Search

• The functional relationship between the heat transport coefficients is explored. • The well-posedness of the Guyer–Krumhansl equation is proved. • The uniform stabilization property is proved. • The results are supported by a numerical demonstration. The Guyer–Krumhansl heat equation has numerous important practical applications in heat conduction problems. In recent years, it turned out that the Guyer–Krumhansl model can effectively describe the thermal behavior of macroscale heterogeneous materials. Thus, the Guyer–Krumhansl equation is a promising candidate to be the next standard model in engineering. However, to support the Guyer–Krumhansl equation's introduction into the engineering practice, its mathematical properties must be thoroughly investigated and understood. In the present paper, we show the basic structure of this particular heat equation, focusing on the differences in comparison to the Fourier heat equation obtained when (τ q , μ 2) → (0 , 0). Additionally, we prove the well-posedness of a particular, practically significant initial and boundary value problem. The stability of the solution is also investigated in the discrete space using a finite difference approach. [ABSTRACT FROM AUTHOR]

A simple yet effective material model was proposed by Zhao et al. (2019) and demonstrated to be capable of modeling the shape transformations of various planar and three-dimensional material samples programmed with the so-called "hard-magnetic soft materials". Based on the aforementioned material model, this paper aims to further accomplish the following two tasks. First, a detailed analysis is performed to investigate the impact of the multiplicative volumetric-distortional split of the deformation gradient tensor applied to the material magnetic energy. Through a trivial boundary value problem, the impact of the volumetric-distortional split is quantified for the strictly incompressible material and the nearly incompressible material, respectively. Second, a finite element procedure based on the three-field variational principle, or the mixed displacement-Jacobian-pressure formulation (Simo et al., 1985; Simo and Taylor, 1991), is developed for the magnetoelastic materials programmed with complex magnetic patterns. Even though the finite element formulation based on the three-field variational principle is a standard and widely adopted technique in the literature, the introduction of the multiplicative split of the deformation gradient into the magnetic energy makes the derivation of the specific finite element terms less trivial. In this work, the finite element formulation and the consistent linearization of the coupled system are derived in detail for the Newton–Raphson iterations. Through the theoretical analysis and numerical examples, the approach based on the distortional part of the deformation gradient is shown to possess computational advantages over its counterpart in the context of a relatively simple penalty method. Moreover, the convergence behaviors of the finite element simulations and the impact of the finite element spaces on the pressure oscillation are analyzed in detail. [ABSTRACT FROM AUTHOR]

Thermal expansion behaviors of carbon fiber/epoxy plain woven composites were experimentally and numerically studied in this paper. The thermal strains and linear coefficient of thermal expansion (CTE) of plain woven composites were measured by a classic dilatometer. Based on the periodical displacement and temperature boundary conditions, two-scale finite element models, i.e. the micro-scale and meso-scale representative volume elements (RVEs) were established to analyze the thermal expansion behaviors of carbon fiber yarns and plain woven composites, respectively. In addition, a neat epoxy resin (NER) model with the same geometrical shape as the filled epoxy resin (FER) was presented to compare their thermal expansion differences. From the results it could be found that the glass transition temperatures of epoxy resin and carbon fiber yarns had significant effects on the thermal expansion behaviors of plain woven composites. The interlacing network of yarns could effectively restrict the FER to make further thermal expansion. The special structure effects of plain woven composites led to nonuniform distributions of thermal stress/strain, which mainly showed that the regions with higher fiber volume fraction produced higher thermal stress/strain. The analyses methods this paper presented can be also used for thermal expansion researches of other complex structure composites. [ABSTRACT FROM AUTHOR]

Isogeometric collocation has emerged as an efficient numerical technique for solving boundary value problems and is a potential alternative for Galerkin based Isogeometric methods. In this investigation, Isogeometric collocation has been proposed for the linear static bending analysis of laminated composite plates governed by Reissner–Mindlin theory. Three formulations are presented in this paper namely, standard primal formulation, mixed formulation and a locking-free primal formulation. The standard primal formulation adopts displacements and rotations as unknown field variables. Mixed formulation considers displacements, rotations and transverse shear forces as the unknown field variables. Locking-free primal formulation is a rotation-free formulation with displacements and transverse shear strains as the unknown field variables. Results for benchmark problems on bending of rectangular laminated composite plates are obtained and compared with the ones existing in the literature. The three formulations of Isogeometric collocation presented in this paper are assessed in terms of accuracy and the computational time required to assemble and solve the problem. [ABSTRACT FROM AUTHOR]

Gaussian elimination with no pivoting and block Gaussian elimination are attractive alternatives to the customary but communication intensive Gaussian elimination with partial pivoting 1 provided that the computations proceed safely and numerically safely , that is, run into neither division by 0 nor numerical problems. Empirically, safety and numerical safety of GENP have been consistently observed in a number of papers where an input matrix was pre-processed with various structured multipliers chosen ad hoc. Our present paper provides missing formal support for this empirical observation and explains why it was elusive so far. Namely we prove that GENP is numerically unsafe for a specific class of input matrices in spite of its pre-processing with some well-known and well-tested structured multipliers, but we also prove that GENP and BGE are safe and numerically safe for the average input matrix pre-processed with any nonsingular and well-conditioned multiplier. This should embolden search for sparse and structured multipliers, and we list and test some new classes of them. We also seek randomized pre-processing that universally (that is, for all input matrices) supports (i) safe GENP and BGE with probability 1 and/or (ii) numerically safe GENP and BGE with a probability close to 1. We achieve goal (i) with a Gaussian structured multiplier and goal (ii) with a Gaussian unstructured multiplier and alternatively with Gaussian structured augmentation. We consistently confirm all these formal results with our tests of GENP for benchmark inputs. We have extended our approach to other fundamental matrix computations and keep working on further extensions. 1 Hereafter we use the acronyms GENP , BGE , and GEPP . [ABSTRACT FROM AUTHOR]

This paper presents an approach for co-state initialization which is a critical step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories typically result in two-point boundary-value problems and are solved by single- or multiple-shooting numerical methods. Accurate initialization of the co-state variables facilitates the numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by the so-called pseudo-equinoctial and three-dimensional finite Fourier series shape-based methods to estimate the initial values of the co-states. The performance of the approach for two interplanetary rendezvous missions from Earth to Mars and from Earth to asteroid Dionysus is compared against three other approaches which, respectively, exploit random initialization of co-states, adjoint-control transformation and a standard genetic algorithm. The results indicate that by using our proposed approach the percent of the converged cases is higher for trajectories with higher number of revolutions while the computation time is lower. These features are advantageous for broad trajectory search in the preliminary phase of mission designs. [ABSTRACT FROM AUTHOR]

The paper presents results of an investigation into mixed convection in a vertically oriented microchannel with slip boundary conditions. Solutions of the problem were obtained analytically and using a numerical approach based on the Lattice Boltzmann method (LBM). The solution yields relations, which enable estimating velocity and temperature profiles and the Nusselt number as functions of the Knudsen, Rayleigh and Prandtl numbers. It was shown that Knudsen number effects are prevailing in the vicinity of the wall, whereas near the centerline of the channel effects of the Rayleigh number are stronger. If the Rayleigh numbers are high, velocity profiles demonstrate M-shapes with a point of minimum at the channel centerline, whereas temperature profiles flatten so that the fluid temperature in the channel cross-section tends to the wall temperature. The temperature jump magnitude on the wall is dependent on the Prandtl number value and decreases with the increasing Prandtl numbers. For almost all combinations of the parameters considered in this paper, higher Knudsen numbers entail heat transfer deterioration except for the case of Pr = 10 and Ra = 100. Increasing the Knudsen number diminishes hydraulic resistance for low Rayleigh numbers, but for high values of the Rayleigh numbers the trend is reversed. It was shown that mixed convection in microchannels can be successfully simulated using the LBM methodology, whose deviation from the analytical solution and is less than 1%. [ABSTRACT FROM AUTHOR]

In this paper the regularities and criteria for the use of the linear theory of coupled thermoelasticity are determined. In this paper we considered axisymmetric problem of coupled thermoelasticity. For which a solution is obtained in closed form. Also, using the method of singular integral equations, boundary value problems for two-dimensional medium with curvilinear boundaries are solved. Numerical results are also presented. [ABSTRACT FROM AUTHOR]

The flexural response of laminated composite and sandwich beams/plates under static distributed loading, classical and non-classical boundary conditions (simply-supported, cantilever and propped-cantilever) and geometric/constitutive heterogeneity of layers is analysed. As structural models, a recently developed equivalent single-layer zig-zag model by the authors, a discrete-layer model and a sublaminate model developed from it in this paper are used. Their contribution is to consider the continuity of the transverse normal stress and its through-thickness gradient at layer interfaces, as prescribed by the elasticity theory in addition to kinematic and transverse shear stress interlayer continuity customary considered in the literature. To this purpose, a piecewise variation of the three displacement components is adopted. The zig-zag amplitude expressions are obtained in closed-form from the enforcement of stress continuity conditions. To be refined without affecting costs, the equivalent single-layer model has variable kinematics and just five unknowns. Instead, sublaminate and discrete-layer models are refined by increasing the number of computational layers and variables. The aim of this paper is to assess whether the equivalent single-layer model having a computational cost comparable to that of classical models can be as accurate ad discrete-layer and sublaminate models. Benchmarks are presented, for which exact elasticity and approximate solutions are available for comparisons in literature. It is illustrated the utility of considering a variable kinematics for obtaining accurate stress predictions from constitutive equations and the transverse normal deformability for keeping equilibrium. The equivalent single-layer model is shown as accurate as discrete-layer and sublaminate models in all cases examined. [ABSTRACT FROM AUTHOR]

This paper reports a multiscale asymptotic analysis and computation for predicting heat transfer performance of periodic porous materials with radiation boundary condition. In these porous materials thermal radiation effect at micro-scale have an important impact on the macroscopic temperature field, which is our particular interest in this study. The multiscale asymptotic expansions for computing temperature field of the problem are constructed, and associated explicit convergence rates are obtained on some regularity hypothesis. Finally, the corresponding finite element algorithms based on the multiscale method are brought forward and some numerical results are given in details. The numerical tests indicate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper. [ABSTRACT FROM AUTHOR]

Based on the dynamic matrix control (DMC) idea, a method is established to simultaneously estimate boundary heat flux for unsteady heat conduction system in this paper. The measured temperature information at two measured points in the internal system is utilized to simultaneously determine transient heat flux q 1 ( t ) and q 2 ( t ) at two boundaries in the system. The algorithm adopts step response function to describe dynamic relationship of the system, without prior supposing the surface heat flux in the next period, and then the boundary heat flux at the present moment is inversed simultaneously through rolling optimization. In order to give attention to both the stability of inversion results, the inversing heat flux q 1 ( t ) and q 2 ( t ) are regularized respectively using different regularization parameters α 1 and α 2 . A method of same temperature discrepancy curve (STDC) is designed to estimate the optimal values ( α 1 ) opt and ( α 2 ) opt of regularization parameters according to discrepancy principle. Numerical experiments are divided into two parts. First of all, compared with the sequential function specification method (SFSM), the effects of the future time steps as well as the measured temperature error on simultaneously inversion results of the boundary heat flux are investigated. Results show that the DMC inversion method established by this paper can use smaller future time steps r to simultaneously estimate transient boundary heat flux of the system, and obviously improve the anti-interference of measured noise. Second, the validity of the inversion results obtained by the proposed method is discussed respectively by cases with different sizes and changing rules of boundary heat fluxes as well as different measured locations. And by comparing with the traditional centralized regularization (CR), the necessity of respectively regularization for each inversing heat flux is confirmed by using different regularization parameters. [ABSTRACT FROM AUTHOR]

The higher-order gradient plasticity theory is successful in explaining the size effects encountered at the micron and submicron length scale. Due to the incorporation of spatial gradients of one or more internal variables in these theories and the associated non-classical boundary conditions, special types of elements in the finite element method maybe necessary. This makes the numerical implementation of this higher-order theory not straightforward. In this paper, a robust but straightforward numerical implementation of higher-order gradient-dependent plasticity theories is presented. The novelty of this paper is in (1) the application of the meshless methods, particularly the moving weighted least square method, combined with the finite element method for the numerical computation of plastic strain gradients, and (2) the numerical implementation of different types of higher-order microscopic boundary conditions at internal/external surfaces, interfaces, and moving elastic–plastic boundaries. The proposed numerical implementation algorithms can be easily adapted in the implementation of any form of higher-order gradient-dependent constitutive models. Examples of applying the current numerical approach is demonstrated for capturing mesh-objective shear band formation and size effect and boundary layer formation in thin films on elastic substrates and metal matrix composites with embedded elastic inclusions through the consideration of stiff, intermediate, and soft interfaces. [ABSTRACT FROM AUTHOR]

Highlights • An analytical solution is proposed for a lined tunnel at a shallow depth. • Accurate zones and 5% error zones for stresses and displacements are defined. • The mutual influence between the liner and the geomaterial is included. Abstract In this paper, we present a solution for the sectional estimation of the stress and displacement fields of a liner and a geomaterial near a shallow buried tunnel. The complex variable method and the discrete Fourier transform are employed in the analytical derivation. The initial boundary conditions are the nonexistence of external loads acting on the liner interior and a Fourier curve obtained by fitting the displacement along the liner interior. Stress and displacement are continuous along the excavation line. In the verification, the stress and displacement fields within the excavation line obtained by the analytical solution agree well with the numerical results. Accuracy decreases as the spatial distance between the geomaterial and the excavation line increases, and the 5% error zones are defined. The accuracy of the solution would fall greatly out of these error zones. In another word, the analytical solution is not a general solution for the whole liner–geomaterial entity, but could serve as a quick sectional estimation, and is suitable for a variety of external loads on the ground surface. [ABSTRACT FROM AUTHOR]

Abstract Distributions of Monge type are a class of strongly regular bracket-generating distributions introduced by I. Anderson, Zh. Nie and P. Nurowski. Their symbol algebras prolong to simple graded Lie algebras, thus allowing one to associate a parabolic geometry to any given Monge distribution. This article is devoted to the classification problem for homogeneous models of Monge distributions of type C 3 in dimension eight, and is complementary to a paper by I. Anderson and P. Nurowski. The general classification algorithm, as well as most of its application to the particular problem, are joint work with Ian Anderson. [ABSTRACT FROM AUTHOR]

Abstract We present a computational framework for the treatment of shear localization in metallic materials under dynamic loading, based on the integration of a shear band tracking strategy into an explicit 3D finite element formulation with embedded weak discontinuities. Within this computational framework, an embedded shear band's mid-surface is represented by an iso-surface of a level set function, which is obtained by solving a heat-conduction type boundary value problem (BVP). The solution of this BVP is carried out either globally over the entire problem domain, or locally at the level of individual elements in the mesh. In this paper, we present a detailed comparison of these global and local algorithmic implementations of the shear band tracking strategy. Numerical results obtained using these two implementations, and using a simplified formulation without shear band tracking, are presented and compared. Moreover, we compare the computational efficiency and parallel scaling performance of the local and global implementations. This comparative study shows that both implementations can simulate the initiation of two independent shear bands and their propagation past each other without merging, whereas only the global implementation can successfully simulate the merging of two branches of a single shear band. This study also confirms that the global implementation is more computationally intensive, since it requires a global system of linear equations associated with the level set BVP to be solved at each time step. Both implementations exhibit very good scalability in domain decomposition-based parallel simulations. Highlights • A 3D FEM formulation for shear localization under dynamic loading is presented. • A weak-discontinuity approach is used to embed shear bands into the FEM mesh. • A level set method is used to track embedded shear bands as they propagate. • Different tracking strategies are compared, with the aid of dynamic experiments. • Results show the importance of ensuring the continuity of propagating shear bands. [ABSTRACT FROM AUTHOR]

Abstract This paper establishes an analysis model to study the vibration behavior of a cracked laminated composite beam with uniform rectangular cross-section based on the Jacobi-Ritz method and the first-order shear deformation theory (FSDT). The boundary conditions of both ends of the cracked laminated beam are modeled as the elastic spring and the beam is divided into two parts by the crack section. The continuous conditions at the connecting face are modeled by the inverse of the flexibility coefficients of the fracture mechanics theory. Ignoring the influence of boundary conditions, displacements admissible functions of cracked laminated beam can be set up as Jacobi orthogonal polynomials. The accuracy and robustness of the present method are evidenced through comparison with previous literature and the results achieved by the finite element method (FEM). Numerical examples are given for free vibration analysis of cracked laminated composite beams with various boundary conditions, which may be provided as reference data for future study. [ABSTRACT FROM AUTHOR]

• We consider a thermoelastic medium with a rigid thread. • We derive new regularized boundary integral equations. • We propose analytic approach for their solution. The paper presents a novel approach for analytic modeling and numerical analysis of spatial problems of thermoelasticity for isotropic solids containing thread-like nondeformable inhomogeneities. The inhomogeneity is removed from consideration as a geometric object, and its influence on the continuum is replaced by sought functions (of heat flux and mechanical forces) distributed along some line (the midline of inhomogeneity) inside the medium. The corresponding integral equations are derived and it is shown that the boundary conditions in this case results in the ill-posed boundary-value problem. A method for regularization of these integral equations is proposed, which allows obtaining an approximate (with arbitrary predetermined accuracy) solution of the problems of thermoelasticity for solids with thread-like inhomogeneities. An analytical approach to solving the obtained equations on the basis of Legendre polynomials is developed. Based on the performed numerical analysis the paper substantiates reliability, convergence and accuracy of the proposed method for the analysis of thermoelastic equilibrium of solids with nondeformable thread-like inhomogeneities. [ABSTRACT FROM AUTHOR]

In this paper a Powell–Sabin finite-element (PS-FEM) scheme is presented for the solution of the 2D Euler equations in supersonic regime. The spatial discretization is based on PS splines, that are piecewise quadratic polynomials with a global C 1 continuity, defined on conforming triangulations. Some geometrical issues related to the practical construction of the PS elements are discussed, in particular, the generation of the control triangles and the imposition of the boundary conditions. A stabilized formulation is considered, and a novel shock-capturing technique in the context of continuous finite-elements is proposed to reduce oscillations around the discontinuity, and compared with the classical technique proposed by Tezduyar and Senga (2006). The code is verified using manufactured solutions and validated using two challenging numerical examples, which allows to evaluate the performance of the PS discretization in capturing the shocks. [ABSTRACT FROM AUTHOR]

Highlights • A kinematic analysis method for tracing the folding process of origami in a three-dimensional space. • Directly control the nodal coordinates by external force on the vertices. • An improved type of bar and hinge unit for origami models, demonstrated to be efficient in numerical analysis. • Folding simulation of diverse numerical origami models in the same framework with concise explanations. Abstract The kinematic analysis of the folding process is important in practical engineering applications of the mechanism of origami. This paper proposes an efficient methodology for tracing the folding process of origami in a three-dimensional space. This method directly controls the nodal coordinates in the origami model activated by external force on the vertices. The deforming path is obtained using an algorithm based on the generalized inverse theory. An improved type of origami unit is presented for the computational calculation. The results demonstrate that the computational efficiency is strongly related not only to the number of the unknowns, but also the singular value of the compatibility matrix of the origami model. Furthermore, the validity and versatility of the proposed method are confirmed through numerical examples, including general origami models, origami with gravity, origami with special boundary conditions, and curved-crease origami. The proposed method is validated to be feasible and efficient in analyzing the folding mechanism of origami structures for kinematic design in structural and mechanical applications. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

An iteration-free method of domain decomposition is considered for approximately solving a boundary value problem for a second-order parabolic equation. A standard approach for constructing domain decomposition schemes is based on a partition of unity for the domain under the consideration. Here a new general approach is proposed for constructing domain decomposition schemes with overlapping subdomains based on indicator functions of subdomains. The basic peculiarity of this method is connected with a representation of the problem operator as the sum of two operators, which are constructed for two separate subdomains with the subtraction of the operator that is associated with the intersection of the subdomains. The present paper proposed a two-component factorized scheme, which can be treated as a generalization of the standard Alternating Direction Implicit (ADI) schemes to the case of a special three-component splitting. The scheme is regionally additive and is constructed using indicator functions of the subdomains. Moreover, it is unconditionally stable if the weight is chosen to be greater than or equal to 0.5. Numerical results are presented for a model two-dimensional problem. [ABSTRACT FROM AUTHOR]

This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivity preserving. [ABSTRACT FROM AUTHOR]

In this paper, we present a phase-field method for Rayleigh instability on a fibre. Unlike a liquid column, the evolutionary dynamics of a liquid layer on a fibre depends on the boundary condition at the solid-liquid interface. We use a Navier–Stokes–Cahn–Hilliard system to model axisymmetric immiscible and incompressible two-phase flow with surface tension on a fibre. We solve the Navier–Stokes equation using a projection method and the Cahn–Hilliard equation using a nonlinearly stable splitting method. We present computational experiments with various thicknesses of liquid thread and fibre. The numerical results indicate that the size of the satellite droplet decreases as the thicknesses of the thread and fibre increase. [ABSTRACT FROM AUTHOR]

Odd–even grid oscillation is an artifact frequently observed in numerical solutions for differential equations when they are discretized by central difference, and it is a critical issue in pursuing high-fidelity simulation of various physical phenomena. Although such oscillation has been a classic topic, there is lack of a direct, complete explanation on its onset and behaviors. From an angle different from those in literature, this paper revisits the topic, and it makes a systematic analysis in conjunction with numerical illustration on the oscillation in model problems, presenting criteria and a rigorous but direct and plain explanation on its presence and behaviors. Two types of odd–even grid oscillation are identified; one comes from dual-mode patterns in numerical solutions, and the other results from inconsistency of boundary conditions. The first type of the oscillation decays with grid spacing, while the second one tends to remain regardless of its size. As a consequence of their presence in single-domain solutions, the two kinds of fluctuation also occur in computation by domain decomposition, and additionally they are altered by algorithms of the decomposition. Further analysis demonstrates that the fluctuation inherited in the model problems also leads to zig-zag forms in solutions for more complicated nonlinear flow problems when they are solved either in a single domain or two subdomains. It is anticipated that understanding of the spurious oscillation obtained in this study will shed light on development of methods for its control and removal. [ABSTRACT FROM AUTHOR]

The Kansa method with the Multiquadric-radial basis function (MQ-RBF) is inherently meshfree and can achieve an exponential convergence rate if the optimal shape parameter is available. However, it is not an easy task to obtain the optimal shape parameter for complex problems whose analytical solution is often a priori unknown. This has long been a bottleneck for the MQ-Kansa method application to practical problems. In this paper, we present a novel sample solution approach (SSA) for achieving a reasonably good shape parameter of the MQ-RBF in the Kansa method for the solution of problems whose analytical solution is unknown. The basic assumption behind the SSA is that the optimal shape parameter is considered to be largely depended on the shape of computational domain, the type of the boundary conditions, the number and distribution of nodes, and the governing equation. In the procedure of the SSA, we set up a pseudo-problem as the sample solution whose solution is known. It is not difficult to obtain the optimal parameter of the MQ-RBF in the numerical solution of the pseudo-problem. The SSA suggests that the optimal shape parameter of the pseudo-problem can also achieve an approximately optimal accuracy in the solution of the original problem. Numerical examples and comparisons are provided to verify the proposed SSA in terms of accuracy and stability in solving homogeneous problems and non-homogeneous modified Helmholtz problems in several complex domains even using chaotic distribution of collocation points. [ABSTRACT FROM AUTHOR]

American-style puttable convertible bonds are often priced with various numerical solutions because the predominant complexity arises from the determination of the two free boundaries together with the bond price. In this paper, two forms of integral equations are derived to price a puttable convertible bond on a single underlying asset. The first form is obtained under the Black–Scholes framework by using an incomplete Fourier transform. However, this integral equation formulation possesses a discontinuity along both free boundaries. An even worse problem is that this representation contains two first-order derivatives of the unknown exercise prices, which demands a higher smoothness of the interpolation functions used in the numerical solution procedure. Thus, a second integral equation formulation is developed based on the first form to overcome those problems. Numerical experiments are conducted to show several interesting properties of puttable convertible bonds. [ABSTRACT FROM AUTHOR]

This paper presents an analytical micromechanics model for predicting the three-dimensional effective elastic properties of multidirectional composite laminates with ply wrinkle defects. A representative volume element (RVE) was chosen for analysis and the geometry of wavy plies in the wrinkled laminates was described by sinusoidal functions. The derivation of the effective elastic moduli was based on the mixed boundary conditions, and a two-step homogenization technique was proposed. The analytical predictions were compared with the published numerical and experimental results for unidirectional and cross-ply carbon/epoxy laminates. The model was also applied to quasi-isotropic laminates, and the effect of wrinkles on their effective properties was examined. The developed analytical micromechanics model was found to accurately predict the in-plane and out-of-plane effective properties of the wrinkled laminates, making it a useful tool for providing information on the relationships between wrinkle defects and the macroscale response of composite laminates and for designing composite structures. [ABSTRACT FROM AUTHOR]

This paper deals with the construction and computation of numerical solutions of a coupled mixed partial differential equation system arising in concrete carbonation problems. The moving boundary problem under study is firstly transformed in a fixed boundary one, allowing the computation of the propagation front as a new unknown that can be computed together with the mass concentrations of CO 2 in air and water. Apart from the stability and the consistency of the numerical solution, constructed by a finite difference scheme, qualitative properties of the numerical solution are established. In fact, positivity of the concentrations, increasing properties of the propagation front and monotone behavior of the solution are proved. We also confirm numerically the t -law of propagation. Results are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, two lattice Boltzmann models for two-dimensional coupled Burgers’ equations are proposed through treating the part or all of convection items as the source term, where the spatial gradient can be calculated by the distribution function. The models can exactly recover the Burgers’ equations without any assumptions. Some numerical tests are also performed to validate the present models. It is found that the proposed models are more accurate and efficient in solving two-dimensional coupled Burgers’ equations. [ABSTRACT FROM AUTHOR]

This paper presents transient numerical simulations of hydraulic systems in engineering applications using the spectral element method (SEM). Along with a detailed description of the underlying numerical method, it is shown that the SEM yields highly accurate numerical approximations at modest computational costs, which is in particular useful for optimization-based control applications. In order to enable fast explicit time stepping methods, the boundary conditions are imposed weakly using a numerically stable upwind discretization. The benefits of the SEM in the area of hydraulic system simulations are demonstrated in various examples including several simulations of strong water hammer effects. Due to its exceptional convergence characteristics, the SEM is particularly well suited to be used in real-time capable control applications. As an example, it is shown that the time evolution of pressure waves in a large scale pumped-storage power plant can be well approximated using a low-dimensional system representation utilizing a minimum number of dynamical states. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solution of the one-dimensional semi-discrete linear Schrödinger equation in unbounded domains. In order to compute the solution on the domain of physical interest, the artificial boundary method is applied to transform the original unbounded domain problem into an initial boundary value problem on a truncated finite domain. We prove the stability of the truncated semi-discrete problem. Then, a fast algorithm is proposed to approximate the nonlocal absorbing boundary condition. The novelty of this fast algorithm is that the stability of the approximate truncated semi-discrete problem is automatically maintained. In the end, numerical examples are presented to demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce, analyze, and numerically illustrate a method for taking into account quantities of interest during the finite element treatment of a boundary-value problem. The objective is to derive a method whose computational cost is of the same order as that of the classical approach for goal-oriented adaptivity, which involves the solution of the primal problem and of an adjoint problem used to weigh the residual and provide indicators for mesh refinement. In the current approach, we first solve the adjoint problem, then use the adjoint information as a minimization constraint for the primal problem. As a result, the constrained finite element solution is enhanced with respect to the quantities of interest, while maintaining near-optimality in energy norm. We describe the formulation in the case of a problem defined by a symmetric continuous coercive bilinear form and demonstrate the efficiency of the new approach on several numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H 1 semi-norm of the difference between itself and the initial value problem solution. [ABSTRACT FROM AUTHOR]

In this paper, we have studied a numerical scheme to solve second order singularly perturbed two-point linear and nonlinear boundary value problems. The boundary layer of this type of problems exhibits at one end (left or right) point of the domain due to the presence of perturbation parameter ε . The quintic B-spline method and suitable piecewise uniform Shishkin mesh have been used. Linear and nonlinear second order singularly perturbed boundary value problems have been solved by the present method. The convergence analysis is also provided and the method is shown to have uniform convergence of fourth order. Numerical results have demonstrated the efficiency of the present method. [ABSTRACT FROM AUTHOR]

This paper addresses analytically the vibroacoustic problem of sound transmission across a rectangular double-wall sandwich panel clamp mounted on an infinite rigid baffle and lined with poroelastic materials. The wave propagation in poroelastic media is described by Biot’s theory and the coupling methods between the poroelastic core and the panel determine the various configurations and associated boundary conditions. The modal superposition theory and the weighted residual (Galerkin) method are employed to account for the finite extension with the clamped boundary and to obtain a double-series solution of the problem through a matrix equation. The sound transmission loss (STL) of the structure is calculated for a single incident wave after validating the analytical model against previous theories and experiments. The numerical results show that the finite panel and clamped boundary influence the STL dominantly in the low-frequency range. The poroelastic materials exhibit strong damping effects on the resonances of STL spectra at high frequencies as well as panel vibrations and enhance significantly the sound insulation performance of the sandwich panel. [ABSTRACT FROM AUTHOR]

Variationally consistent selective homogenization is applied to a class of gradient-enhanced dissipative materials which is adopted for the mesoscale modeling. The adopted standard first order homogenization assumption results in the classical equilibrium equation for a local continuum on the macroscale, while the internal variables “live” on the mesoscale only. Among the issues considered in the paper, we note (i) the variationally consistent setting of homogenization of gradient theory on the mesoscale, (ii) the variational basis of the SVE-problem (SVE = Statistical Volume Element) in the time-incremental setting. The SVE-problem is formulated for the classical boundary conditions (Dirichlet and Neumann) pertinent to the standard momentum balance as well as the “micro-momentum” balance. The weak format of the SVE-problem constitutes the stationarity condition of an incremental SVE-potential, which represents an extension of the situation for a single-phase continuum model. The macroscale stress in a given time-increment is derivable from an incremental “macroscale pseudo-elastic strain energy”. Moreover, the saddle-point properties of the SVE-potential are shown to form the basis for establishing upper and lower bounds on the pseudo-elastic strain energy. Bingham viscoplasticity with gradient-enhanced hardening is chosen as the prototype model problem for the numerical evaluation. The computed stress–strain response relations confirm the theoretical predictions of the influence of different combinations of boundary conditions on the SVE. [ABSTRACT FROM AUTHOR]

The paper presents the Finite Element formulation of the equations proposed by Tsiampousi et al. (2016) for coupled consolidation in unsaturated soils. Their coupling is discussed in relation to a conceptual model which divides soil behaviour into zones ranging from fully saturated to dry states. The numerical simulation of a laboratory experiment involving drainage of water from a vertical column of sand is used to validate the equations. Finally, the example of rainfall infiltration into a cut slope highlights how aspects of the conceptual model are reflected in the numerical analysis of boundary value problems involving unsaturated soils. [ABSTRACT FROM AUTHOR]

This paper presents a general non-linear computational formulation for rotation-free thin shells based on isogeometric finite elements. It is a displacement-based formulation that admits general material models. The formulation allows for a wide range of constitutive laws, including both shell models that are extracted from existing 3D continua using numerical integration and those that are directly formulated in 2D manifold form, like the Koiter, Canham and Helfrich models. Further, a unified approach to enforce the G 1 -continuity between patches, fix the angle between surface folds, enforce symmetry conditions and prescribe rotational Dirichlet boundary conditions, is presented using penalty and Lagrange multiplier methods. The formulation is fully described in the natural curvilinear coordinate system of the finite element description, which facilitates an efficient computational implementation. It contains existing isogeometric thin shell formulations as special cases. Several classical numerical benchmark examples are considered to demonstrate the robustness and accuracy of the proposed formulation. The presented constitutive models, in particular the simple mixed Koiter model that does not require any thickness integration, show excellent performance, even for large deformations. [ABSTRACT FROM AUTHOR]

This paper presents a semigroup approach for inverse source problems for the abstract heat equation, when the measured output data is given in subject to the integral overspecification over the spatial domain. The existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed. Such representation permits the derivation of sufficient conditions for the uniqueness of the solution. Also an approximation method based on the optimal homotopy analysis method (OHAM) is designed, and the error estimates are discussed using graphical analysis. Moreover, we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data. The proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations. The accuracy and stability of the method are discussed and compared with several finite-difference techniques. Computational results show efficiency and high accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper numerically investigated the coupled flow and heat transfer of a parabolic trough collector (PTC), with the non-uniform heat flux boundary condition on the absorber wall and the rarefied gas effects in the annular vacuum gap being taken into consideration. A fully coupled cross-sectional heat transfer model is established with Direct Simulation Monte Carlo (DSMC) method for the rarefied gas flow and heat transfer in the vacuum annual gap. The PTC tube efficiency can be obtained from the above simulation for a given HTF temperature. Such simulation is conducted for several specified HTF temperature and different efficiency data are obtained. These data are fitted by an equation. This equation is then used to advance the HTF temperature in the axial direction. In such a way a simplified 3D model for the design of a PTC receiver is obtained. Cross-sectional simulation results show that when the gas pressure is less than 0.1 Pa further decrease in pressure makes no further contribution to reduce the heat loss. The effects of periphery non-uniform distribution of heat flux, coating material emissivity, envelope diameter and HTF inlet velocity on the PTC efficiency are discussed. An operation variant is proposed by using the 3D model by which the total PTC tube length can be reduced for a given thermal load. [ABSTRACT FROM AUTHOR]

The spatial–temporal spreading of a new invasive species in a habitat has interest in ecology and is modeled by a moving boundary diffusion logistic partial differential problem, where the moving boundary represents the unknown expanding front of the species. In this paper a front-fixing approach is applied in order to transform the original moving boundary problem into a fixed boundary one. A finite difference method preserving qualitative properties of the theoretical solution is proposed. Results are illustrated with numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we propose two systematic strategies to recover the gradient on the boundary of a domain. The recovered gradient has comparable superconvergent property on the boundary as that in the interior of the domain. This superconvergence property has been validated by several numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, inverted finite element method is used for solving two-dimensional second order elliptic equations with a Dirichlet boundary condition in an exterior domain. After laying down the method, and after giving an estimate of the error, we detail how its implementation can be accomplished. Numerical results show the high efficiency and the accuracy of the method, especially for equations with infinitely varying coefficients. [ABSTRACT FROM AUTHOR]