustness, which can be considered as an efficient tool for the guidance in ship design stage.