相关论文: Differential quadrature element for second strain …
In a previous work of the first authors, a non-holonomic model, generalising the micromorphic models and allowing for curvature (disclinations) to arise from the kinematic values, was presented. In the present paper, a generalisation of the…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical…
Consider the scattering of a time-harmonic elastic plane wave by a periodic rigid surface. The elastic wave propagation is governed by the two-dimensional Navier equation. Based on a Dirichlet-to-Neumann (DtN) map, a transparent boundary…
In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surface force components. As a result the tractions between…
We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence…
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the…
This study presents the application of variable-order (VO) fractional calculus to the modeling of nonlocal solids. The reformulation of nonlocal fractional-order continuum mechanic framework, by means of VO kinematics, enables a unique…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
In recent papers the author introduced a simple alternative to isoparametric finite elements of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
The variational static formulation contributed in [International Journal of Engineering Science 143, 73-91 (2019)] is generalized in the present paper to model axial and flexural dynamic behaviors of elastic nano-beams by nonlocal strain…
In this paper we study the controllability and the stability for a degenerate beam equation in divergence form via the energy method. The equation is clamped at the left end and controlled by applying a shearing force or a damping at the…
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral…
Intensity distributions of linear wave fields are, in the high frequency limit, often approximated in terms of flow or transport equations in phase space. Common techniques for solving the flow equations for both time dependent and…
We classify all the six derivative Lagrangians of gravity, whose traced field equations are of second or third order, in arbitrary dimensions. In the former case, the Lagrangian in dimensions greater than six, reduces to an arbitrary linear…
The paper presents an analysis of the dynamic behaviour of discrete flexural systems composed of Euler--Bernoulli beams. The canonical object of study is the discrete Green's function, from which information regarding the dynamic response…
A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order $C^0$-continuous $H^2$-nonconforming finite element is constructed for the…
The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equations for linear isotropic bodies - in a modern…
In the stability analysis of an equilibrium, given by a stationary point of a functional F[n] (free energy functional, e.g.), the second derivative of F[n] plays the essential role. If the system in equilibrium is subject to the…