Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Stress fields in general composite laminates
1996
A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The …
A unifying variational framework for stress gradient and strain gradient elasticity theories
2015
Abstract Stress gradient elasticity and strain gradient elasticity do constitute distinct continuum theories exhibiting mutual complementary features. This is probed by a few variational principles herein presented and discussed, which include: i) For stress gradient elasticity, a (novel) principle of minimum complementary energy and an (improved-form) principle of stationarity of the Hellinger–Reissner type; ii) For strain gradient elasticity, a (known) principle of minimum total potential energy and a (novel) principle of stationarity of the Hu–Washizu type. Additionally, the higher order boundary conditions for stress gradient elasticity, previously derived by the author (Polizzotto, Int…
THE MINIMIZING TOTAL VARIATION FLOW WITH MEASURE INITIAL CONDITIONS
2004
In this paper we obtain existence and uniqueness of solutions for the Cauchy problem for the minimizing total variation flow when the initial condition is a Radon measure in ℝN. We study limit solutions obtained by weakly approximating the initial measure μ by functions in L1(ℝN). We are able to characterize limit solutions when the initial condition μ=h+μs, where h∈L1(ℝN)∩L∞(ℝN), and μs=αℋk⌊ S,α≥0,k is an integer and S is a k-dimensional manifold with bounded curvatures. In case k<N-1 we prove that the singular part of the solution does not move, it remains equal to μs for all t≥0. In particular, u(t)=δ0 when u(0)=δ0. In case k=N-1 we prove that the singular part of the limit solution …
Two non-zero solutions for Sturm–Liouville equations with mixed boundary conditions
2019
Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem.
Filament sets and homogeneous continua
2007
Abstract New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament , non-filament , and ample , with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.
Subharmonic phase-lock criteria for a class of weakly non-linear high-order oscillators
1985
Subharmonic frequency entrainment of high-order weakly non-linear oscillators is investigated. For the class of circuits considered, equations are first derived which provide the first approximation values for the amplitudes and phases of the two main spectral components of the steady-state waveform. Necessary and sufficient stability criteria are then derived in explicit from. The example worked out (a negative conductance double-tuned oscillator) shows the efficiency and ease of use of the proposed method.
Four solutions for fractional p-Laplacian equations with asymmetric reactions
2020
We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at positive infinity, at most linear at negative infinity). By means of critical point theory and Morse theory, we prove that, for small enough values of the parameter, such problem admits at least four nontrivial solutions: two positive, one negative, and one nodal. As a tool, we prove a Brezis-Oswald type comparison result.
Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems
2017
We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…
G1-Blend between a Differentiable Superquadric of Revolution and a Plane or a Sphere Using Dupin Cyclides
2008
In this article, we present a method to perform G1-continuous blends between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. These blends are patches delimited by four lines of curvature. They allow to avoid parameterization problems that may occur when parametric surfaces are used. Rational quadratic Bezier curves are used to approximate the principal circles of the Dupin cyclide blends and thus a complex 3D problem is now reduced to a simpler 2D problem. We present the necessary conditions to be satisfied to create the blending patches and illustrate our approach by a number of superellipsoid/plane and superellipsoid/sphere blending examples.