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Thin-walled tubular deployable composite boom (DCB) has gained significant attention due to its lightweight, simple structure and high packaging efficiency. The experimental and numerical simulation methods were employed in this paper to investigate the folding behavior of the DCB. Using T700/epoxy unidirectional reinforced prepreg as raw material, DCB specimens were prepared by the vacuum bag method. To complete the folding experiments of DCB specimens, a folding mechanism was designed and manufactured. Folding experiments of DCB specimens were conducted and folding moment versus rotational displacement curves were measured. In addition, a Finite Element Model (FEM) was established to predict the folding behavior of the DCB. Different failure criteria were considered in the numerical analysis, including the Tsai‐Hill criterion and maximum stress criterion. Prediction results using the FEM were compared with experimental results, and both sets of results were in good agreement. It is shown that the DCB can achieve the folding function without failure. The research results in this paper are of great significance to the practical engineering application of the DCB. [Display omitted] • Six tubular deployable composite boom specimens and a precise folding mechanism were designed and prepared. • Folding experiments were conducted to measure the folding moment and rotational displacement curves. • A finite element model for predicting the folding behavior of the tubular deployable composite boom was established. [ABSTRACT FROM AUTHOR]

A computationally efficient method to study the in-plane and out-of-plane dimensional instability of thin paper sheets under the influence of moisture changes is presented. The method explicitly resolves the bonded and the free segments of fibers in the sheet, capturing the effect of anisotropic hygroexpansion at the fiber level. The method is verified against a volumetric model. The importance of longitudinal fiber hygroexpansion is demonstrated in spite of the absolute value of longitudinal hygroexpansion being an order of magnitude lower than the transverse hygroexpansion component. Finally, the method is used to demonstrate the formation of macroscopic sheet curl due to a moisture gradient in structurally uniform sheets in the absence of viscoelastic or plastic constitutive behavior and through-thickness residual stress profiles. [ABSTRACT FROM AUTHOR]

• Elasticity and failure behaviors of the resin-coated aramid paper are analysed. • A novel segmented equivalent mechanical model of the material is proposed. • Equivalent mechanical parameters of multi-layer structure are derived theoretically. • Proposed model performs well in ultrasonic cutting simulation of Nomex honeycomb. • Difficulty of modelling and CPU time of simulation are reduced significantly. Nomex honeycomb, as the core part of sandwich structure, has been widely used in the aviation and aerospace industries. Ultrasonic cutting, as a technology that can reduce machining defects, has been highlighted in recent years, but some problems in the cutting process still need to be investigated significantly. Finite element method (FEM) offers an alternative way of in-depth understanding of the problems. However, the multi-layer structure of the Nomex honeycomb cell wall, which is the resin-coated aramid paper, makes it difficult to establish a detailed multi-layered finite element (FE) model at a macro-scale level. Therefore, a novel segmented material mechanical model, which is applicable to the equivalent single-layer model, is proposed based on the analysis of the mechanical behaviour of the multi-layer structure of the resin-coated aramid paper. Moreover, the calculating method of equivalent mechanical parameters of the multi-layer structure are proposed theoretically. The proposed method is first verified by FE models at a micro-scale level in both single-layer and multi-layer approaches. Additionally, simulations and experiments are performed to verify that the proposed method performs well in the simulation of ultrasonic cutting for Nomex honeycomb, and the difficulty of modelling and CPU time of simulation are reduced significantly. [Display omitted] [ABSTRACT FROM AUTHOR]

A novel higher-order multi-scale computational approach for efficient nonlocal gradient elasticity simulation of composite materials is proposed in this paper. Based on the use of decoupling technique, raw fourth-order nonlocal gradient equations with periodically oscillatory coefficients are decoupled as the new second-order multi-scale equations for reducing the continuity requirements when implementing multi-scale simulation. Next, a novel macro-micro coupled multi-scale computational model with higher-order corrected terms is rigorously devised for high-resolution multi-scale and nonlocal analysis of composite materials via multi-scale asymptotic analysis. Then, the local error analysis of higher-order multi-scale solutions in the point-wise sense illustrates that establishing higher-order asymptotic corrected terms plays a vital role in investigating the micromechanical mechanisms. Moreover, a rigorous global error estimation with an explicit rate of higher-order multi-scale solutions is first derived in the energy norm sense. In addition, an efficient multi-scale numerical algorithm is presented to effectively simulate nonlocal gradient elasticity problems of composite materials based on finite element method (FEM). And we also derive the convergence estimation of the proposed numerical algorithm. Finally, numerical experiments are conducted to gauge the efficiency and accuracy of the proposed higher-order multi-scale method. This paper offers a unified higher-order two-scale computational framework for enabling nonlocal gradient elasticity behavior simulation of composite materials. [ABSTRACT FROM AUTHOR]

In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope (the 4-simplex) and tetrahedral prism elements. More generally, our objective is to construct high-order finite element function spaces that maintain conformity with infinite-dimensional spaces of a carefully chosen de Rham complex in four dimensions. This paper is a natural extension of the companion paper entitled "Conforming finite element function spaces in four dimensions, part I: Foundational principles and the tesseract" by Nigam and Williams (2024). In contrast to Part I, in this paper we focus on two of the most popular elements which do not possess a full tensor-product structure in all four coordinate directions. We note that these elements appear frequently in existing space-time finite element methods. In order to build our finite element spaces, we utilize powerful techniques from the recently developed 'Finite Element Exterior Calculus'. Subsequently, we translate our results into the well-known language of linear algebra (vectors and matrices) in order to facilitate implementation by scientists and engineers. [ABSTRACT FROM AUTHOR]

The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This is especially true for high-order, mixed finite element methods which often must satisfy an inf-sup condition in order to ensure stability. With this in mind, the primary objective of this paper and a companion paper is to provide a wide range of explicitly stated, conforming, finite element spaces in four dimensions. In this paper, we construct explicit high-order conforming finite elements on 4-cubes (tesseracts); our construction uses tools from the recently developed 'Finite Element Exterior Calculus'. With a focus on practical implementation, we provide details including Piola-type transformations, and explicit expressions for the volumetric, facet, face, edge, and vertex degrees of freedom. In addition, we establish important theoretical properties, such as the exactness of the finite element sequences, and the unisolvence of the degrees of freedom. [ABSTRACT FROM AUTHOR]

The mechanical response of three different structural core sandwich panels in out-of-plane compression and shear has been analyzed. Specific core shapes examined are arc-tangent, wavy trapezoidal and hemispherical. Unit cells consisting of representative elements of the core attached to face sheets were selected for analysis. Both face sheets and core were assumed made from paper. Finite element analysis employing large deformation and rotations and orthotropic elastic–plastic behavior was used. The results show that the arc-tangent and trapezoidal cores are prone to collapse by extensive bending and buckling, whereas the hemispherical core behaved more stably in compression and shear. Core sheets with a hemispherical shape were prepared from copy paper sheets in a specially designed forming machine. Sandwich test specimens were prepared from this core and tested in out-of-plane compression, and the load-displacement response was compared to predictions from finite element simulations. The experimental and finite element results were consistent. [ABSTRACT FROM AUTHOR]

In order to solve the deficiencies of traditional board-level assembly CubeSat, such as low modularity, complex assembly process and poor scalability, a sandwich module assembly structure and method with no drive components is proposed, which can achieve quick connection and flexible assembly between modules. First, the proposed CubeSat standard module can be compatible with the standard interface of traditional CubeSat. The 4-in-1 interface of Mechanical-Electrical-Thermal-Data does not occupy the internal space of the standard module, and the electrical and thermal interfaces meet the requirements of CubeSat in-orbit work. Secondly, in order to improve the reliability of the connection between the modules, a plug-in connection scheme of the mechanical interface was designed. Finally, a genetic algorithm was used to optimize the interface size, so that it has better plug-in performance. The simulation results show that the performance of the male interface of titanium alloy material is the best, and the error between the finite element analysis and genetic algorithm results is less than 4.8 %, which is consistent with the actual tensile test results of the optimized prototype, and meets the mechanical requirements of the launch process and space orbit operation for CubeSat. The test results can guide production and provide a reference for subsequent engineering applications of CubeSat modular assembly. • In this paper, a standardized modular assembly method of CubeSat sandwich structure is designed. The assembly structure does not include driving parts, is simple in form, can be quickly connected, is flexible in assembly mode, and does not occupy the internal space of the standard module. • A standard 4-in-1 connection device was designed in this paper, including four interfaces: mechanical, electrical, thermal and data, which can achieve "plug and play". • This paper uses genetic algorithm to optimize the structure of the mechanical connection male joint, and obtains the optimal configuration of the male joint. This ensures the reliability, firmness and stability of mechanical connections, and meets the mechanical requirements of CubeSats during launch and in orbit. [ABSTRACT FROM AUTHOR]

The tensile response of dense fiber-based materials like paper or paperboard is mainly dependent of the properties of the fibers, which store most of the elastic energy. In this paper, we investigate the influence of geometrical and material parameters on the mechanical response of the pulp fibers used in paper manufacturing. We developed a three-dimensional finite element model of the fiber, which accounts for microfibril orientation of cellulose fibril, and the presence of lignin in the secondary cell wall. The results showed that the change in the microfibril orientation upon axial straining is mainly a geometrical effect, and is independent of the material properties of the fiber, as long as the deformations are elastic. Plastic strain accelerates the change in microfibril orientation and thus makes it material-dependent. The results also showed that the elastic modulus of the fiber has a non-linear dependency on microfibril angle, with elastic modulus being more sensitive to the change of microfibril angle around small initial values of microfibril angles. Based on numerical results acquired from a 3D fiber model supported by available experimental evidence, we propose an anisotropic-kinematic hardening plasticity model for a fiber within a beam framework. The proposed fiber model is capable of reproducing the main features of the cyclic tensile response of a pulp fiber, such as stiffening due to changing microfibril angle. The constitutive model of the fiber was implemented in a finite-element model of the fiber network. By using the fiber network model, we estimated the level of strain that fiber segments accumulate before the typical failure strain of the entire network is reached. [ABSTRACT FROM AUTHOR]

In this paper, we consider a finite element approximation of an optimal control problem governed by a time fractional wave equation. We first prove the well-posedness and regularity of the optimal control problem. Furthermore, we discuss the fully discrete scheme and analyze its stability and a priori error estimate. Numerical experiments are given to illustrate the theoretical findings. • The weak solution to the time fractional wave equation is studied under low regular data. • The well-posedness and regularity of the optimal control problem are proven. • Numerical schemes exist the first-order and second-order accuracy in time and space respectively. [ABSTRACT FROM AUTHOR]

The electrochemical discharge machining (ECDM) is an advanced and promising technology for fabricating micro structures. This method is effectively applicable for non-conductive hard and brittle materials micromachining, such as glass and ceramics. However, the ceramics high melting point and intense heat exchange effects during microchannel fabrication lead to the easy dissipation of thermal energy and the difficulty in processing. To address this issue and expanded the ECDM processing range. This paper dedicated to the investigation of the material removal mechanism and process characteristics for the alumina ceramic surfaces microchannels preparation. Firstly, this study explained the difference of the ECDM critical applied voltage and gas film generation mechanism by analyzing the volt-ampere characteristic curve of 20 wt% NaOH electrolyte with a tool immersed depth of 2 mm and 10 mm respectively. Then, a thermal removal finite element model (FEM) for ECDM was developed. The heat cumulative and intermittent cooling effects applied on the alumina ceramic surface dominated the materiel removal. Additionally, it can be found that the microchannel machining accuracy and bottom surface quality depended on the Gaussian heat source characteristics, gas film formation mechanism, heat accumulation effect, and temperatures spatial and temporal distribution. And a series of single factor experiments for evaluating the parametric studies such as the effect of discharge frequency, applied voltage, duty ratio and tool feed rate on the fabricated microchannel performance are executed. Finally, the complex three-dimensional structures of cross microchannel grid and zigzag microchannel array with variable depth were successfully fabricated on aluminum oxide ceramic surface. Notably, the results highlighted and enriched the ECDM stability, consistency and applicability for alumina ceramic surface microchannel fabrication. [ABSTRACT FROM AUTHOR]

In this paper we use the weighted discontinuous Galerkin finite element method to solve the dual-porosity-Brinkman coupling model. The dual-porosity model describes fluid flow in a dual-porosity medium composed of matrix and microfractures, while the Brinkman equation describes fluid flow in hydraulic fractures or conduits containing "debris filling" or "proppant filling". The two models are coupled by the four physically effective interface conditions, which are constructed based on the fundamental properties of the dual-porosity model and the Brinkman-Darcy model. We provide a weighted discontinuous discrete scheme for the model and derive the optimal error estimates. Through numerical experiments, we verify the properties of the model and the advantages of the numerical method, such as the optimal convergence rate of the numerical solution and the simulation of the flow characteristics around hydraulic fractures and conduits. [ABSTRACT FROM AUTHOR]

• The compressive buckling analysis of cracked nanosheets is performed by XFEM, considering small-scale effect. • The contribution of this work is the study of buckling of nanosheets in the presence of a crack. • The studied variables include small-scaling parameter, crack length, nanosheet dimensions, and boundary supports. • The results show that the cracking phenomenon and the increase of its length intensify the nonlocal effect. The process used to produce nanosheets may cause damage such as cracks in them. These cracks can adversely affect the buckling capacity of nanosheets. The main contribution of this research endeavor is to extend the previous studies on undamaged nanosheets to the cracked ones concerning the size-dependent effect. On the nanoscale, the assumption of material continuity, which is the fundamental assumption in classical continuum mechanics, is not valid. In this case, nonlocal non-classical theories are employed to analyze nanosheets. The present paper examines the nonlocal buckling of cracked graphene sheets under uniaxial and biaxial loads. To this end, the governing equations are developed based on the first-order shear deformation theory and using Eringen's nonlocal elasticity theory. Moreover, cracked nanosheets with various boundary conditions are analyzed via the extended finite element method. The variables under study are the small scaling parameter, crack length, nanosheet dimensional parameters, and support conditions. The results indicate that while the small scaling parameter reduces the critical buckling capacity of nanosheets, the presence of a crack in the nanosheet and the increase in its length intensify the nonlocal effect. In addition, as the aspect ratio of the nanosheet increases from one, the nonlocal effect decreases gradually. The small-scale effect increases by constraining the edges of the cracked nanosheets. [ABSTRACT FROM AUTHOR]

• A fully coupled three-dimensional THMC model (DEHydrate) is developed for simulating hydrate dissociation. • The numerical results obtained from the proposed model are in good agreement with those from other simulations. • Only a small fraction of gas produced from radial hydrate dissociation is collected from the wellbore. • The model provides an effective tool to predict the mechanical behavior during hydrate dissociation. Due to high energy density and huge reserves, many trial projects worldwide have been conducted to exploit natural gas hydrates (NGH). However, most of them did not meet the commercialization requirements because of submarine hazards, low gas production and sand production. Therefore, it is important to investigate the NGH dissociation process. In this paper, a fully coupled multiphase, strongly nonlinear three-dimensional (3D) thermal–hydro–mechanical–chemical model (DEHydrate) is developed to consider the multiphysics behaviours including solid-liquid-gas multiphase flow, heat transfer, NGH phase transition and solid deformation during hydrate dissociation. The model is solved using a fully implicit finite element method. The gas-liquid flow and heat transfer are simulated by low-order elements while the solid deformation is calculated by high- or low-order elements. The behaviours of the multiphase seepage and geomechanics are fully coupled and the physical properties of the reservoir are updated iteratively based on changes in pressure, temperature and displacement. The DEHydrate simulator provides an effective tool to predict the evolution of reservoir mechanical behavior during hydrate dissociation, including transient pressure, temperature, displacement and stress in the reservoir, as well as multiphase saturation, hydrate dissociation rate/mass and gas production rate/mass. During the NGH dissociation, the initial stage exhibits a rapid dissociation rate of up to 206.23 kg/(d·m) for NGH layer with a length of 600 m and a thickness of 22 m, which subsequently decreases to 11.64 kg/(d·m). Only a small portion of the gas generated during NGH dissociation is collected at the wellbore (approximately 35.6 % after 100 days), while the majority remains trapped in the reservoir. In addition, throughout NGH dissociation, the reservoir matrix continues to move toward the wellbore in the horizontal direction. While in the vertical direction, the reservoir matrix below the wellbore moves upwards, with decreasing displacement due to low-pressure diffusion, while the reservoir matrix above the wellbore moves downwards, with increasing displacement. The largest displacements occur near the wellbore during the early stage of NGH dissociation, while in the late stage, the largest displacements occur above the reservoir. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a lowest-order locking-free weak Galerkin (WG) finite element scheme for the grad-div formulation of linear elasticity problems. The scheme uses linear functions in the interior of mesh elements and constants on edges (2D) or faces (3D), respectively, to approximate the displacement. An H (d i v) -conforming displacement reconstruction operator is employed to modify test functions in the right-hand side of the discrete form, in order to eliminate the dependence of the L a m e ´ parameter λ in error estimates, i.e., making the scheme locking-free. The method works without requiring λ ‖ ∇ ⋅ u ‖ 1 to be bounded. We prove optimal error estimates, independent of λ , in both the H 1 -norm and the L 2 -norm. Numerical experiments validate that the method is effective and locking-free. [ABSTRACT FROM AUTHOR]

The present paper investigates static deformation, free vibration, and patch loading response of one-dimensional (1D) hexagonal quasicrystal (QC) plates by the symplectic method. The Hamiltonian system is established by utilizing the variational principle, and then the symplectic analytical solutions of the extended displacement and traction vectors are obtained with simply supported boundary conditions. Numerical examples illustrate the effect of stacking sequence on the bending deformation of multilayered plates made up of QC and crystal materials. Moreover, the effects of the patch region, frequency, and phonon-phason coupling elastic coefficients on the corresponding problems are investigated. The symplectic analytical solutions presented in the article can be further used as benchmarks for numerical methods, such as the finite integral transformation and finite element methods. • The Hamiltonian system for dynamic equations of 1D hexagonal QC is established using the variational principle. • Analytic solutions of 1D hexagonal QC are rationally derived by the symplectic method. • The static deformation, free vibration, and patch loading response of 1D hexagonal QCs plates are investigated. • Some numerical tests are illustrated to justify the symplectic method. [ABSTRACT FROM AUTHOR]

• An accurate algorithm is presented for transcranial magneto-acoustic-electrical stimulation. • Unstructured mesh used in mesh discretization facilitates the pre-processing. • Our algorithm possesses higher calculation accuracy and faster convergence rate. • The developed model can achieve superior computational efficiency. • The proposed method is insensitive to mesh distortion. In this paper, a numerical method for simulating transcranial magneto-acoustic-electrical stimulation (TMAES) is presented. The smoothed finite element method (SFEM) is applied to calculate the magnetic field and the Rayleigh integral (RI) is used for solving the ultrasonic field. Three-node triangular and four-node tetrahedral elements are set as the background cells for constructing the smoothing domains (SDs). A gradient smoothing technique (GST) is applied over each SD to obtain the magnetic flux density. The discretized system equations are obtained by using the generalized smoothed Galerkin weakform. To solve the sound pressure, the ultrasonic transducer is discretized into a series of micro-elements. The acoustic pressure in the problem domain is then equal to the superposition of that generated by the individual micro-element. Finally, the current density can be calculated by the magneto-acoustic coupling effect. Numerical examples demonstrate that SFEM can improve accuracy, convergence rate, and efficiency to 10, 1.8, and 4 times those of FEM, respectively. In the calculation of coupled fields, SFEM-RI also improves the accuracy by 2.5 times. Additionally, the presented method possesses the property of insensitivity to mesh distortion. [ABSTRACT FROM AUTHOR]

In our previous work, the coaxial electrostatic spinning method was applied to construct nanofiber/SiBCN ceramic aerogel with an elytra-mimetic structure. The material presented excellent mechanical, insulation, oxidation resistance, and other properties. Based on preliminary experiments and literature reports, the integrated heat transfer behavior of nanofiber/SiBCN composite ceramic aerogels in high-temperature environments was affected by several factors, such as coaxial fiber size properties, fiber particle content, interactions, and spatial distribution. Moreover, the above factors overlapped and interacted with each other, and it was hard to generalize a clear law of action through traditional experiments and characterization. Therefore, the paper constructed a representative volume unit (RVE) model based on the complex spatial distribution characteristics of composite aerogels, using fractal theory, Rosseland equation theory, and multiphase model theory. This paper investigated the fiber and particle content, the size characteristics of the coaxial fibers, and the overall heat transfer process in high-temperature environments using the finite element method. The finite element simulated the effective thermal conductivity of multiphase aerogel composites under multiple parameters, such as fiber occupancy, fiber core-shell diameter ratio, temperature, and heat transfer mode. We obtained the property parameters of the complex composition of the material through fractal theory. The model was combined with finite elements to study the fiber particle content, the size characteristics of coaxial fibers, and the integrated heat transfer process in high-temperature environments. The fibers improved the absorption and reflection of thermal radiation with increasing fiber mass fraction, leading to improved ability of ceramic fiber aerogel to extinguish light. The fibers had a larger area to absorb and reflect thermal radiation. Based on the excellent extinction ability of SiC fibers, the composite ceramic aerogel had improved thermal performance at a specifically fiber-to-shell diameter ratio through a comprehensive multifactor simulation analysis. [ABSTRACT FROM AUTHOR]

Poly-(meta-phenylene isophthal-amide) (PMIA) is regarded as an ideal insulating medium for electronic devices owing to its excellent chemical stability and breakdown strength. However, the poor thermal conductivity limited the application under complex electrical-thermal environment. In this work, the size-graded AlN/PMIA composite papers were fabricated, with a multi-scale structure of matrix and fillers, and maintain qualified stability, mechanical strength and electrical insulation properties. With doping 40 wt% of 10 μm AlN and 10 wt% of 200 nm AlN, the optimum paper with in-plane (λ ∥) and out-of-plane (λ ⊥) of optimal paper reached thermal conductivity of 17.3 W/(mK) and 1.96 W/(mK) is obtained, and the breakdown strength increased to 69 kV/mm. The improvement mechanism brought by size-graded fillers was further revealed by the co-simulation of finite element method and loop nesting algorithm. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code. [Copyright &y& Elsevier]

Abstract: A finite element procedure, developed in order to account for the effect of high anisotropy at folding of coated papers, is presented. The anisotropic behaviour (with very low stiffness in the thickness direction) is modelled using stiff structural elements (trusses and beams). The numerical results indicate that high elastic anisotropy leads to lower strain levels at folding than reported in previous analyses where this effect was not accounted for. High plastic anisotropy, on the other hand, will contradict this result. [Copyright &y& Elsevier]

Folding of coated paper is examined numerically using the finite element method. Particular emphasis is put on the behaviour of field variables relevant for cracking of the coating layers. In the numerical analysis, the basepaper is modelled as an anisotropic elastic–plastic material (both elastic and plastic anisotropy is accounted for) while the constitutive behaviour of the coating layers are approximated by classical (Mises) elastoplasticity. The numerical results suggest, among other things, that particular forms of plastic anisotropy can substantially reduce the maximum strain levels in the coating. It is also shown that delamination buckling, in the present circumstances, will have a very small influence on the strain levels in the coating layer subjected to high tensile loading. [Copyright &y& Elsevier]

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]

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 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]

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: The rolling of a cylindrical drum on a stack of separate paper sheets is studied using the finite element method. A two-dimensional model under plane strain conditions is considered. The material of the sheets is modelled by a linearly elastic orthotropic constitutive law. The friction between the various contacting surfaces is modelled by the conventional Coulomb''s law. As a result of the FEM-calculations, the time development of the displacements, stresses and strains of the paper layers is obtained. The slip behaviour at the various contacting surfaces is presented. The micro-slip pattern of the contacting surfaces in the nip area and, particularly, at the trailing edge of the nip, seems to be the main reason for the tightening effect of the nip. The results are compared to the corresponding results for a solid elastic block under the rolling cylinder. [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]

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]