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This paper introduces a linear version of the reduced multibody system transfer matrix method for studying the eigenvalue problems and steady-state responses of tree multibody systems. The core idea is to recursively transfer mechanical information between elements, utilizing a directed rooted tree to depict the system topology. Reduced transfer equations are provided for both spatial rigid and flexible bodies. For flexible bodies, the derivation is based on the dynamical equations from the finite element method and component mode synthesis. The effectiveness and numerical stability of this method is validated through three numerical examples. • A novel recursive method is introduced for eigenvalue problems and steady-state responses of tree multibody systems. • A directed rooted tree depicts information transfer in systems and presents a recursive algorithm. • Derivation for flexible bodies utilizes dynamical equations from the finite element method or component mode synthesis. • This recursive method is concise, highly structured, and highly programmable. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two one-parameter families of quadratic polynomial enrichments designed to enhance the accuracy of the classical Crouzeix–Raviart finite element. These enrichments are realized by using weighted line integrals as enriched linear functionals and quadratic polynomial functions as enrichment functions. To validate the effectiveness of our approach, we conduct numerical experiments that confirm the improvement achieved by the proposed method. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the dimensionality reduction of unknown finite element (FE) solution coefficient vectors in two-grid Crank-Nicolson FE (TGCNFE) method for the spatial fractional nonlinear Allen-Cahn (SFNAC) equations. For this reason, a new TGCNFE method for the SFNAC equations is first established and the unconditional stability and convergence (errors) of TGCNFE solutions are demonstrated. Subsequently, the most important thing is to use a proper orthogonal decomposition to reduce the dimension of the unknown FE solution coefficient vectors of the TGCNFE method for the SFNAC equations and to construct a new reduced-dimension extrapolation TGCNFE (RDETGCNFE) method, and demonstrate the unconditional stability and errors of RDETGCNFE solutions. Finally, the correctness of the obtained theoretical results of unconditional stability and errors is validated by some numerical experiments. [ABSTRACT FROM AUTHOR]

This paper presents a new approximate solution to study the settlement of rigid footings resting on a soft soil improved with groups of encased stone columns. The solution development is fully analytical, but finite element analyses are used to verify the validity of some assumptions, such as a simplified geometric model, load distribution with depth and boundary conditions. Groups of encased stone columns are converted to equivalent single encased columns with the same cross-sectional area and the same ratio of encasement stiffness to column diameter. In this way, the problem becomes axially symmetric. Soft soil is assumed as linear elastic but plastic strains are considered in the column using the Mohr-Coulomb yield criterion and a non-associated flow rule with a constant dilatancy angle. Soil profile is divided into independent horizontal slices and equilibrium of stresses and compatibility of deformations are imposed in the vertical and horizontal directions. The solution is presented in a closed form and may be easily implemented in a spreadsheet. Comparisons of the proposed solution with numerical analyses show a good agreement for the whole range of common values, which confirms the validity of the solution and its hypotheses. • A new analytical solution to study the settlement of rigid footings on a soft soil improved with encased stone columns. • A simplified model of a single column with the same area and the same ratio of encasement stiffness to column diameter. • The approximate analytical solution may be easily implemented in a spreadsheet. • A simplified calculation example and the corresponding calculation code are presented. • Comparisons with numerical analyses show a good agreement. [ABSTRACT FROM AUTHOR]

In this paper, we mainly resort to a proper orthogonal decomposition (POD) method to study the reduced-dimension of unknown mixed finite element (MFE) solution coefficient vectors in the two-grid Crank-Nicolson MFE (TGCNMFE) method for the nonlinear wave equation and build a preserving accuracy reduced-dimension extrapolated TGCNMFE (RDETGCNMFE) method for the nonlinear wave equation. For this purpose, we first build a new TGCNMFE method for the nonlinear wave equation and demonstrate the existence, unconditional stability, and error estimates for the TGCNMFE solutions. From there, we build a preserving accuracy RDETGCNMFE method for the nonlinear wave equation by using the POD method to decrease the dimension of unknown TGCNMFE solution coefficient vectors and employ the matrix analysis to analyze the existence, unconditional stability, convergence, and errors for the RDETGCNMFE solutions. We finally make use of numerical experiments to verify our theoretical results and to show the advantages of RDETGCNMFE method. [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of a history-dependent mixed hemivariational-variational inequality arising in contact mechanics. The contact problem concerns the deformation of a viscoelastic body with long memory, subject to a general friction law on one part of the boundary and a frictionless Signorini condition on another part of the boundary. The solution existence and uniqueness of the history-dependent mixed hemivariational-variational inequality based on a Lagrange multiplier approach are proved. Then, a fully discrete scheme is introduced and studied. The trapezoidal rule is used to approximate the integral in the history-dependent operator. For the spatial discretization, the linear finite elements are used to discretize the displacement field, and dual basis functions are used in the approximation of the Lagrange multiplier. Optimal order error estimates are derived for the displacement and the Lagrange multiplier under appropriate solution regularity assumptions. Numerical results are presented to illustrate the theoretical prediction of the convergence orders. [ABSTRACT FROM AUTHOR]

• An exact matrix-form solution is proposed for analyzing multiple non-circular tunnels in layered media. • Generalized complex variable theory, conformal mapping and fast Fourier transform are used in derivation. • The proposed solution avoids complicated coefficient determinations and iterative algorithm. • Effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels are discussed. This paper presents a matrix-form complex variable method that can predict the stress and displacement field around multiple tunnels in layered media. The proposed matrix-form method avoids complicated coefficient determinations and iterative algorithm, which effectively improves the computation efficiency. Firstly, the expressions for the stress and displacement field are given under the generalized complex variable theory. The conformal mapping technique and fast Fourier transform algorithm are used to formulate the matrix-form expressions of boundary conditions. Considering the boundary conditions of the tunnels and soil interfaces, the global matrix solution for multiple tunnels in layered media are obtained by assembling the matrix solutions of all single layers. The present theory is verified by comparison with the existing literature, finite element analysis and field data in engineering practices, and several numerical examples are given to reveal the effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels. [ABSTRACT FROM AUTHOR]

• A hybrid method by integrating the advantages of frequency-wavenumber method and finite element method. • The entire process simulation from the source to the local terrain has been achieved. • Seismic response of mountains due to point dislocation source. • The crustal velocity structure and source parameters influence the seismic response. This paper proposes a hybrid method to analyze seismic responses from the source to complex terrain. The hybrid method is based on the domain reduction idea, dividing the overall model into global domain (including the source and propagation path) and local domain (including complex terrain). For the propagation of seismic wave fields in the global domain, a frequency-wavenumber method based on the exact dynamic stiffness matrix is adopted. For the local domain, the finite element method combined with the artificial boundary substructure method is used to analyze the seismic response of complex terrain. The advantage of this hybrid method is that the frequency-wavenumber method can accurately and efficiently calculate the three-component ground motion of the global large-scale model, while the finite element method has a variety of elements and constitutive models, which can finely simulate the local complex terrain. We take the Zigong Xishan Park site as the research object, and verify the correctness of the hybrid method. Based on this, we use the hybrid method to simulate the seismic response of the site, focusing on the propagation process of seismic waves on the mountain surface, the spatial distribution of peak ground displacement, and the effects of crustal velocity structure and source parameters on the seismic response of the mountain. The results show that the propagation of seismic waves and the distribution of peak ground displacement are closely related to changes in terrain, and the crustal velocity structure and source parameters have significant effects on the seismic response of the mountain. [ABSTRACT FROM AUTHOR]

• This manuscript firstly establishes a half vehicle-pavement-continuous beam bridge (VPCB) coupled system analytical model. • It is innovatively that the bridge and vehicle initial conditions are considered into analytical model. • The pavement road surface local deterioration is simulated by increasing the local roughness level of the road surface. At present, the highway bridge field is in a period of vigorous development, and the application of continuous beam bridges is becoming more extensive, so the related safety research is particularly important. However, there are few studies on the vehicle-bridge coupled interaction of continuous beam bridges, and the influence of pavement is not considered. In order to ensure that the theoretical research can better serve the engineering practice, it is urgent to establish a more refined and more complex vehicle-bridge coupled model. In this paper, a vehicle-pavement-continuous beam bridge (VPCB) coupled system model is established. A half-vehicle model is adopted, the pavement is simulated by a continuous and uniform spring damper, and the bridge is a three-span continuous beam bridge. The motion equation of VPCB system is established and deduced using D 'Alembert principle and modal superposition method. The dynamic responses of VPCB system are calculated by Newmark- β method. Here, the continuous beam bridge mode functions are fitted based on the modal vector of the continuous beam calculated by the finite element model. The correctness of the method is verified by existing literatures. The effects of bridge pavement, vehicle speed, bridge second span length, the pavement equivalent spring stiffness coefficient k p and damping coefficient c p , road roughness on VPCB system are studied. The results show that the pavement can reduce the bridge dynamic amplification factor (DAF) and the vehicle acceleration to improve the ride comfort. The dynamic responses of the vehicle and the bridge contain each other's natural frequencies. The responses of VPCB system increase with the vehicle velocity, the vehicle responses are more affected than the bridge responses. The pavement equivalent stiffness and damping coefficient has little effect on the system. The responses of vehicle and bridge increase with the increase of the bridge second span length. When the vehicle travels each span of the three-span continuous beam bridge, the time history curve of the pavement deformation under the tire resembles a sine wave. When the local roughness level of the road surface increases, the system responses at the deteriorated position suddenly increases, and the responses of the subsequent position will also be affected. The larger the roughness grade, the more obvious the responses increase. The effect on the system responses of the whole pavement damage is more significant than the local pavement damage. [ABSTRACT FROM AUTHOR]

This article introduces a unified mixed finite element framework based on a saddle-point formulation that applies to time-dependent fourth order linear and nonlinear problems with clamped, simply supported, and Cahn-Hilliard type boundary conditions. The classical mixed formulations lead to large matrix systems that demand huge storage and computational time making the schemes expensive, especially for the time-dependent problems. The proposed scheme circumvents this by employing biorthogonal basis functions that lead to sparse and positive-definite systems. The article discusses a mixed finite element method for the biharmonic problem and the time-dependent linear and nonlinear versions of the extended Fisher-Kolmogorov equations equipped with the aforementioned boundary conditions. The wellposedness of the scheme is discussed and a priori error estimates are presented for the semi-discrete and fully discrete finite element schemes. The numerical experiments validate the theoretical estimates derived in the paper. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a mixed variational formulation for the Navier-Stokes equations with variable viscosity that depends nonlinearly on the velocity gradient. Differently from previous works in which augmented terms are added to the formulation, here we employ a technique that had been previously applied to the stationary Boussinesq problem and the Navier-Stokes equations with constant viscosity. Firstly, a modified pseudostress tensor is introduced involving the diffusive and convective terms and the pressure. Secondly, by using the incompressibility condition, the pressure is eliminated, and the gradient of velocity is incorporated as an auxiliary unknown to handle the aforementioned nonlinearity. As a consequence, a Banach spaces-based formulation is obtained, which can be written as a perturbed twofold saddle point operator equation. We address the continuous and discrete solvabilities of this problem by linearizing the perturbation and employing a fixed-point approach along with a particular case of a known abstract theory. Given an integer ℓ ≥ 0 , feasible choices of finite element subspaces include discontinuous piecewise polynomials of degree ≤ ℓ for each entry of the velocity gradient, Raviart-Thomas spaces of order ℓ for the pseudostress, and discontinuous piecewise polynomials of degree ≤ ℓ for the velocity as well. Finally, optimal a priori error estimates are derived, and several numerical results confirming in general the theoretical rates of convergence, and illustrating the good performance of the scheme, are reported. [ABSTRACT FROM AUTHOR]

In this paper, a novel linearized second-order energy-stable fully discrete scheme for the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation is introduced, along with a superconvergence analysis of the conforming finite element method (FEM). Through skillful decomposition of the nonlinear term u ∇ ⋅ u , a new linearized second-order fully discrete scheme is developed. This scheme requires fewer iterations and exhibits higher computational efficiency compared to the nonlinear approach. Furthermore, it maintains energy stability, enabling direct numerical solution boundedness in the H 1 -norm, which represents an improvement over the L ∞ -norm boundedness reported in previous literature. Secondly, relying on this boundedness and the high-precision results of the bilinear element, we derive the unconditional error estimates for superclose and global superconvergence without any restrictions on the time step size Δ t and spatial mesh size h. Finally, numerical examples are presented to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the superconvergent behavior of a two-grid finite element method (FEM) with 2-step backward differential formula (BDF2) for nonlinear dispersive wave equation. By introducing an auxiliary variable q = u t for the original variable u , the problem is transformed into a parabolic system. With the help of the combination technique of the interpolation and Ritz projection, the superclose and superconvergent estimates for the above two variables in H 1 -norm are obtained under the lower regularity of the exact solution compared with the standard Galerkin FEM. Finally, some numerical results are provided to show the correctness of the theoretical predictions and good performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is contributed to explore how a Crank-Nicolson weak Galerkin finite element method (WG-FEM) addresses the singularly perturbed unsteady convection-diffusion equation with a nonlinear reaction term in 2D. The problem and some asymptotic behavior results are given for the exact solution and its derivatives with the parameter ε. These results are essential for proving the uniform convergence of the proposed WG-FEM. A tensor product Shishkin mesh featuring piece-wise discontinuous bilinear polynomials is employed to handle the layers for uniform convergence at different parameter values of ε. An error estimate ‖ u N − I N u ‖ W G is presented, where I N u denotes the vertex-edge-cell interpolation of the solution u , and ‖ ⋅ ‖ W G denotes the Weak Galerkin norm. The optimal uniform convergence order is demonstrated for semi-discrete and fully discrete schemes. Various numerical experiments are conducted to validate the optimal order of convergence demonstrated by the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate the well-posedness and regularity of mild solution to a stochastic active fluids model driven by the additive noise. A fully-discrete scheme is proposed for solving the given model, which is based on the finite element method for spatial discretization and the backward Euler method for temporal discretization. By overcoming the difficulty of error analysis caused by the discrete Laplacian operator, we obtain the convergence results of the developed scheme. Finally, some numerical examples are provided to validate the theoretical results and we also simulate the motion states of the active fluids. [ABSTRACT FROM AUTHOR]

Nonlocal problems involving fourth-order terms pose several difficulties such as numerical discretization and its related convergences analysis. In this paper, the well-posedness of the extended Fisher-Kolmogorov equation with nonlocal diffusion is first analyzed using the Faedo-Galerkin technique and the classical compactness arguments. Moreover, we adopt a BDF2 scheme for time discretization and a mixed Galerkin scheme for spatial discretization. Then, we derive the optimal order convergence rates of the fully discrete system. Finally, some numerical simulations and convergence results are provided to confirm the theoretical results and the accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a method to predict the through-thickness moisture content distribution and associated induced deformations of paper and cardboard sheets as they are subjected to relative humidity changes. The transient moisture diffusion problem is solved using a “natural” analytic approach that has previously been applied for solving transient heat conduction in multi-layer solids. The deformation behaviour of the sheet during the moisture diffusion process is predicted using a semi-analytical approach based on a Rayleigh–Ritz minimization of the total potential energy. Geometrically nonlinear effects are taken into account. Curvatures of the originally flat sheet are predicted as a function of time, as are the shapes of the sheet for steady-state condition. As multiple solutions exist, stability is studied. The developed model was used to study the deformation behaviour of one paper and two cardboard sheets. Comparisons with finite-element results demonstrate that the developed model provides accurate results. The displacements obtained for steady-state conditions are within +6%. Comparisons with previous steady-state analyses reveal important differences in the shape of one cardboard sheet. This suggests that the moisture diffusion process may influence the configuration assumed by the sheet at steady-state equilibrium. Hence, it may be necessary to take the moisture diffusion into account in the analysis to accurately predict the hygro-mechanical behaviour of paper or cardboard sheets. [Copyright &y& Elsevier]

Abstract: This paper presents analysis of a 3-dimensional engineered structural panel (3DESP) having a tri-axial core structure made from phenolic impregnated laminated-paper composites with and without high-strength composite carbon-fiber fabric laminated to the outside of both faces. Both I-beam equations and finite element method were used to analyze four-point bending of the panels. Comparisons were made with experimental panels. In this study, four experimental panels were fabricated and analyzed to determine the influence of the carbon-fiber on bending performance. The materials properties for finite element analyses (FEA) and I-beam equations were obtained from either the manufacturer or in-house material tensile tests. The results of the FEA and I-beam equations were used to compare with the experimental 3DESP four-point bending tests. The maximum load, face stresses, shear stresses, and apparent modulus of elasticity were determined. For the I-beam equations, failure was based on maximum stress values. For FEA, the Tsai-Wu strength failure criterion was used to determine structural materials failure. The I-beam equations underestimated the performance of the experimental panels. The FEA-estimated load values were generally higher than the experimental panels exhibiting slightly higher panel properties and load capacity. The addition of carbon-fiber fabric to the face of the panels influenced the failure mechanism from face buckling to panel shear at the face–rib interface. FEA provided the best comparison with the experimental bending results for 3DESP. [Copyright &y& Elsevier]

Paper-like electronics with thin multi-layer structures, which can be repeatedly bent and twisted like paper, are promising for diverse innovation application. Employing surface-mounted flexible strain sensors is a general way to monitor the bending characteristics of each layer inside paper-like electronics, however, the deviation of measured strain will reach up to 15% on account of the layer-to-layer interface sliding, neutral axes offset resulted from the extra effect of the flexible strain sensor. Here, we proposed a precise measurement method to evaluate the surface bending strain of paper-like electronics by using flexible sensors. In combination with the effects of the thickness, length, etc, a strain compensation model has been established to compensate the measurement deviation. Meanwhile, a slip failure model has been developed to guide the design of the sensitivity unit within the non-sliding area of the flexible sensor. Validated by finite element analysis and experiment, the bending strain of paper-like electronics (eg., ∼50 μm) can be evaluated much more accurate compared to the frequent access one. The newly-proposed method provides a powerful basis for further research of paper-like electronics. [ABSTRACT FROM AUTHOR]

Abstract: An anisotropic elasto-plastic constitutive model of paper material is presented. It is formulated in a spatial setting in which anisotropic properties are accounted for by use of structural variables. A multiplicative split of the deformation gradient is employed to introduce plasticity. A similar approach is used to model the plastic deformation of the substructure. The yield surface adopted is based on the Tsai–Wu failure criterion, used previously to model failure of paper material. A non-associated plasticity theory is employed to calibrate the model to experimental data. It turns out that a multi-axial loading situation is needed to calibrate the model and here a biaxial tension test is audited. The model was implemented into a finite element environment and the creasing process of a corrugated board panel is investigated. [Copyright &y& Elsevier]

Abstract: A new paper separation and feed mechanism is proposed to realize a highly reliable paper handling system for printers and copiers. The paper-separation system consisted of a pair of parallel electrodes and a paper pile between the electrodes. Electrostatic separation of a piece of paper was possible from the top of the pile when the applied voltage exceeded the threshold needed to generate an electrostatic force larger than the weight of the paper. The threshold voltage was on the order of several kilovolts, and it agreed with the numerical value calculated using the finite element method (FEM) for the electrostatic field. Based on these basic investigations, a prototype mechanism for paper separation and feeding was constructed. It consisted of a roller-type separation electrode coated with an insulating film, a biased charger roller in contact with the separation roller to charge the insulating film on the separation roller, a ground electrode, and a paper pile situated between the electrodes. When an electrostatic field was applied between the biased charger roller and the ground electrode on which the paper pile was mounted, only the top sheet of paper separated, adhering electrostatically to the roller. The sheet was then fed rotating the separation roller. Using this system, reliable paper separation and feed was realized and a feed speed over 600mm/s was demonstrated. [Copyright &y& Elsevier]

• Dynamic modelling of soft tissue deformation based on the dynamic model decomposition. • No prior knowledge of the system governing equation is required. • Construct a reduced-order model by extracting the essential features of the full model. This paper studies a new approach to dynamic modelling of soft tissue nonlinear deformation behavior based on dynamic model decomposition. This approach derives the deformation relationship between two continuous time points from correlated system snapshots. Subsequently, it constructs a reduced-order system by extracting most relevant information via thin-singular value decomposition to capture dynamic characteristics of the full-order deformation system. Unlike the existing methods which mainly rely on the establishment of complex constitutive equations for governing soft tissue deformation, the proposed method conducts tissue deformation directly from measured samples without involving constitutive governing equations. Simulation results show that the proposed method not only achieves real-time performance, but also sustains similar accuracy as the nonlinear finite element method. [ABSTRACT FROM AUTHOR]

In this paper, we present a new error analysis of a class of charge-conservative finite element methods for stationary inductionless magnetohydrodynamics (MHD) equations. The methods use the standard inf-sup stable Mini/Taylor–Hood pairs to discretize the velocity and pressure, and the Raviart–Thomas face element for solving the current density. Due to the strong coupling of the system and the pollution of the lower-order Raviart–Thomas face approximation in analysis, the existing analysis is not optimal. In terms of a mixed Poisson projection and the corresponding estimate in negative norms, we establish new and optimal error estimates. In particular, we prove that the method with the lowest-order Raviart–Thomas face element and Mini element provides the optimal accuracy for the velocity in L 2 -norm, and the method with the lowest-order Raviart–Thomas face element and P 2 − P 1 Taylor-Hood element supplies the optimal accuracy for the velocity in H 1 -norm and the pressure in L 2 -norm. Furthermore, we propose a simple recovery technique to obtain a new numerical current density of one order higher accuracy by re-solving a mixed Poisson equation. Numerical results are provided to verify the theoretical analysis. • New and optimal error analysis of charge-conservative finite element methods are established. • A simple recovery technique is proposed to obtain a new current density with higher accuracy. • Numerical examples are provided to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of nonlinear multi-term time fractional wave equations. Based on the Galerkin finite element method (FEM) in space and the L 2- 1 σ formula in time, combined with the corresponding fast algorithm, an efficient fully discrete scheme is constructed. The unconditional optimal convergence property in H 1 -norm of the proposed scheme is discussed by utilizing the time-space splitting technique. Furthermore, the optimal L 2 -norm convergence and the H 1 -norm superconvergence results of the method are obtained. Finally, several illustrative numerical experiments are performed to verify the theoretical results. Compared with the existing works, studying the convergence of FEMs for the nonlinear fractional wave equation is a great challenging task, and there are significant differences in research approaches. [ABSTRACT FROM AUTHOR]

We present an application of stable finite element (FE) approximations of convection-diffusion initial boundary value problems (IBVPs) using a weighted least squares FE method, the automatic variationally stable finite element (AVS-FE) method [1]. The transient convection-diffusion problem leads to issues in classical FE methods as the differential operator can be considered a singular perturbation in both space and time. The stability property of the AVS-FE method, allows us significant flexibility in the construction of FE approximations in both space and time. Thus, in this paper, we take two distinct approaches to the FE discretization of the convection-diffusion problem: i) considering a space-time approach in which the temporal discretization is established using finite elements, and i i) a method of lines approach in which we employ the AVS-FE method in space whereas the temporal domain is discretized using the generalized- α method. We also consider another space-time technique in which the temporal direction is partitioned, thereby leading to finite space-time "slices" in an attempt to reduce the computational cost of the space-time discretizations. We present numerical verifications for these approaches, including numerical asymptotic convergence studies highlighting optimal convergence properties. Furthermore, in the spirit of the discontinuous Petrov-Galerkin (DPG) method by Demkowicz and Gopalakrishnan [2–6] , the AVS-FE method also leads to readily available a posteriori error estimates through a Riesz representer of the residual of the AVS-FE approximations. Hence, the norm of the resulting local restrictions of these estimates serves as error indicators in both space and time for which we present multiple numerical verifications in mesh adaptive strategies. [ABSTRACT FROM AUTHOR]

In this paper, we consider the linearized backward Euler finite element scheme for the Navier-Stokes-Poisson-Nernst-Planck (NSPNP) equations. We aim to derive the unconditional error estimates of all variables in l ∞ (L 2) and l ∞ (H 1) norms. Compared with some previous results, we remove the mesh restriction. In addition, we derive two important physical properties for the proposed numerical scheme. Finally, three numerical examples are implemented to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

The characteristics of the piezo-stack and the flexible mechanism are both influenced by temperature, which induces the performance change of piezoelectric actuators in low-temperature. This study investigates how temperature affects the dynamics model's stiffness, damping, driving force, and friction. An axial heat conduction model based on Fourier's heat conduction law was established, and finite element analysis was carried out to study the temperature distribution of the piezo-stack. Moreover, finite element analysis was carried out at various temperatures to investigate the impact of temperature on the flexible mechanism's deformation. Based on the aforementioned study, a dynamics model with variable stiffness and damping is proposed in this paper, and the simulation results are verified. In the experiment, the effects of temperature, voltage, and frequency on the output performance of the piezoelectric actuator were investigated separately using impedance and amplitude-frequency characteristic curves to determine the resonant frequency and damping ratio of the flexible mechanism at low temperatures. Theory and experiment show that high stiffness and low piezoelectric constants at low temperatures reduce the piezoelectric actuator's output displacement, friction reduction will enhance the driving displacement of the piezoelectric actuator, and the effect of damping on output displacement is insignificant. This study offers significant theoretical value and guidance for the use of piezoelectric actuators in low-temperature situations. • Temperature distribution across a piezo stack via mechanical series and electrical parallel connections. • Calculate stiffness, damping, and piezo constants at low temperatures, integrate them with a dynamics model for simulation. • Assess the influence of dynamics model parameters on piezo actuators through theoretical simulations and experiments. • Clarify the effect of each parameter of the dynamics model on the performance of piezoelectric actuators by means of experimental and theoretical simulations. [ABSTRACT FROM AUTHOR]

The scaled boundary finite element method (SBFEM) is a semi-analytical numerical approach based on the scaled boundary coordinates. Recently, the method which uses interpolations in both the circumferential and radial directions has also been developed based on the scaled boundary representation. However, the stress fields are always discontinuous within the S-elements by both the original SBFEM and the latter method. In this paper, a new class of quadrilateral elements with interior smoothness is constructed by extending the B-net method based on the area coordinates into the S-net method based on the scaled boundary coordinates. In the S-net method, the Bernstein bases are separately applied to discretize both circumferential and radial directions in each sub-triangle of an S-element (or quadrilateral element), and the smoothness conditions between adjacent triangles can be simply represented in the form of linear equations. Then, by using the S-net method, we obtain a new class of quadrilateral elements with interior smoothness and high-order completeness. The shape functions or interpolation bases can be obtained explicitly and determined by the same interpolation nodes of the S-element as the original SBFEM. Some numerical tests also show that the proposed elements can obtain good results. • A new class of quadrilateral FEM elements is constructed in the scaled boundary coordinates with interior C 1 continuity. • The B-net method based on the area coordinates is extended into the S-net method based on the scaled boundary coordinates. • The new elements overcome the stress singularity at the scaling centre and stress discontinuity inside the S-element. • The high-order completeness of the new elements is proved theoretically and thus the convergence is guaranteed. • The extended S-net method can construct new polygonal elements with high-order continuity. [ABSTRACT FROM AUTHOR]

This paper proposes an extended virtual element method based on the combination of the extended finite element method and the virtual element method on interface-unfitted meshes for solving elliptic interface problems. The well-posedness of the discrete problem is shown and the optimal error estimate is derived, which is independent of the location of the interface relative to the mesh and the contrast between the diffusion coefficients. Numerical experiments verify the theoretical results. [ABSTRACT FROM AUTHOR]

Hydrogen storage vessels in hydrogen refueling stations are densely arranged, so high-speed fragments generated by explosion accidents may endanger adjacent vessels. It is of great significance to explore the dynamic responses and damage modes of hydrogen storage vessels under impact loads to promote the intrinsic safety development of hydrogen storage vessels. In this paper, a finite element analysis model is developed for simulating the dynamic responses of vessels under the impact of fragments. The influences of the number of winding layers, impact velocity, fragment mass, and fragment shape are investigated. The results show that fragment impact is a kind of local damage behavior with two typical stages of hitting and rebounding. The impact resistance of vessels increases with the number of winding layers. Impact velocity and fragment mass are positively related to deformation and damage. Conical fragments have stronger damage abilities, while spherical fragments cause greater deformation. [Display omitted] • The dynamic response and damage modes of vessels under impact were investigated. • The impact resistance of vessels increases with the number of winding layers. • Different factors have different effects on the damage and deformation of vessels. • System energy is mainly converted into internal energy. [ABSTRACT FROM AUTHOR]

In this paper, we report an innovative approach of using spark plasma sintering (SPS) combining with finite element modeling (FEM) to investigate the transient behavior of nuclear fuels. The temperature ramping rates of the SPS with special tooling can be controlled from 5 to 10 °C/s up to 500 °C/s, mimicking prototypical thermal profiles of the loss-of-coolant-accident (LOCA) and reactivity-induced-accident (RIA) events, respectively. The fresh UO 2 pellets with micron grain size are synthesized by SPS. Their fracture and fragmentation behaviors are investigated under transient thermal testing, and temperature-gradient and thermal-stress are calculated by FEM. The micron-sized fresh UO 2 displays good thermal shock stability and anti-cracking performance under the LOCA thermal test. Under simulated RIA conditions, the UO 2 fuels crack due to the stress induced by the large thermal gradient. The unique capability of SPS with controlled temperature ramping enables a cost-effective approach for rapid screening and high throughput evaluation of nuclear fuels under power transients. [ABSTRACT FROM AUTHOR]

In simulations involving fluid-structure interactions, the partitioned coupling approach allows calculating the fluid flow and the structural displacement using different solvers, which are coupled by a structure-to-fluid algorithm. This partitioned scheme can result in non-conforming meshes at the solid-fluid interface, especially when the fluid and the structure meshes contain elements of different characteristic sizes. In this context, a mesh-interpolation technique is required to transmit the nodal information from one mesh to the other. This paper focuses on comparing radial basis functions and k-nearest neighbours interpolations on fluid-structure interaction test cases. Indeed, those are fast and flexible techniques requiring no topological information other than relative distances between nodes, allowing a straightforward transfer of nodal data between non-conforming meshes. This feature is particularly favourable in the Particle Finite Element Method (PFEM), where remeshing procedures result in significant changes of the finite element discretisation at the fluid-structure interface. Accordingly, our contribution compares the interpolations in a PFEM/FEM partitioned scheme, using 2D and 3D benchmark problems. [ABSTRACT FROM AUTHOR]

In this paper, one non-iterative two-grid parallel stabilized finite element method based on overlapping domain decomposition is developed and investigated for the Stokes problem. The lowest-order finite element pairs P 1 − P 1 are utilized to approximate the velocity and pressure, respectively. The difference between a consistent and an under-integrated mass matrices is chosen as the stabilized term to circumvent the so-called inf-sup condition. Algorithm distributes legitimately residuals into local domains with a partition of unity. Error estimates are rigorously established. Theoretical results indicate that patches of diameter H | l n H | (| l n H | − l n | l n H |) or H | l n H | are sufficient to preserve optimal convergence rates with a proper configuration between the coarse mesh size H and the fine mesh size h in 2-D or 3-D case, respectively. Finally, some numerical experiments are reported to support our theoretical results. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to investigate the error analysis for the damped Boussinesq equation with the Ciarlet-Raviart mixed finite element method, focusing on achieving superconvergence. By employing a skillful mean technique and a high precision estimate of the bilinear element, as well as combining with projection and interpolation technique, we first obtain a superclose error estimate between interpolation of the exact solution and numerical solution. Subsequently, by applying an interpolation post-processing approach, we efficiently derive a global superconvergence result. Finally, several numerical results are presented to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

Supercritical water oxidation (SCWO) is well known as a promising end-of-pipe technology for treatment of hazardous wastes. Safety is undoubtedly the first concern as the SCWO should be operated under a harsh chemical and physical environment, including high temperature, high pressure, and high corrosive medium and plugging risk. This paper is the first report about a tube explosion incident that encountered during continuous SCWO treatment of industrial sludge. 3D imaging, Scanning Electron Microscope - Energy Dispersive Spectroscopy (SEM-EDS) and 3D finite element analysis are used to analyze the incident tube comprehensively. The results indicate that the incident tube was working at a hash corrosive environment of subcritical water and chloride, which leads to all of general, pitting and intergranular corrosions. Of which, the pitting is the most severe one that finally results to perforation. Then, leakage took place. Soon afterwards, the hard inorganic particle from sludge plugged the leaking pore for a second, but immediately split it as a big hole due to the local high pressure around the leaking pore. Finally, explosion occurred. Three lessons are drawn for the future safe design and operation of SCWO, i.e., selecting suitable pressure bearing material, checking regularly, and executing safety regulations. [Display omitted] [ABSTRACT FROM AUTHOR]

• A semi-analytical solution to incipient sliding contact on viscoelastic layered solids is proposed. • The spring-like interface between the coating and substrate is considered. • A two-step procedure is performed to verify the validity of the solution. • The influences of variation in parameters on the contact behaviors are analyzed. This paper presents a semi-analytical solution to the incipient sliding contact between a rigid sphere and a viscoelastic layer-elastic substrate with spring-like interface. In this solution, Papkovich–Neuber potentials in frequency domain are applied to calculate the influence coefficients (ICs) based on the surface and interface conditions; the elastic constant in the elastic solution is replaced by the creep function to cover the time-dependent characteristics of the viscoelastic layer; discrete convolution-fast Fourier transform (DC-FFT) is used to obtain the displacements and stresses caused by the external load; conjugate gradient method (CGM) is employed to compute the pressure on the top surface of the viscoelastic layer. The validity of the solution is verified by a previous method and the finite element method (FEM), where the relaxation and creep functions of the viscoelastic layer are expressed as Prony series. Influences of variations in parameters on the surface pressure, normal displacement and von Mises stress are analyzed by a parametric study of the time, relaxation time, relaxation modulus, stiffness coefficients, coating thickness and friction coefficient. The results indicate that this solution can predict the contact behaviors of viscoelastic layered half-space and may serve as a numerical experiment in research of coating materials. [ABSTRACT FROM AUTHOR]

In this paper, a combined scheme of edge/node-based smoothed finite element method (ENS-FEM) and the mixed interpolation of the tensorial components for the three-node triangular element (MITC3) named a ENS-MITC3 is developed to investigate the static and free vibration for functionally graded (FG) porous shells. The effective material properties of FG porous shells are estimated using the rule of mixture, which incorporates an additional term for porosity in the through-thickness direction. The improved first-order shear deformation theory (FSDT) is used to accurately describe the shear stress distributing evenly throughout the thickness and is zero on the top and bottom surfaces of the doubly curved shell. Using Hamilton's principle, the governing equation of FG porous shells is established. The obtained numerical results of a ENS-MITC3 are compared with other existing methods in the literature to show the effectiveness of the present method. Then, the effect of geometric parameters, porosity coefficients and power law indexes on the displacements and natural frequencies of FG porous curved shells are examined. [ABSTRACT FROM AUTHOR]