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Analytical techniques used for estimating thermoelastic damping by incorporating both mechanical and thermal interactions between surfaces and the rest of the bulk are intricate and challenging due to the limited understanding of the damping mechanisms in extra-thin films subjected to forced vibrations. This paper proposes a modified model to analytically calculate the thermoelastic damping of ultrathin elastic films due to surface effects and analyzes the thermoelastic damping variation with different factors through numerical experiments on two materials. The model considers surface stresses derived from the elastic surface theory using Kirchhoff's kinetic hypothesis and determines thermoelastic damping by considering thermal dissipation and elastic potential energy. The results show that surface effects significantly influence the thermoelastic damping of the film, and the specific behavior of a thin film's thermoelastic damping with respect to film thickness is impacted by various factors, including material property, the variation range of film thickness, and the forced vibration frequency. This study provides insights into the thermoelastic damping behavior of thin films and has important implications for the development of nanoscale oscillators in MEMS or NEMS systems. [ABSTRACT FROM AUTHOR]

Bi-layer lattice-filled sandwich structures have good application prospects for multi-physics problems; however, high-precision numerical analysis methods are lacking. Recently, the newly proposed asymptotic homogenization method called the novel numerical implementation of asymptotic homogenization (NIAH) was further developed based on the Mindlin plate theory, which is a potential method for overcoming the above limitation. This study investigates the feasibility of this method for Bi-layer lattice-filled sandwich structures. The obtained results are compared to those from homogenization methods developed based on the Kirchhoff theory, and accordingly, the influence of the shear effect on the accuracy of the structural responses of the considered structures is studied. Subsequently, the impacts of the size effect, macrostructure type, and lattice type are also considered. The analysis results showed that, for most cases, the NIAH method can yield high-precision results for Bi-layer lattice-filled sandwich structures. When the number of lattice cells is insufficient or different layers of the lattice have excessive differences in their stiffness, the accuracy of the results obtained using the NIAH method is degraded. [ABSTRACT FROM AUTHOR]

In this paper, numerical analysis for free vibration of simply supported thin rectangular plates has been simulated using Ansys. The vibration of plate follows Kirchhoff plate theory. The natural frequency calculated using Ansys has been compared with Levy type solution results available in the literature. It is observed that the natural frequencies of the simply supported rectangular plate is in close agreement with exact solution results as reported in literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following critical nonlocal problem: { M ⁢ (∬ℝ2N |u(x) − u(y)|2/|x − y|N+2s⁢ 𝑑x 𝑑y) ⁢(− Δ)su = λ/uγ + u2s*−1 in ⁢ Ω, u > 0 in Ω, u = 0 in ⁢ ℝN∖Ω, where Ω is an open bounded subset of ℝ N with continuous boundary, dimension N > 2s with parameter s ∈ (0 , 1), 2*s = 2N /(N − 2s) is the fractional critical Sobolev exponent, λ > 0 is a real parameter, γ ∈ (0 , 1) and M models a Kirchhoff-type coefficient, while (−Δ)s is the fractional Laplace operator. In particular, we cover the delicate degenerate case, that is, when the Kirchhoff function M is zero at zero. By combining variational methods with an appropriate truncation argument, we provide the existence of two solutions. [ABSTRACT FROM AUTHOR]

In this paper, we study the following Kirchhoff type equation: −(1 + b ∫ℝN |∇u|2dx) Δu + u = a(x) ƒ(u) in ℝN, u ∈ H1 (ℝN), where N ≥ 3, b > 0 and ƒ(s) is asymptotically linear at infinity, that is, ƒ(s) ∼ O(s) as s → + ∞. By using variational methods, we obtain the existence of a mountain pass type solution and a ground state solution under appropriate assumptions on a(x). [ABSTRACT FROM AUTHOR]

Abstract In this paper the authors deal with a class of parabolic type Kirchhoff equations, which were considered in Han and Li (2018), where global existence and finite time blow-up of solutions were studied when the initial energy was subcritical, critical and supercritical. Their results are complemented in this paper in the sense that a new blow-up criterion will be given for nonnegative initial energy and upper and lower bounds for blow-up time will be derived. [ABSTRACT FROM AUTHOR]

In this paper, we concern ourselves with the following Kirchhoff-type equations: { - (a + b ⁢ ∫ ℝ 3 | ∇ ⁡ u | 2 ⁢ 𝑑 x ) ⁢ △ ⁢ u + V ⁢ u = f ⁢ (u) in ⁢ ℝ 3 , u ∈ H 1 ⁢ (ℝ 3) , \left\{\begin{aligned} \displaystyle-\biggl{(}a+b\int_{\mathbb{R}^{3}}\lvert% \nabla u\rvert^{2}\,dx\biggr{)}\triangle u+Vu&\displaystyle=f(u)\quad\text{in % }\mathbb{R}^{3},\\ \displaystyle u&\displaystyle\in H^{1}(\mathbb{R}^{3}),\end{aligned}\right. where a, b and V are positive constants and f has critical growth. We use variational methods to prove the existence of ground state solutions. In particular, we do not use the classical Ambrosetti–Rabinowitz condition. Some recent results are extended. [ABSTRACT FROM AUTHOR]

This paper presents an analytical research on the dynamic interaction problem between a pre-stressed plate and a transversely isotropic multilayered half-plane subjected to a moving load. The pre-stressed plate is governed by the Kirchhoff plate theory, and the transversely isotropic multilayered half-plane is solved by the analytical layer-element method. Combining the frictionless contact and displacement compatibility conditions between the plate and the soil, the contact stress and the deflection of plate in the Fourier transform domain are derived. With the aid of the inverse Fourier transform, the actual solutions can be further achieved. Numerical examples are given to illustrate the influence of load speed, the rigidity of plate, the axial force applied on the plate and the stratified character of the soil. [ABSTRACT FROM AUTHOR]

In order to analyze the displacement and stress of thin plate for cement concrete pavement with rectangle shape and resting on Winkler soil foundation, an analysis model was set up based on the theory of elastic thin plate on Winkler foundation. According to elasticity Kirchhoff theory of thin plates and Winkler soil foundation model, the expressions of displacement and stress were yielded by using the inverse Hankel transform. Numerical method was employed to calculate displacement and stress of the thin plate. Results showed that displacement and stress corresponded with using the method from Code for Highway Design-Pavement. Results showed that the method can provide a new computation method for displacement and stress of the thin plate about cement concrete pavement. [ABSTRACT FROM AUTHOR]

To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we propose a family of distances that can be tuned to quantify structural changes occurring on a graph at different scales: from the local scale formed by the neighbors of each vertex, to the largest scale that quantifies the connections between clusters, or communities. Our approach results in the definition of a true distance, and not merely a notion of similarity. We propose fast (linear in the number of edges) randomized algorithms that can quickly compute an approximation to the graph metric. The third contribution involves a fast algorithm to increase the robustness of a network by optimally decreasing the Kirchhoff index. Finally, we conduct several experiments on synthetic graphs and real networks, and we demonstrate that we can detect configurational changes that are directly related to the hidden variables governing the evolution of dynamic networks. [ABSTRACT FROM AUTHOR]

We consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhofftype equations with Robin boundary data as follows: −M( ∫ Ω 1 p( x ) | ∇ u | p( x ) dx+ ∫ ∂Ω β( x ) p( x ) | ∇ u | p( x ) dσ )div( | ∇ u | p( x )−2 ∇ u )=f( x,u ) in Ω, | ∇ u | p( x )−2 ∂u ∂v +β( x ) |u| p( x )−2 u=0 on ∂Ω, where β ∈ L∞ (∂Ω) and f : Ω × ℝ → ℝ satisfies the Carathéodory condition. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions. [ABSTRACT FROM AUTHOR]

This research purposed a new family of finite elements for spherical thick shell based on Nzengwa-Tagne’s model proposed in 1999. The model referred to hereafter as N-T model contains the classical Kirchhoff-Love (K-L) kinematic with additional terms related to the third fundamental form governing strain energy. Transverse shear stresses are computed and C0 finite element is proposed for numerical implementation. However, using straight line triangular elements does not guarantee a correct computation of stress across common edges of adjacent elements because of gradient jumps. The gradient recovery method known as Polynomial Preserving Recovery (PPR) is used for local interpolation and applied on a hemisphere under diametrically opposite charges. A good agreement of convergence results is observed; numerical results are compared to other results obtained with the classical K-L thin shell theory. Moreover, simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental form tensor present in the kinematics of this model. The analysis of the thickness ratio shows difference between the classical K-L theory and N-T model when the ratio is greater than 0.099. [ABSTRACT FROM AUTHOR]

In this paper, we develop a mixed Legendre-Galerkin spectral method to approximate the buckling problem of simply supported Kirchhoff plates subjected to general plane stress tensor. By the spectral theory of compact operators, the rigorous error estimates for the approximate eigenvalues and eigenfunctions are provided. Finally, we present some numerical experiments which support our theoretical results. [ABSTRACT FROM AUTHOR]

On the basis of the modified strain gradient theory, the present paper deals with the theoretical analysis of the free vibration of coupled double-FGM viscoelastic nanoplates by Kelvin-Voigt visco-Pasternak medium. To establish static equilibrium of atoms on the each nanoplate surface, the effects of the surface layers are considered. The properties of material in the thickness direction vary according to the power low distribution. Kirchhoff plate assumption and Hamilton's variational principle are employed to achieve the partial differential equations for three different cases of vibration (out-of-phase, in-phase, and one nanoplate of the system being stationary) and corresponding boundary conditions. Navier's approach which satisfies the simply supported boundary conditions applied to analytically investigate the size effect on the natural frequencies of double-FGM viscoelastic nanoplate systems. Numerical studies are carried out to illustrate the influence of viscoelastic damping structural of the nanoplates, damping coefficient of the visco-Pasternak medium, independent length scale parameter, aspect ratio, surface properties, and other factors on the frequency behavior system. Some numerical results of this research illustrate that the frequencies may increase or decrease with respect to the sign of the surface properties of FGMs. [ABSTRACT FROM AUTHOR]

The paper deals with the following equation of Kirchhoff type, - (1 + b(∫R3∣▿ u∣u2dx)r) ▿u + u = k(x) -∣u∣q-2u +θ(g(u)+ λh(x)u with x ∊ R3, where u ∊ H1(R3), b > 0; 0 < r < 2; q ∊ [2(r + 1), 6),θ is a small constant, λ is a parameter, and a weight function h(x) ≥ 0. It is known that the linear operator -Δu + u - λh(x)u is coercive if 0 < λ < λ1(h) and is non-coercive if λ > λ1(h), where λ1(h) is the first eigenvalue of the operator -Δu + u with the weight h(x). Under suitable conditions on the functions k(x) and g(s), it is shown that the equation has a positive solution for any λ ∊ (0; λ1(h)) and two positive solutions for λ ∊ (λ1(h); λ1(h) + ~δ) with ~δ > 0 small. The conditions imposed on k(x) and g(s) are much weaker than those used before, thereby generalizing several existing results on the existence of positive solutions for this type of Kirchhoff equations. [ABSTRACT FROM AUTHOR]

We propose a method for imaging small-scale diffraction objects in complex environments in which Kirchhoff-based approaches may fail. The proposed method is based on a separation between the specular reflection and diffraction components of the total wavefield in the migrated surface angle domain. Reverse-time migration was utilized to produce the common image gathers. This approach provides stable and robust results in cases of complex velocity models. The separation is based on the fact that, in surface angle common image gathers, reflection events are focused at positions that correspond to the apparent dip angle of the reflectors, whereas diffracted events are distributed over a wide range of angles. The high-resolution radon-based procedure is used to efficiently separate the reflection and diffraction wavefields. In this study, we consider poststack diffraction imaging. The advantages of working in the poststack domain are its numerical efficiency and the reduced computational time. The numerical results show that the proposed method is able to image diffraction objects in complex environments. The application of the method to a real seismic dataset illustrates the capability of the approach to extract diffractions. [ABSTRACT FROM AUTHOR]

We study the existence of exponential attractor for the Kirchhoff equations with strong nonlinear damping and supercritical nonlinearity u t t − σ ( ‖ ∇ u ‖ 2 ) Δ u t − ϕ ( ‖ ∇ u ‖ 2 ) Δ u + f ( u ) = h ( x ) . The main result is that the nonlinearity f ( u ) is of supercritical growth. In this case we establish an exponential attractor in natural energy space by using a new method based on the weak quasi-stability estimates (rather than the strong one as usual). [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of critical points for the following functional constrained on $${S_c=\{u\in H^1(\mathbb{R}^N)| |u|_2=c\}}$$ : where N = 1, 2, 3 and a, b > 0 are constants. The constraint problem is L-critical. We showed that I( u) has a constraint critical point with a mountain pass geometry on S if $${c > c^*:=(2^{-1}b|Q|_2^{\frac{8}{N}})^{\frac{N}{8-2N}}}$$ , where Q is the unique positive radial solution of $${-2\Delta Q+(\frac{4}{N}-1)Q=|Q|^{\frac{8}{N}} Q}$$ in $${\mathbb{R}^N}$$ . For 0 < c < c, I( u) has no critical point on S, and we proved the existence of minimizers for a new perturbation functional on S: [ABSTRACT FROM AUTHOR]

This paper presents a new numerical algorithm for a dynamic analysis of thin plate structures based on the combined finite-discrete element method (FDEM). A nonlinear analysis of thin plates subjected to static or dynamic load has been provided. The model uses 3-noded triangular finite elements and is implemented in the open source FDEM package - Yfdem. The performance of the new model on simple benchmark tests is presented. [ABSTRACT FROM AUTHOR]

A novel surface heat flux calibration method is presented applicable to nonlinear inverse heat conduction problems. Quasi-linearization of the nonlinear heat equation is achieved by combining the Kirchhoff transform with time-domain rescaling based on the local temperature measurement. At each time step, the thermophysical properties are held constant throughout the spatial domain though allowed to vary with advancing time. The rescaled forms are then resolved through a calibration framework. The proposed calibration formulation is expressed in terms of Volterra integral equation of the first kind. This functional equation relates the rescaled net unknown surface heat flux to the rescaled net calibration surface heat flux and their corresponding rescaled Kirchhoff transformed variables for the in-depth temperature measurements during the calibration test and unknown runs. Tikhonov regularization is introduced for generating a family of predictions based on the Tikhonov parameter. The L-curve strategy is used for selecting the proper regularization parameter. In this paper, favourable numerical results are demonstrated verifying both accuracy and robustness of the rescaling calibration approach in the presence of significant experiment noise. The methodology works well for a variety of practical isotropic materials. This approach does not require knowledge of the probe position but presently requires knowledge of the host material’s thermal diffusivity. [ABSTRACT FROM PUBLISHER]

Abstract: A partition of unity method for the displacement obstacle problem of clamped Kirchhoff plates is considered in this paper. We derive optimal error estimates and present numerical results that illustrate the performance of the method. [Copyright &y& Elsevier]

This paper aims to investigate the nonlinear dynamics of a thin-plate workpiece during milling process with cutting force nonlinearities. By modeling the thin-plate workpiece as a cantilevered thin plate and applying the Hamilton's principle, the equations of motion of the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations. Using the Galerkin's approach, the equations of motion are reduced to a two-degree-freedom nonlinear system. The method of Asymptotic Perturbation is utilized to obtain the averaged equations in the case of 1:1 internal resonance and foundational resonance. Numerical methods are used to find the periodic and chaotic oscillations of the cantilevered thin-plate workpiece. The results show that the cantilevered thin-plate workpiece demonstrate complex dynamic behaviors under time-delay effects, the external and parametric excitations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis issue for coupled systems on networks with mixed delays and reaction-diffusion terms (CSNMRs). By employing Lyapunov method and Kirchhoff's Theorem in graph theory, a systematic method is proposed to guarantee exponential stability of CSNMRs. Two different kinds of sufficient criteria are derived in the form of Lyapunov function and coefficients of the system, respectively. Finally, a numerical example is given to show the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

Abstract: In the analysis of interior acoustic problems, the time domain boundary element method (TBEM) suffers the monotonically increasing instability when using the direct Kirchhoff integral. This instability is related to the non-oscillatory static acoustic mode describing the constant spatial response in an enclosure. In this work, nonphysical natures of non-oscillatory static mode influencing the instability of TBEM calculation are investigated, and a method for stabilization is studied. In TBEM calculation, the static mode is represented by two non-oscillatory eigenmodes with different eigenvalues. The monotonically increasing instability is caused by the unstable poles of non-oscillatory eigenmodes as well as very small, very low frequency noise of an input signal. Interior problems with impedance boundary condition also exhibit the monotonically increasing instability stemming from its pseudo non-oscillatory static mode due to the lack of dissipation at very low frequencies. Calculation of transient sound fields within rigid and lined boxes provides numerical evidences. It is noted that the stabilization effort by modifying the coefficient matrix based on the spectral decomposition can be used only for correcting the unstable pole. The filtering method based on the eigen-analysis must be additionally used to avoid the remaining instability caused by very low frequency noise of input signal. [Copyright &y& Elsevier]

SUMMARY We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation schemes (Hauret et al. [2]) to Kirchhoff plate theory. We show that a special class of meshes derived from an arbitrary triangulation of the domain, the diamond meshes, results in the automatic satisfaction of the corresponding inf − sup condition for Kirchhoff plate theory. The attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests. We also provide a reinterpretation of the diamond approximation scheme for Kirchhoff plate theory within the framework of discrete mechanics. In this interpretation, the discrete moment-equilibrium problem is formally identical to the classical continuous problem, and the two differ only in the choice of differential structures. It also follows that the satisfaction of the inf − sup condition is a property of the cohomology of a certain discrete transverse differential complex. This close connection between the classical inf − sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The main purpose of this paper is to unify and improve Theorems 3.1–3.3 in Wu (2012) [8] as well as some results in other literature such as Theorems 1–4 in Wu (2011) [9]. We present a new proof technique to conclude the existence of high energy solutions for the Kirchhoff-type system under some assumptions that are weaker than those in Wu (2012) [8]. [Copyright &y& Elsevier]

The acoustic backscatter from pressure release prolate spheroids and a three-dimensional representation of a fish swimbladder (Chilean jack mackerel, Trachurus symmetricus murphyi) was calculated using four target strength models (Kirchhoff-approximation, Kirchhoff-ray-mode, finite element solution of the Helmholtz equation, and prolate-spheroid-modal-series). Smoothly varying errors were found in the Kirchhoff-approximation and Kirchhoff-ray-mode model results when compared to the other models, and provide objective criteria for constraining the use of the KA and KRM models. A generic correction technique is also proposed for the prolate spheroid estimates and tentatively tested on a jack mackerel swimbladder, resulting in improvements to the target strength estimates from the Kirchhoff-approximation and Kirchhoff-ray-mode models. [ABSTRACT FROM AUTHOR]

We are concernedwith the existence of multiple solutions to the nonhomogeneousKirchhoff type equation ... in R³, where a, b are positive constants, ..., we can find a constant mp > 0 such that for all p E (1,5) the equation has at least two radial solutions provided |h|2 < mp. [ABSTRACT FROM AUTHOR]

This paper discusses a priori error analysis of a C0 discontinuous Galerkin method (CDG) for Kirchhoff plates (cf. [17]). With the help of error estimates of a L² orthogonal projection operator and an interpolation operator due to [1,13], we obtain the error estimate for the CDG method in energy norm, following the technique in [6]. The error estimate in H¹ norm is also offered via the duality argument. Several numerical results are performed to support the theory obtained. [ABSTRACT FROM AUTHOR]

We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic integrals for a thin elastic rod with intrinsic twisting for both the cases of circular and non-circular cross sections. Our results can be easily reduced to the results without the intrinsic twisting that have been reported. Through calculation, we find that the Noether symmetry can be more directly and easily used than the Mei symmetry in finding the first integrals for the thin elastic rod. These first integrals will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the elastic rod model for DNA. [ABSTRACT FROM AUTHOR]

Abstract: Based on new modified couple stress theory a model for composite laminated Reddy plate is developed in first time. In this theory a new curvature tensor is defined for establishing the constitutive relations of laminated plate. The characterization of anisotropy is incorporated into higher-order laminated plate theories based on the modified couple stress theory by Yang et al. in 2002. The form of new curvature tensor is asymmetric, however it can result in same as the symmetric curvature tensor in the isotropic elasticity. The present model of thick plate can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model for cross-ply composite laminated Reddy plate of couple stress theory with one material’s length constant is used to demonstrate the scale effects. Numerical results show that the present plate model can capture the scale effects of microstructure. Additionally, the present model of thick plate model can be degenerated to the model of composite cross-ply laminated Kirchhoff plate and Mindlin plate of couple stress theory. [Copyright &y& Elsevier]

In this article a hypersingular boundary element method (BEM) for bending of thin anisotropic plates is presented. A new complex variable fundamental solution is implemented in the algorithm. For spatial discretization a collocation method with discontinuous quadratic elements is adopted. The domain integrals arising from the transversely applied load are transformed analytically into boundary integrals by means of the radial integration technique. The considered numerical examples prove that the novel BEM formulation presented in this study is much more efficient than previous formulations developed for the analysis of this kind of problems. [ABSTRACT FROM AUTHOR]

We carry out model and numerical studies for a three-dimensional, anisotropic, nonisothermal, two-phase steady state transport model of proton exchange membrane fuel cell (PEMFC) in this paper. Besides fully addressing the conservation equations of mass, momentum, species, charge and energy equations arising in the PEMFC, we present some efficient numerical methods for this model to achieve a fast and convergent nonlinear iteration, comparing to the oscillatory and nonconvergent iteration conducted by commercial flow solvers or in-house codes with standard finite element/volume method. In a framework of a combined finite element-upwind finite volume method, Kirchhoff transformation plays an important role in dealing with the discontinuous and degenerate water diffusivity in its transport equation. Preconditioned GMRES solver together with Newton's linearization scheme make the entire numerical simulation more efficient. Three-dimensional numerical simulations demonstrate that the convergent physical solutions can be attained within 30 steps. Numerical convergence tests are also performed to verify the efficiency and accuracy of the presented numerical algorithms and techniques. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of determining the equilibrium of composite strands consisting of a single core yarn surrounded by n-helical side yarns with pre-twists in the absence of any external load: the self-equilibrium configuration (SEC). We formulate the self-equilibrium problem on the basis of the Kirchhoff rod model in which the contact between yarns in three-dimensional space is taken into account in order to include large helical angles and geometrical constraints. We numerically determine the SECs and elucidate the effect of the following factors on them: the pre-twist of each yarn, the ratio of Young’s modulus of the core yarn to that of the side yarn, and the number of side yarns. The present results allow us to characterize the initial unloaded state of composite strands. [Copyright &y& Elsevier]

Abstract: A finite element (FE) approach is presented for the analysis of the Mindlin plate model (MPM) problems. It is based on the definition of a fictitious deflection that takes into account the correct interdependence between the generalized displacements in both the continuous and FE discretized schemes. This implies that the proposed approach is free-shear locking and is characterized by a good level of accuracy, even for low order FEs. Moreover some interesting relationships between some fundamental quantities in the FE analysis of MPM problems and the corresponding quantities in the FE analysis of the Kirchhoff plate model (KPM) problems have been evidenced. [Copyright &y& Elsevier]

Abstract: This paper presents a development of the finite strip method based on the shallow shell theory of Marguerre. Most of existing semi-analytical finite strips are based on the plate theories of Kirchhoff and of Mindlin. As it is showed in the paper, the plate theories can be considered as the particular cases of the shallow shell theory. Numerical results show the efficiency of the finite strip based on the shallow shell theory in the buckling analysis of prismatic structures which have curved corners. [Copyright &y& Elsevier]

We study finite element methods for the displacement obstacle problem of clamped Kirchhoff plates. A unified convergence analysis is provided for C¹ finite element methods, classical nonconforming finite element methods and C0 interior penalty methods. Under the condition that the obstacles are sufficiently smooth and that they are separated from each other and the zero displacement boundary constraint, we prove that the convergence in the energy norm is O(h) for convex domains. [ABSTRACT FROM AUTHOR]

Abstract: A nonlinear boundary value problem related to an equation of Kirchhoff is considered. The existence of positive solutions is proved through alternative Leray–Schauder’s type combined with Krasnoselskii’s fixed point theorem. Numerical methods are presented and a result of local convergence is established. [Copyright &y& Elsevier]

Abstract: In this investigation, the Gaussian decomposition and the Fresnel–Kirchhoff diffraction methods are compared from different view points. The virtues and faults of each method and also the reliable region of each one are discussed. This work is based on a numerical method for both the circular and elliptic Gaussian beams and results are compared with experimental data. This study is useful for materials exhibit optical Kerr effect such as two photon absorption and thermo-optical nonlinearities. [Copyright &y& Elsevier]

Abstract: For very large systems of equations arising from 3D finite element formulation, pre-conditioned iterative solvers are preferred over direct solvers due to their reduced memory requirements. However, in the finite-element analysis of thin structures such as beam and plate structures, iterative solvers perform poorly due to the presence of poor quality elements. In particular, their efficiency drops significantly with increase in the aspect ratio of such structures. In this paper, we propose a dual-representation based multi-grid framework for efficient iterative analysis of thin structures. The proposed iterative solvers are relatively insensitive to the quality of the elements since they exploit classical beam and plate theories to spectrally complement 3D finite element analysis. This leads to significant computational gains, as supported by the numerical experiments. [Copyright &y& Elsevier]

Abstract: We introduce a new framework for the development of thin plate finite elements, the “twist-Kirchhoff theory”. A family of rectangular plate elements is derived that takes advantage of the special structure of this new theory. Particular attention is focused on the lowest-order member of the family, an eight degree-of-freedom, four-node element with mid-side rotations whose stiffness matrix is exactly computed with one-point Gaussian quadrature. We prove a convergence theorem for it and various error estimates. These are also generalized to the higher-order elements in the family. Numerical tests corroborate the theoretical results. [Copyright &y& Elsevier]

Abstract: A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. A solution for the electrical potential along the thickness direction of the piezoelectric layer satisfying the open circuit electric boundary condition is developed for the first time. The mechanical model and solutions for the vibration analysis of the piezoelectric coupled circular plate are then established based on the developed electrical potential, the Kirchhoff plate model, and the Maxwell equation. The first four mode shapes and the corresponding resonant frequencies of the plate with two standard boundary conditions are presented in numerical simulations and compared with those of a piezoelectric coupled plate with the closed circuit condition. The simulations show that the resonant frequencies of the open circuit piezoelectric coupled plate are higher than those of the closed circuit piezoelectric coupled plate. Corresponding discussions are thus provided for the higher piezoelectric effect from the open circuit piezoelectric layer. [Copyright &y& Elsevier]

Focused electromagnetic waves have applications in many areas, such as antennas, hyperthermia, and integrated optical systems. High frequency field expressions are derived around feed point of a cylindrical hyperbolic symmetrical focusing lens using the Maslov's method. Maslov's method is a systematic procedure for predicting the field in the caustic region combining the simplicity of ray and generality of the transform method. Numerical computations are made for field pattern around the caustic of a hyperbolic symmetrical focusing lens. The results are found in good agreement with obtained using Kirchhoff's approximation. [ABSTRACT FROM AUTHOR]

Abstract: FFT-based convolution is proposed to numerical solve Fresnel–Kirchhoff integral in Fresnel regime carefully and in a very shorter time in comparison to direct solving convolution. To show its capability, the algorithm was implemented to evaluate amplitude of a diffracted plane wave at the focal plane of photon sieves with different focal lengths. The calculated amplitudes are completely the same calculated via convolving operation but has advantageous of taking very very shorter time. The calculation was also repeated using single-FFT algorithm that produce same result for all ranges either below or upper the sampling criteria and different results in comparison to the other two methods. [Copyright &y& Elsevier]

Lightweight shell structures have gained significant popularity in the engineering design as they offer high load carrying capacity for low cost. While classical Finite Element models of such structures have been extensively used in practice, the shell formulations for Isogeometric Analysis (IGA), particularly for Kirchhoff‐Love shell structures [1], have demonstrated benefits arising from the smooth geometry description and the highly accurate solutions that are enabled. Moreover, the direct use of CAD‐models for the structural simulations is possible based e.g. on the Isogeometric B‐Rep Analysis (IBRA) [2]. Herein the application of IBRA to Fluid‐Structure Interaction (FSI) simulations of wind turbines is demonstrated, thus naturally extending IBRA to coupled multiphysics problems. [ABSTRACT FROM AUTHOR]

Almost all the mesh-free methods are restricted to 2-D problems owing to the difficulty in generating 3-D grids. One effective way to overcome this limitation is to utilize the concept of hierarchical modeling for elastic structures. It was introduced originally for the dimensionally-reduced analysis of 3-D structures, but it can be used for the reverse purpose. By assuming the displacement field in the thickness direction with polynomials, the in-plane displacement could be approximated by 2-D mesh-free method. Inspired this motivation, this paper intends to demonstrate the numerical analysis of plate-like structures by 2-D natural element method (NEM). The polynomial order in the thickness direction is defined by the model level, and a number of hierarchical models are constructed by sequentially increasing the model level. The mid-surface of structure is discretized into a NEM grid and the corresponding in-plane displacement field is approximated according to a locking-free selectively reduced integration technique. The numerical experiments are performed to illustrate and validate the proposed method. Both the central deflection and the stress resultants are investigated with respect to the model level and compared with the full 3-D elasticity. In addition, the modeling error of hierarchical models is examined with respect to the thickness and the model level, and the convergence characteristic to the total number of grid points is compared with FEM. • 3-D plate-like structures were successfully and effectively analyzed by making use of 2-D NEM and the hierarchical models. • All the hierarchical models, except for the (1,1,0) model, approach to the Kirchhoff plate theory, as the structure thickness decreases. • The stress resultants of hierarchical models approach to those of 3-D elasticity as the model level increases. • NEM provides more accurate results for thin elastic structures and it leads to lower approximation error in coarse grids. [ABSTRACT FROM AUTHOR]