Search results for "Boundary value problem"
showing 10 items of 551 documents
Internal spring distribution for quasi brittle fracture via Symmetric Boundary Element Method
2009
Abstract In this paper the symmetric boundary element formulation is applied to the fracture mechanics problems for quasi brittle materials . The basic aim of the present work is the development and implementation of two discrete cohesive zone models using Symmetric Galerkin multi-zone Boundary Elements Method . The non-linearity at the process zone of the crack will be simulated through a discrete distribution of nodal springs whose generalized (or weighted) stiffnesses are obtainable by the cohesive forces and relative displacements modelling. This goal is reached coherently with the constitutive relation σ − Δ u that describes the interaction between mechanical and kinematical quantities…
Elliptic 1-Laplacian equations with dynamical boundary conditions
2018
Abstract This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.
A Variationally Consistent Time Modelling of Elastic-Plastic Constitutive Equations
1991
A general energy-based time discretization method for evolutive analysis is presented. Most known time integration procedures (mid-point rule, backward difference, etc.) are shown to be particular cases of it. For space continuous systems, a sequence of weighted boundary value problems of deformation-theory plasticity are obtained, each characterizable by a number of variational principles useful for finite element discretization.
A generalized porous medium equation related to some singular quasilinear problems
2014
Abstract In this paper we study the existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is { − ∑ m = 1 ∞ a m Δ u m = f in Ω u = 0 on ∂ Ω , where Ω is a bounded domain of R N , a m is a sequence of nonnegative real numbers, and f is in L q ( Ω ) , q > N 2 .
A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates
2019
Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…
Vibration-based identification of mechanical properties of orthotropic arbitrarily shaped plates: Numerical and experimental assessment
2018
Abstract An innovative procedure is introduced for the identification of the mechanical parameters of orthotropic plates of arbitrary shape, under various boundary conditions, based on vibration data. The method employs a combination of a convenient Rayleigh-Ritz approach and Particle-Swarm Optimization to estimate elastic constants of the orthotropic material in a straightforward manner, without requiring computationally demanding iterative Finite Element analyses. Specifically, the pb-2 Rayleigh-Ritz procedure is extended and applied to deal with orthotropic plates, simplifying the approach to more easily treat generic plate shapes, taking advantage of the Green's theorem. The method is t…
AN APPLICATION OF A FIXED POINT THEOREM FOR NONEXPANSIVE OPERATORS
2014
Abstract. In this note, we present an application of a recent xed point theorem by Ricceri to a two-point boundary value problem. KeyWords and Phrases: Fixed point, nonexpansive operator, two-point boundary value problem. 2010 Mathematics Subject Classi cation: 34K10, 47H09, 47H10.
Existence Results for Periodic Boundary Value Problems with a Convenction Term
2020
By using an abstract coincidence point theorem for sequentially weakly continuous maps the existence of at least one positive solution is obtained for a periodic second order boundary value problem with a reaction term involving the derivative \(u'\) of the solution u: the so called convention term. As a consequence of the main result also the existence of at least one positive solution is obtained for a parameter-depending problem.
Ordinary (p_1,...,p_m)-Laplacian system with mixed boundary value
2016
In this paper we prove the existence of multiple weak solutions for an ordinary mixed boundary value system with (p_1,...,p_m)-Laplacian by using recent results of critical points.
Confined Crystals on Substrates: Order and Fluctuations in Between One and Two Dimensions
2010
The effect of lateral confinement on a crystal of point particles in d = 2 dimensions in a strip geometry is studied by Monte Carlo simulations and using phe- nomenological theoretical concepts. Physically, such systems confined in long strips of width D can be realized via colloidal particles at the air-water interface, or by adsorbed monolayers at suitably nanopatterned substrates, etc. As a generic model, we choose a repulsive interparticle potential decaying with the twelfth inverse power of distance. This system has been well studied in the bulk as a model for two- dimensional melting. The state of the system is found to depend very sensitively on the boundary conditions providing the …