Search results for " solution"
showing 10 items of 3084 documents
Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations
2014
Abstract A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functio…
Grain growth in Na 0.5 Bi 0.5 TiO 3 -based solid solutions
2019
This paper discusses effects of different dopants, sintering technique and parameters on microstructure and properties of pure and Yb, Er-doped Na0.5Bi0.5TiO3 (NBT). All stoichiometric compositions follow the abnormal grain growth mechanism (AGG) and exhibit a bimodal grain size distribution. Bi over-stoichiometry, two step sintering and hot pressing are effective inhibitors of AGG. Microstructure of sintered NBT greatly influences such properties as dielectric permittivity and depolarization temperature.
Template-Free Supracolloidal Self-Assembly of Atomically Precise Gold Nanoclusters : From 2D Colloidal Crystals to Spherical Capsids
2016
We report supracolloidal self-assembly of atomically precise and strictly monodisperse gold nanoclusters involving p-mercaptobenzoic acid ligands (Au102-pMBA44) under aqueous conditions into hexagonally packed monolayer-thick two-dimensional facetted colloidal crystals (thickness 2.7 nm) and their bending to closed shells leading to spherical capsids (d ca. 200 nm), as controlled by solvent conditions. The 2D colloidal assembly is driven in template-free manner by the spontaneous patchiness of the pMBA ligands around the Au102-pMBA44 nanoclusters preferably towards equatorial plane, thus promoting inter-nanocluster hydrogen bonds and high packing to planar sheets. More generally, the findin…
Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation
2011
We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discus…
Interlaminar stresses in laminated composite beam-type structures under shear/bending
2000
A boundary integral model for composite laminates under out-of-plane shear/bending is presented. The formulation proposed allows one to determine the elastic response of generally stacked composite laminates having general shape of the cross section. The integral equations governing the ply behavior within the laminate are deduced starting from the reciprocity theorem for beam-type structures. The ply integral equations are obtained by employing the analytical expression of the fundamental solution of generalized plane strain anisotropic problems. The laminate model is completed by imposing the displacement and stress continuity along the interfaces and the external boundary conditions. The…
Types and Multiplicity of Solutions to Sturm–Liouville Boundary Value Problem
2015
We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.
Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers.
2004
Translation Matrix Formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional (1D) periodic stratified structure. This modal approach allows to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to Second Harmonic Generation (SHG) in the undepleted pump regime.
Spherical Harmonics Expansion of Fundamental Solutions and Their Derivatives for Homogeneous Elliptic Operators
2017
In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansion…
Nonlocal Third Order Boundary Value Problems with Solutions that Change Sign
2014
We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.
AN ANALYTICAL SOLUTION OF KINEMATIC WAVE EQUATIONS FOR OVERLAND FLOW UNDER GREEN-AMPT INFILTRATION
2010
This paper deals with the analytical solution of kinematic wave equations for overland flow occurring in an infiltrating hillslope. The infiltration process is described by the Green-Ampt model. The solution is derived only for the case of an intermediate flow regime between laminar and turbulent ones. A transitional regime can be considered a reliable flow condition when, to the laminar overland flow, is also associated the effect of the additional resistance due to raindrop impact. With reference to the simple case of an impervious hillslope, a comparison was carried out between the present solution and the non-linear storage model. Some applications of the present solution were performed…